Wikipedia talk:WikiProject Elements/Archive 44

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Group 3 StateOfMatter please

Introduction

This page is nearing the 1M bitsize, the Group 3 discussion is running for some 3 months now.

It would be useful if the discussion could be condensed but not frozen into an intermediate StateOfMatter overview: those points, arguments, results that should be kept and reused. Gaseous parts can be let go. When we do nothing, all will be lost and no consequences can be implemented.

Ideas? Suggestions? For starters, probably we need an ~outsider, at least not involved contributors ;-). -DePiep (talk) 17:23, 2 April 2020 (UTC)

@Double sharp, Sandbh, R8R, Droog Andrey, and Dreigorich: pinging the most active participants. Are there any sections (particularly from the top, with the last comments in January or early February) that can be closed and archived relatively soon? Since I haven't commented much (and haven't been swayed one way or the other, nor would I be particularly willing to get involved in a heated debate if I shared my preexisting opinions on the matter), I could try to write short summaries of those sections, but I'd like to be sure those threads are closed first and perhaps input on which parts can be omitted entirely from any such summaries.

+1 to DePiep that the page is uncomfortably long to navigate and that the Group 3 discussion completely dwarfs anything else on this talk page. The ~2.8 kB I archived earlier was barely anything by comparison, so more needs to go soon, and again I'd rather not demolish something if it's still being built. ComplexRational (talk) 21:27, 2 April 2020 (UTC)

(CR, I can handle a long Talk ;-). There are two 400-day talk links in top. My first concern is the reasoning & arguing we want to keep. Producing sound, learnful and usable conclusions). -DePiep (talk) 21:59, 2 April 2020 (UTC)

yep. Maybe start a new ==level section, TOC first? Gives opportunity to redesign the setup, support the reasoning lines. (ie, TOC from scratch & heliview, or drone as it is called today). Worth making all this productive.

Oh and why not invite an outsider from further away, say WP:PHYSICS, WP:CHEM, WP:MATH—they are smart!, and even "All PT is physics" will boil down to ... maths, WP:MILHIST. -DePiep (talk) 21:51, 2 April 2020 (UTC)

I've archived the whole thing into Archive 42. Double sharp (talk) 10:17, 7 April 2020 (UTC)

Main lines table

Well, here is a summary of what seem to be the main lines of argumentation so far:

#

In the red corner (Sandbh)

In the blue corner (DS and DA as I understand him, Lu)

Sandbh response

DS response

0

There is no silver bullet or one-shot solution. The use of multiple considerations to triangulate a solution is consistent with the role of classification science, as well as the premise that ‘Classes are usually defined by more than two attributes…’ (Jones 2010.

Chemically active valence subshells resolve the question immediately: 4f is active in La and not in Lu, 5f is active in Ac and not in Lr.

Avoiding a needless multiplication of considerations and instead going to one that underpins them all is perfectly in keeping with the philosophy of simplest sufficient complexity, since this single consideration corresponds to reality.

Possible 4f involvement in La is one consideration among many
Frex, we may note d-involvement in Ca, Sr, Ba but no one counts them as d-metals

The s block is the only exception because of preemptive filling. That's where the real symmetry break lies: we have p involvement in Li and Be, too. Nowhere else in the periodic table but the s block do we have this kind of problem, unless you insist on creating it with a Sc-Y-La table, which incidentally also creates the unprecedented problem of Lu-Lr as a "pair out of place": in the f block, zero f involvement (not even to cohesively strengthen bonds like d in Zn, or to populate antibonding orbitals and result in reluctance to bond like s in He or p in Ne).

I insist: we must stick to electronic considerations, or we will never be able to get rid of Be-Mg-Zn or B-Al-Sc looking at chemistry alone.

1

An approximate but useful line can be drawn between groups 3-4 per:

transition metals properties
ionic v covalent tendencies
aqueous chemistry (oxides)
halide chemistry; and
compound formation.

More generally, group 3 behave chemically per groups 1-2 rather than 4-5+

There is no such gap, approximate or not. Transition metal properties come in gradually, monotonically increasing as K < Ca < Sc < Ti < V < Cr as the importance of the d orbitals and lower oxidation states than the group state grows. Ionic vs covalent as a sweeping dichotomy overlooks the real trend that is going on (ionic character increases gradually with increasing EN difference), and so does aqueous chemistry differences (the acidity of a cation grows with decreasing radius, increasing charge, and increasing electronegativity of the original element). In general, Sc and Y are intermediate between groups 2 and 4, but La-Ac are more like group 2 and Lu-Lr are more like group 4. We should pick the second trend to homogenise the d block.

If periodicity was really about chemical similarity first and foremost, Be and Mg would go over Zn.

The gradation of chemical properties among the elements is coarse enough to permit rough boundary lines to be drawn
Chemists make use of these rough line, if only subconsciously, in thinking of the chemistry of different elements
On Be and Mg over Zn, among other things, compare the reduction potentials: group 2 = Be: −1.97; Mg −2.356; Ca −2.84; Sr −2.92; Ba: −2.92 ● group 12 = Zn −0.76; Cd −0.4; Hg +0.85

The rough lines really in use by chemists have nothing to do with group divides, just look at Wulfsberg's Principles of Descriptive Inorganic Chemistry. On Be-Mg-Zn, I quote Jensen:

“

From a chemical point of view, Zn and Cd most resemble Be and Mg, not only in terms of their atomic radii, ionic radii, and electronegativities (Table 4), but also in terms of the structures of their binary compounds and in their ability to form complex ions with a wide variety of oxygen and nitrogen donor ligands (including complex hydrates and amines). Indeed, prior to the introduction of electronic periodic tables, the similarity between Be and Mg and Zn and Cd was often considered to be greater than the similarity between Be and Mg and the rest of the alkaline earth metals (Ca–Ra). Many inorganic texts written before the Second World War placed their discussion of the chemistry of Be and Mg in the chapter dealing with the Zn subgroup rather than in the chapter dealing with the Ca subgroup, and the same is true of many older periodic tables, including those originally proposed by Mendeleev (34, 35). Even as late as 1950, N. V. Sidgwick, in his classic two-volume survey of The Chemical Elements and Their Compounds, felt that it was necessary to justify his departure from this scheme in the case of Mg (36): The gap between magnesium and the succeeding elements is sufficient to make it desirable to treat the magnesium compounds separately, but in the general discussion we may include it along with the alkaline earths metals proper, the elements from calcium to radium.... There has been much argument as to whether magnesium has the properties of a member of group IIA (alkaline earth metals) or IIB (zinc, cadmium, mercury); in fact of course it has resemblances to both. It is found in nature rather with the A elements than with the B. In its chemistry it shows analogies to both subgroups; in its power of complex formation it stands between the two, and seems to come nearer to B than A, but this is a natural result of its small size...."

”

2

Double periodicity of the f block. First noticed by Klemm (1929). Affirmed by the well-regarded Russian chemist Shchukarev (1974).

The stability of +2 gradually increases until Eu and then plummets at Gd. Then it increases until Yb and then plummets at Lu. Exactly like the trend of +2 for the 3d row: it gradually increases in stability until Mn, then goes down and again at Fe, then increases until Zn and plummets at Ga. Just look at the standard electrode potentials: for the actinides it is even clearer. Same idea for each, 3d/4f/5f drowning, so that the last element Ga/Lu/Lr that is so happy to be in the +3 state and doesn't like any other one very much must be getting it from somewhere else. Double periodicity really supports Sc-Y-Lu.

P.S. "Well-regarded" is just argument from authority. It even cuts both ways, too: Landau and Lifschitz are even more well-regarded and supported Sc-Y-Lu.

F-block double periodicity is shifted 1 place right due to delayed start of filling of 4f sub-shell—with a valence electron—in the gaseous, solid, and ionic states
The d-block doesn't follow this pattern; there's no delayed start here.
Sc-Y-Lu obscures start of filling of f block (it'd appear to start @ La) and visually truncates its double periodicity (it'd be cut off & Yb whereas it'd actually end in d block).
In Shchukarev’s words, the "correctness of placing of imitators before Gd and Cm as well as Lu and Lr, would be lost."

In chemically relevant environments, La can show 4f involvement just as well, so there is no significant delayed start. (La metal already shows f involvement, anyway.) So the fact that Sc-Y-Lu makes the f filling appear to start at La makes it more congruent with the facts of chemistry. Ground-state anomalies don't matter if they have no effect on chemistry. With the logic of "imitators", one should extend the d block till Ga because Mn²⁺ and Zn²⁺ can be thought of as imitating the configurations of Fe³⁺ and Ga³⁺. (Note that the most stable state of Sc is Sc³⁺, with zero 3d electrons.)

3

Lanthanide contraction runs from trivalent Ce (4f¹) through Yb (4f¹³) to Lu (4f¹⁴). From La to Lu there is a resulting 16.5% reduction in ionic radius.

There is no consistent criterion, applicable to the whole of the periodic table, that will give such a result. Sure, Ce³⁺ is the first common Ln ion to show an f electron (Ce⁴⁺ doesn't). If we ask for a common +3 oxidation state, we cannot generalise this anywhere else as there's no such thing outside the 4f row. If we ask for a common ion at least, Ti³⁺ is the first common TM ion to show a d electron, so the d element contraction starts at Ti. Which is obviously nonsense. The lanthanide contraction as a chemical phenomenon runs La³⁺ to Lu³⁺: as a representative of block involvement (which is the same way the other contractions are important), it runs from La to Yb (neutral atoms as the only consistent possibility). In no case does Ce to Lu make sense.

Per G&E, similar contractions occur in each row o' the periodic table
In the d-block e.g. ionic radii decrease by 20.5 pm from Sc³⁺ to Cu³⁺

But there is never a characteristic oxidation state common for everybody outside the 4f row. The only sensible ones are 0 (neutral atoms), and +2 (getting rid of the outer s electrons) for d, f, and g elements only. Both of those choices imply immediately that Yb is the last element of the 4f row.

If you want to use +3 like you quote here: I just remark that Sc³⁺ has no d electron, so by the logic you use to start the f contraction at Ce, the d contraction must start at Ti. Which is, as I said, obviously nonsense.

4

The direct impact of the progressive occupation of the 4f sub-shell in the trivalent cations of the lanthanides culminates at Lu (per #3) and affects all of its chemistry, as is the case with Ce to Yb

The d electrons of Ga³⁺ affect all of its chemistry too, that doesn't make Ga a d block element. Just saying that Lu is typically considered a lanthanide will not be enough: yttrium also has perfectly lanthanide-like chemical properties and is often included with the Ln for comparison (going towards the REM category), but yttrium obviously has basically zero f involvement. Chemical categories can transcend periods, groups, and blocks because the relationship going from electron configurations to chemistry is complicated: that doesn't make the periods, groups, and blocks not useful.

Ga³⁺ is impacted by the d-block contraction, but is not a contributor to it, since the d sub-shell is filled at Zn
Lu³⁺ is a contributor to the Ln contraction, since that is where the f-shell is completed
Y does not have "perfectly" Ln-like chemical properties since it has no f sub-shell
I agree[!] with DS' last sentence

If you insist on +3 cations, like you do when you quote Sc³⁺ to Cu³⁺, the d shell is filled at Ga³⁺ only, not at Zn³⁺. +2 makes far more sense, it gets rid of the outer s electrons, and avoids the deadly problem that outside the 4f row there's no obvious characteristic oxidation state.

Yttrium chemistry is near-universally discussed in comparison with the lanthanides, being so similar to Ho. In fact, this clearly shows that Lu is the right heavier congener of Sc and Y: that way, all three elements involved have zero valence f involvement, but still have Ln-like chemistry. This is destroyed with a Sc-Y-La group 3.

5

There's no need to consistently extend arguments to elsewhere on the periodic table [Sandbh to revisit]

A double standard is not science.

There are more patterns and relationships among the elements than those by group or period.
The fact that a relationship, pattern, or argument may not have universal applicability across the periodic table does not diminish its validity
For example, G&E discuss the diagonal relationships between Li-Mg, Be-Al, and B-Si
The fact of limited extensions of such relationships to the rest of the periodic table is essentially pointless

The periodic table is supposed to be based on the fundamental patterns only. It's not periodicity if it doesn't apply everywhere. That doesn't mean patterns that exist only partially are invalid, only that they cannot be admitted as foundational principles for the PT.

6

Simplest sufficient complexity is a sufficient, so to speak.

It is indeed. But not simplifying the situation beyond anything that could correspond to reality. Not to mention that a double standard is by definition unnecessary complexity as it requires two standards when you could have gotten by with one.

I agree[!]
The converse holds true: there is no need to exceed the simplest sufficient complexity criterion, or make something more complex than it needs to be for the application in mind

The idea of a group divide is simplified beyond anything that could correspond to reality. It is not of sufficient complexity, whereas generalising Fajans' rules produces something that is.

7

If blocks are defined in terms of their predominating differentiating electrons (Scerri & Parsons 2018) an La table has one less differentiating electron discrepancy than is the case for an Lu table

DEs are often not well-defined (there's no single differentiating electron from vanadium 3d³4s² to chromium 3d⁵4s¹), so they should be ignored. Not only that, but chemically speaking ground-state electron configuration anomalies always mean absolutely nothing: Nb d⁴s¹ and Ta d³s² don't match, but act similarly, for example. Far better to look at the chemically active valence subshells that don't change and point straight to Lu under Y. Why should La and Ac be treated differently from Th and Lr, which show a chemically irrelevant delayed collapse just as well?

The d/e in Cr, quite simply, is a d electron
Sandbh to revisit

No it isn't. You've added two d electrons and removed one s one. By no stretch of the imagination is there a single DE.

8

Electronic blocks do not always correlate with chemistry-based blocks; the latter are more relevant to chemistry

They are totally subjective, since there are lots of chemically defensible categories, and everything is a continuum in behaviour; therefore it is not useful to consider such things

There is no continuum; there is rather a semi-continuum
Chemists have been drawing dividing lines on periodic tables since Hinrichs (1869)
Subjectivity does not matter if the sample size is big enough
For example, the list of metalloid lists based on 192 lists
Or the IUPAC survey of nearly 200 chemistry texts

There is absolutely a continuum, just look at all the examples I raised in the thread. Chemists have been drawing dividing lines indeed, but they have also drawn them in different places, as is totally expected for a continuum, where different things are illuminated by drawing the division in slightly different places.

9

DEs are simpler to determine that chemically active valence sub-shells

An ill-defined criterion will always be too simple to be simple.

DE's are so simple to define that Scerri did not even bother in his d/e based argument with Parsons

Then what is the DE from vanadium 3d³4s² to chromium 3d⁵4s¹? You've added two d electrons and removed one s one. By no stretch of the imagination is there a single DE.

10

The notion of a most chemically important sub-shell supports an La table

There is no such thing (hybridisation is common everywhere), and f is absolutely not one of the most important subshells for Lu and Lr because it isn't a valence subshell at all.

The f-subshell is the raison d'être of the Ln and impact every aspect of their chemistry, including as seen in Lu and Lr

It also impacts every aspect of the chemistry of Hf-Rn and Rf-Og because of the 4f and 5f contractions, that doesn't make them f elements. To be an f element, you need the f orbitals to be working as valence orbitals. Which is something that happens for La-Yb and Ac-No and is woefully lacking for Lu and Lr, just as it is for Hf-Rn and Rf-Og.

11

The positions of Lu-Lr at the end of the f block are analogous to the position of the Zn group at the end of the d block. Thus Zn²⁺ is d¹⁰; Lu³⁺ is d¹⁴.

Except that the Zn group have their d electrons contributing in their compounds' valence regions, and the same cannot be said for the f electrons of the Lu group. Indeed, Lu and Lr in the f block are an egregious "pair out of place" which never use the f electrons directly for chemistry; this is not true for the Zn group, just look at ZnF₂ as an example for starters.

Comparison of different oxidation states is artificially shifting the boundaries: the important thing that unites the d and f blocks is there's only two s electrons outside the characteristic filling subshell (that will at least be close to the ground state), so you have to compare +2 states throughout (Zn²⁺ vs Yb²⁺). Otherwise, we again arrive at the same problem: there's no analogy to the rôle of the +3 oxidation state across the Ln anywhere else, the early 3d metals are unhappy in the +2 state.

d-electron involvement is peripheral, bordering on "noise" or desperation
It could hardly be said that the chemistry of Zn is like that of a d-block metal
As a high order argument my red cell argument stands
A characteristic oxidation state common for everybody is not required in order to observe analogies in end-of-block configurations

This is a continuum, as usual. As we approach the end of a d series, involvement of d electrons shrinks as the d orbitals collapse. That's why the late 3d and 4d metals (Co onwards, Pd onwards) are so unhappy to go beyond the +2 state, which ideally is only getting rid of s electrons. That doesn't prevent the d electrons from having an effect in these +2 compounds, anyone can see that there's a continuity of trends with Zn-Cd-Hg reasonably continuing on from Cu-Ag-Au.

Without characteristic oxidation states, choice will be arbitrary. A Zn²⁺ vs. Yb²⁺ analogy gives a different answer from a Zn²⁺ vs. Lu³⁺ analogy.

Comparing compounds of Cu/Ag, Zn/Cd, Ga/In, one can clearly see that the shift from valence d involvement to incomplete screening happens between groups 12 and 13, not 11 and 12 (doi:10.1016/0368-2048(75)80018-1).

12

The trend in the d block shows a gap between La and Hf because the lanthanide contraction intervenes there

That is based on La argument 3, which has already been debunked. Therefore the conclusion doesn't follow. In actuality the f contraction runs La through Yb and precedes the d block, as evidenced by chemically active valence subshells (La-Yb show 4f involvement, Lu doesn't) and double periodicity of oxidation state relative stability (as evidenced by standard reduction potentials, see point 2). The d block should therefore show a continuous trend Lu-Hf-...-Hg.

Not to mention that a split block would be absolutely unprecedented throughout the whole table and constitute a flagrant violation of periodicity.

Even G& E recognise the contraction runs from Ce to Lu
For double periodicity it has been known since 1929 that this applies to Ce to Lu; see row 2
A split d-block is commonly seen in 32-column tables, since this follows from the popularity of the La form, by a 4:1 margin over the Lu form
It follows that no such precedent or flagrant violation periodicity exists

La is universally plotted on the contraction; row 2 has already been rebutted; and just because the split block is common does not mean it is right.

13

The periodic law implies, ceteris paribus, that since La represents the first recurrence of comparable periodicity after Y it should be the one to go under Y rather than Lu.

False as otherwise group 3 must begin B-Al-Sc. You have to look at electronic structure as well.

I agree with the second sentence; B-Al are p-elements; Sc is a d-element

In the characteristic +3 oxidation state, B³⁺ is [He], Al³⁺ is [Ne], Sc³⁺ is [Ar]. Chemical trends are more linear with B-Al-Sc. Not to mention that Sc has partial p occupancy anyway in the condensed phase.

The same argument applies against Sc-Y-La: speaking in terms of electronic structure, La has low-lying f orbitals that become occupied in compounds, Sc and Y don't.

14

La lacks a 4f valence electron; what 4f involvement there is, is marginal

False. In chemical environments, 4f can certainly be occupied for La. La actually has the second-biggest 4f contribution of the lanthanides (behind only cerium) in the metal, see Gschneidner's paper. This is exactly what you would expect, as it precedes the collapse after which 4f gets quite hard to use because it's near the xenon core. In reality, La f involvement is of the same type and order as that of Th, which almost everybody claims is an f element. Just try to explain cubic complexes and high coordination numbers without f orbitals.

While 4f can "certainly be occupied" the incidence of such is marginal compared to d¹s² involvement (the 4f tail wagging the d¹s² tail, not!)
4f presence in La metal is controversial
more relevant is the presence of 2.5[!] d electrons in La metal compared to 1.5 in Lu.
5f involvement in Th is uncontroversial
4f involvement in cubic complexes and high CN compounds is contentius

If it is contentious, where is any other explanation? f involvement is absolutely needed on symmetry grounds.

By this logic we may equally well claim that there are no 4f elements at all, because 4f is small and the direct bonding participation of 5d6s is always bigger.

15

As reported by IUPAC, the majority of chemistry text books show Sc-Y-La tables

Most of which are really Sc-Y-* tables, in my experience. Not to mention that it's only a 2/3 majority in favour of Sc-Y-La (1/6 for Sc-Y-*, 1/6 for Sc-Y-Lu) even if you misread Sc-Y-La* = Sc-Y-* tables as Sc-Y-La tables, and reading them properly will leave Sc-Y-La and Sc-Y-* butting their heads at the top with a sizeable 1/6 minority for Sc-Y-Lu that only keeps growing. The majority of chemists who actually step back and think about the situation support a Sc-Y-Lu table: their opinion counts more than a silent majority that doesn't defend itself.

Ahem. Sarcasm alert. Yes, IUPAC must be involved in a conspiracy.
Obviously your experience counts for the nearly 200 chemistry texts they examined
As you know, the work of the chemists who have done such an analysis in favour of Lu have been far too narrow in their scope to come up with their findings and, consequently, have failed to generate a dispute on the radar of the chemistry establishment.
The silent majority doesn't need to defend itself since there is naugth of any substance that would warrant this

There is no conspiracy, only a bald statement of fact that if the asterisk is shown inside the group 3 column (rather than after it), we are dealing with a Sc-Y-* table, not a Sc-Y-La table. Lu arguments are based on real chemical, physical, and atomic considerations, and have increasingly been taken up.

16

Collocation of the rare earth series (Sc-Y-La-Ce-…-Lu); group 3 is a pre-lanthanide triad, not a post-lanthanide triad

A nonsensical trend in the first place (the only sensible extrapolation down from Sc, Y, and La is to go to Ac), and a human-made category that neglects the trivalent actinides only because of their natural occurrence, which is hardly important for chemistry. The second half is based on argument 3, which is already debunked.

all categories are "human-made"
the rare-earth category, which excludes Ac, is widely encountered in chemistry
most chemists will only ever encounter Th and U
The Sc-Y-La-Ce-Pr etc path is natural

That's why to go for electronic categories that are not human-made at all. There's nothing natural about the Sc-Y-La-Ce-... path, just plot the trends.

17

An La table is more regular in the context of +2 +3 +4 “maximum oxidation state” horizontal triads than is the case for an Lu table

Why should we care about a regularity that doesn't exist for the poster children of great group trends (groups 1 and 17)?

As you would appreciate, it exists for group 1, with their +1 maximum oxidation states and for group 17, with their +7 maximum oxidation state (with the exception of F, at 0).

Nope. Only if you ignore the spurious looking at adjacent groups, because the noble gases destroy this trend as soon as they go past the 0 oxidation state. Far better to use electronic considerations to predict where the maximum oxidation state line is likely to go up or down. And even use them to predict all plausible oxidation states (outside the really formal ones for things like TMs in formal negative oxidation states).

18

Isodiagonality is 1 of the 3 patterns characterising the PT. An La table has 1 more of these relationships than an Lu table and is therefore more regular in this context

Most elements aren't in the region of the periodic table where isodiagonality is important (i.e. horizontal and vertical trends proceed at about equal rates), so why should we care? Isodiagonality is not fundamental, it is a linear combination of the really important horizontal and vertical trends, just like knight's-move relationships.

Isodiagonality encompasses:

29 elements;
in all blocks; and
12 groups

And how is 29 out of 118 anywhere near a majority?

19

The 1st IE is a key indicator of periodic trends. +1 cations of Sc, Y, La show properties consistent with these; Lu⁺¹ behaves rather differently, possibly due to its 4f¹⁴ sub-shell.

Why should we care about what happens in the chemically totally irrelevant +1 oxidation state for these elements?

P.S. How do B⁺, Al⁺, Sc⁺ vs Ga⁺ behave?

Because, as I said in cell 1, "The 1st IE is a key indicator of periodic trends."
On your PS, I have no idea

Only because letting go of the first electron is the starting point of chemistry. It is rarely the endpoint, so the +1 oxidation state is not something useful to look at.

On the PS, this will surely show increased similarity of B-Al-Sc vs. Ga because of the lack of a d subshell in the first three.

20

Historically, Sc-Y-La has stood the test of time

If we were writing in 1940, Be-Mg-Zn would have stood the test of time, too. What matters is that the majority of chemists actually relooking at the issue have come to the conclusion that Sc-Y-La doesn't make sense, and they outweigh the silent sources who don't discuss the issue of group 3 composition at all.

Historically, Sc-Y-La came from the time when we previously did not know about the f block: the 5f elements that we knew "pretended" to be d elements. Therefore we thought all fifteen lanthanides belonged below yttrium, and we misguidedly picked La as the prototype. But this mistake obscures the point of blocks (the subshells being used for chemistry), and drags group 3 into the odd lack of double periodicity that should by rights only appear in the s block! That ruins many regularities in the periodic table's trends because they all, at length, lead to this block filling and Madelung rule. Now that we know the real sequence of chemically active subshells, there's no reason to perpetuate this historical error.

On Be-Mg-Zn, see row 1, column 3
On chemists looking at group 3, see row 15, column 3
On when we did not know about the f-block, even when we did Lu stayed there
Even when it was realised we did this on the basis of the wrong electron configuration, Lu stayed there because nothing changed about is chemistry
It's ironic that an Lu table results in more irregularities among fundamental properties across the table, and cognitive dissonance with respect to chemical relationships between or within groups or series of elements
While Nature does not care about aesthetics, the composition of group 3 as Sc-Y-La-Ac appears to be more consistent with the texture of the world.

The conclusion about Lu based on wrong electron configurations was corrupted. If the premise is falsified, the conclusion has to be arrived at another way, or not at all. We have to look at the real fundamental properties, which as I have demonstrated throughout my column universally support Sc-Y-Lu. Sc-Y-La is based only on double standards which, if applied consistency to B-Al-Sc or Be-Mg-Zn, will usually give the wrong answer.

21

Arguments supporting Sc-Y-La are mutually reinforcing, consistent with the nature of periodic table as an integrated, complex structure whereas Lu in group 3 unravels this rich tapestry of chemical relationships

As shown above, from a real chemistry perspective (which isn't just isolated facts, but table-wide generalisations), Sc-Y-La fails at all of the important ones and Sc-Y-Lu passes with flying colours. Everything in a Sc-Y-Lu table goes back to the basic principles of periodic trends, mediated from idealised electron configurations by means of the trends in atomic radii, preferred oxidation states (multiple ones for almost all elements) and electronegativity, as excellently expounded by Gary Wulfsberg in his book Principles of Descriptive Inorganic Chemistry. A Sc-Y-La starts with inconsistency in its criteria (most criteria that argue for Sc-Y-La also argue for similar rearrangements like B-Al-Sc or Be-Mg-Zn) and is the result of only picking individual facts without asking where they come from.

Many of the La arguments are mistaking the fundamental criteria of element placement, which I insist must be applicable in full generality and impartiality to all elements, from hydrogen to however large an element has been theoretically probed at the moment (seems to be E173 now, with a glimpse of the 6g series at E184); otherwise you have a double standard which is not science. Periodic trends and chemical similarities do not come first. Otherwise we have a hard time explaining nitrogen and moscovium in the same group (the latter shouldn't even show a +5 state, so much for maximum oxidation states), and will be wringing our hands without any end deciding between Be-Mg-Ca and Be-Mg-Zn (chemically speaking, the latter is also a strong link, in some ways stronger due to similar EN and atomic radii). It is electronic structure in chemically relevant environments that decides the matter, and in one fell swoop disposes of the problems of helium and group 3 in a single instant. Where periodic trends and chemical similarities come in is after the matter has been decided by this criterion, to confirm that the results show periodicity.

As you intimated there is no simple relationship between electron structure and chemistry
See my item 5 column 3 re patterns and trends and the fact they needn't have universal applicability to be relevant
N and Mc in the same group is no harder than the difference between N and P, or O and Po
On Be-Mg-Ca and Be-Mg-Zn see see row 1, column 3; feel free to take that one up with the chemical establishment

Precisely. That's why we have to use electronic structure and not chemistry for the basic drawing of the PT, or else Be-Mg-Zn becomes a problem, and N-P or O-Po become very weird in the same group. You yourself have noted that the push against it was based on electronic periodic tables, and as can be seen from column 4, the chemical establishment was for a while in favour of Be-Mg-Zn! That suggests Sc-Y-Lu should become scientifically better once the consensus shifts to it, which is absurd.

Chemical and physical trends only come as a confirmation to make sure the trends predicted by electronic structure make sense.

22

A symmetrical outcome has no more fundamental merit than an asymmetrical outcome; the supposed superiority of symmetry is a culture-specific Western concept

A symmetrical outcome has fundamental merit if the basic symmetry it rests on exists. Just look at the perfect n+l symmetry of the list of chemically active subshells.

I agree

^_^

23

The key problem afflicting all the significant La arguments, as far as I can see, is locality. Such arguments focus on one extremely local feature and don't work for the rest of the periodic table (e.g. all arguments stemming from +3 being the common state in the lanthanide contraction). In some sense, focusing on ground-state or condensed-phase electron configurations only leads naturally to this problem, because they exclude part of chemistry from consideration and are therefore not holistic enough to serve as a basis for the periodic table. Or focusing on supposed gaps in chemical behaviour between group 3 and following groups: this is a common trap, because we all like our specialties, but Fajans' rules immediately implicate that these gaps move depending on conditions.

Chemically active valence subshells are precisely chosen not to move and to avoid locality. They also explain precisely why it's not relevant to say "oh, but Sc-Y-La does the group 2 trend, and Sc-Y-Lu does the group 4 trend". It's true, but we know that the s-block is the weirdo which starts early. That 4f, 5f, and 5g show delayed collapse is not to do with the fact that they're f and g orbitals, but because we are in the heavy elements by the time we start filling them. Note that Lu already has a low-lying 6p state, and Lr clearly shows that 6d has undergone a delayed collapse too. And somehow, the delayed collapses of 4f, 5f, and 6d make no significant difference for the chemistry of the elements concerned, which still use the as yet uncollapsed characteristic orbitals.

See row 5, column 3
As noted, in looking at a forest you appear to focus on the leaves or needles on the supporting branches of each tree, and you can't see or choose to ignore, the trunks of each tree, and the topography of the forest
In classification terms, I attempt to derive a collective classification, based on the most common or important data points, that matches up with periodic table boundaries
You respond by looking at the entirety of the data points involved, included the non-representative items, and attempt to draw boundaries among that.
I've previously (unkindly) called this the downwards drill of complexity, or fogging, because in its detail it obscures the broad contours of the situation
As Nelson (2011), a chemist, wrote:

"…care needs to be taken to remember that…[this classification scheme] is only an approximation, and can only be used as a rough guide to the properties of the elements. Provided that this is done, however, it constitutes a very useful classification, and although purists often despise it because of its approximate nature, the fact is that practising chemists make a great deal of use of it, if only subconsciously, in thinking of the chemistry of different elements."

Nope. After looking at everything, I can distill everything into simple statements:

An element is placed in the periodic table according to its number of valence electrons and the chemically active subshells they can go into.

Acidity and covalency increase as electronegativity and oxidation state increase, and as atomic radius decreases.

One must look at the whole forest ("oxidation states stable in water" is hardly including non-representative items) in order to drag out the right generalisations like these, but once done, they work pretty much 100%, and when they don't it's because some other factor hasn't been included (e.g. steric hindrance explaining why CCl₄ doesn't violently hydrolyse in water). That cannot be said for supposed group divides or all of those overly local Sc-Y-La arguments.

I have decided to terminate my participation in the main thread, as I will lack the time for it from tomorrow and there is no point in repeating myself more than I already have been doing. I will only fill in responses in my column 4 here, if Sandbh adds anything else to column 3. Double sharp (talk) 06:41, 5 April 2020 (UTC)

@Double sharp and DePiep: That's good. My column 3 is complete. Over to you, subject to your time commitments. An excellent summary, from which I'll attempt to provide DePiep with an immediate overview. Sandbh (talk) 08:20, 5 April 2020 (UTC)

@Sandbh: I've completed the table with my column 4 (somewhat in a rush, to get it done before other RL concerns won't allow it). So I think we've summarised everything. Double sharp (talk) 08:25, 5 April 2020 (UTC)

Immediate overview

Background (18 bullets)

Group 3 has been Sc-Y-La-Ac since about the 1920s
A few chemists in the 1920's and 1930's assigned Lu rather than La to group 3
In the 1940s it was realised that placing Lu in the f-block was ostensibly wrong since the 4f sub-shell was completed at Yb, rather than at Lu, as previously thought
Since this discovery did not change anything of the chemistry of Lu, nothing happened; Lu stayed where it was the end of the f-block
DS contends that this is itself somewhat problematic, because once the premises are falsified the conclusion has to at least be derived by alternative means. In other words, reasons based on electron configuration for the placement of La under Y can no longer be admitted, and this should have resulted in the composition of group 3 being relooked at.

From about the 1950s onwards a few physicists (mainly) argued that some properties of Lu suggested it'd be better placed under Y instead of La
These arguments were mostly based on a single property, and did not attract significant attention
Jensen (1983) published a rather longer article arguing for Lu in group 3, and reiterating some of the past arguments
Not much notice was taken of Jensen, although he caused some non-critical excitement among a few chemists, and some more papers supporting Sc-Y-Lu-Lr appeared
DS and I (2017) comprehensively "dismissed" Jensen's article in our submission to IUPAC, noting many of his arguments were unbalanced

DS (2020) later retracted his dismissal, once he learnt more in 2018 from Droog Andrey about the issue. Previously, we dismissed as flawed Jensen's arguments that group 3 only showed trends similar to group 4+ if Sc-Y-Lu was chosen, because a Sc-Y-La group 3 has trends similar to groups 1 and 2, which we thought were chemically closer to group 3: but DS considers now that actually Sc and Y are chemically intermediate between group 2 and 4, and so that this should not be a strong argument after all, and that electronic bases are sounder than chemical bases for reasons that he will consider later in this summary.
Scerri and Parsons (2018) assessed Jensen as being too selective in his arguments
Scerri (chair of the IUPAC project looking at this issue) has said several times that the group 3 question can't be resolved by comparisons of the properties of La and Lu
DS contends that this is simply due to the fact that the road from electron configurations to chemistry is complicated. Without considering electronic structure, the group II question (whether Be and Mg should go over Ca or over Zn) that previously was an issue before WWII would be equally unresolvable. And there would also be questions about B-Al-Sc: see footnote 1. Once chemically relevant electron configurations across all chemically plausible environments are considered, we recover the ideal electron configurations of the Madelung rule the presence of valence f involvement for La and Ac and its absence for Lu and Lr is decisive for DS.
As it is for Jensen (2009), see footnote 2

3
Sc
Y
La*
Ac**

The IUPAC project team surveyed nearly 200 chemistry texts (a survey to which Sandbh contributed) and established a 4:1:1 distribution between Sc-Y-La-Ac, Sc-Y-Lu-Lr, and Sc-Y-*-** (the last option not being considered as a future possibility by the current IUPAC project team)
DS contends the IUPAC project team are likely to have misinterpreted these chemistry texts. A table with the asterisks * and ** for "following elements" in the same cells as La and Ac, part of a group 3 column (as shown to the right), is literally speaking a Sc-Y-*-** table in terms of what elements it claims to be in group 3, not a Sc-Y-La-Ac table. Under this interpretation, the lead of Sc-Y-La-Ac over Sc-Y-Lu-Lr is weakened.
DS also notes the majority of sources whose focus is the group 3 issue support Sc-Y-Lu-Lr, and this statistic is more meaningful wrt the dispute than the literature that is not focusing on this. The idea of d orbital hybridisation as an explanation of hypervalence for 3p elements is alive and well in many texts, but obviously the literature we should reflect is that in which it was debunked by specialists (quantum chemists) back in the 1990s. This case serves as evidence that the textbook literature may well be behind the latest scientific knowledge, and further weakens the significance of the survey of the IUPAC project team.

__________
¹ Regarding group II, Jensen wrote in 2003: "From a chemical point of view, Zn and Cd most resemble Be and Mg, not only in terms of their atomic radii, ionic radii, and electronegativities (Table 4), but also in terms of the structures of their binary compounds and in their ability to form complex ions with a wide variety of oxygen and nitrogen donor ligands (including complex hydrates and amines). Indeed, prior to the introduction of electronic periodic tables, the similarity between Be and Mg and Zn and Cd was often considered to be greater than the similarity between Be and Mg and the rest of the alkaline earth metals (Ca–Ra). Many inorganic texts written before the Second World War placed their discussion of the chemistry of Be and Mg in the chapter dealing with the Zn subgroup rather than in the chapter dealing with the Ca subgroup, and the same is true of many older periodic tables, including those originally proposed by Mendeleev (34, 35)." Rayner-Canham (2011) also quotes Greenwood and Earnshaw (1997) in their contention "that magnesium is atypical of group 2 (though beryllium is even more so)".

Regarding group III, Rayner-Canham (2012) wrote: "In this pair of groups, Greenwood and Earnshaw (1997) have discussed the way in which aluminum can be considered as belonging to Group 3 as much as to Group 13, particularly in its physical properties. The Canadian geochemist, Habashi, has suggested that there are so many similarities between aluminum and scandium that aluminum’s place in the Periodic Table should actually be shifted to Group 3 (Habashi 2010). In terms of the electron configuration of the tripositive ions, one would indeed expect that Al³⁺ (electron configuration, [Ne]) would resemble Sc³⁺ (electron configuration, [Ar]) more than Ga³⁺ (electron configuration, [Ar]3d¹⁰). In terms of their comparative solution behaviour, scandium(III) resembles both aluminum(III) and gallium(III). For each ion, the free hydrated cation exists only in acidic solution. On addition of hydroxide ion to the respective cation, the hydroxides are produced as gelatinous precipitates. Each of the hydroxides re-dissolve in excess base to give an anionic hydroxo-complex, M(OH)₄⁻. There does seem to be a triangular relationship between these three elements. However, scandium does more closely resemble aluminum rather than gallium in its chemistry. If hydrogen sulfide is bubbled through a solution of the respective cation, scandium ion gives a precipitate of scandium hydroxide, while aluminum ion gives a precipitate of aluminum hydroxide. By contrast, gallium ion gives a precipitate of gallium(III) sulfide. Also, scandium and aluminum both form carbides, while gallium does not."

DS notes that this suggests an analogy to why Sc-Y-La has often passed without comment: Y³⁺ and La³⁺ both have noble gas configurations, which grants them some second-order similarities, whereas Lu³⁺ does not. The fact, however, that this argument is not used to make group 3 start B-Al-Sc, or group 4 go C-Si-Ti-Zr-Ce-Th, suggests to him that more important considerations are at play for element placement.

__________
² Jensen wrote: "...it is inconsistent for Lavelle [a La-Ac proponent] to dismiss (ref 1, Note 4) the (n – 1)d² ns² valence configuration of Th as an inconvenient irregularity that should not affect its assignment to the f-block as an idealized (n – 2)f² ns² element and then turn around and insist that it is absolutely verboten to entertain the idea that La and Ac may have similar irregular valence configurations corresponding to an idealized (n – 2)f¹ ns² valence configuration. After all both elements have low-lying empty f orbitals, which is more than can be said for Lu and Lr. Indeed, more than a quarter of the elements in the d- and f-blocks have irregular valence configurations and in several instances these irregularities apply to the majority of the elements within a given group. The simple fact is that the periodic table is based on idealized electronic configurations rather than on actual configurations and in this fashion functions in chemistry much as the ideal gas law or the concepts of ideal crystals and ideal solutions." Although Lavelle replied to Jensen's article, this point was left unaddressed.

Current state of affairs (39 bullets)

Philosophical

Sandbh considers a difference between DS and him to be that DS likes to drill down into details whereas Sandbh focuses on the broad contours of each situation
DS disputes this difference. To DS, both him and Sandbh consider a broad-strokes generalisation with the minimal complexity needed for a good framework. DS considers Sandbh's approach to have too little complexity, because DS contends that it fails to work when generalised to the whole table.
Sandbh contends that local patterns and generalisations remain valid and useful

Oxidation states

Frex, Sandbh focuses on the most common oxidation states of the elements e.g. Zn = +2, Yb = +3
Sandbh calls this the simplest sufficient complexity that derives useful information
DS focuses on e.g. Zn²⁺ vs. Yb²⁺
Here +2 for Yb is not the most common oxidation state; it decomposes water, and thus only Yb³⁺ occurs in aqueous solution.
DS notes that by this logic one cannot find the proper start of the 3d contraction either: the most common oxidation states of Sc, Ti, and V, according to Wulfsberg, are Sc³⁺, Ti⁴⁺, and V⁵⁺, which have no d electrons to cause any contraction! The situation for 4d and 5d is even worse with the group oxidation state being the main one till Tc⁷⁺ and Re⁷⁺! +2 is the only reasonable shared state to apply to transition elements (d, f, and g block) as it corresponds to removing the outer s electrons; the only other reasonable choice is neutral atoms, which makes sense for main group elements (s and p blocks) too.

Lanthanide contraction

We differ on what is meant by the lanthanide contraction (LC), which is caused by the progressive occupancy of the 4f sub-shell
I (Sandbh) take the LC to span the trivalent cations of Ce to Lu i.e. Ce³⁺ 4f¹ to Lu³⁺ 4f¹⁴, which accords with Goldschmidt who discovered the LC in 1925
DS takes the LC to run along the neutral Ln atoms, to accord with the way all other contractions (e.g. scandide) are defined. (Otherwise, the scandide contraction cannot start at Sc because its major oxidation state is Sc³⁺ 3d⁰.) In this case La may have 4f occupancy in chemical environments, and the contraction ends at Yb [Xe]4f¹⁴6s² which is the last element that uses the 4f electrons for chemistry. Notably, Greenwood & Earnshaw (G&E) include La in the LC.
G&E instead say La is "included for completeness" (p. 1232) i.e. not because it is a part of the LC—since La has no contraction-causing 4f valence electron—but rather to have something to compare the ionic radius of Ce³⁺ to
DS notes the idea that La is not strictly speaking a Ln is basically obsolete now and doesn't make chemical sense given how similar it is to Ce-Lu, so it should be included in the chemical Ln contraction as well as the electronic one

Sandbh says there are broadly comparable contractions in each period of the PT, including the actinide contraction and the scandide contraction
DS notes that those contractions do not have the chemical significance of the Ln contraction, only the electronic significance; they are more important for their impact on the subsequent elements, precisely because of the lack of a common oxidation state. (Appealing to a common +3 state for the actinide contraction requires considering Th³⁺, Pa³⁺, and U³⁺ that decompose water; for other contractions it only gets worse.) They are not comparable to the chemical Ln contraction that spreads across La-Lu.

Patterns

I (Sandbh) say patterns seen only in parts of the periodic table e.g. the well-known diagonal relationships between Li-Mg, Be-Al, and B-Si, are valid in considering periodic trends and relationships
Rayner-Canham, a UK professor of chemistry, has written extensively on such patterns and a book of his on the same topic is due to be published on 25 August 2020
Rayner-Canham, in his Inorganic Chemist's Periodic Table (which notably is Sc-Y-Lu), only colours in the patterns when they appear, and is totally comfortable with the idea that these patterns are only local, calling isodiagonality just "one of the valid linkages among the chemical elements". He recognises many different patterns and understands that for different elements, different ones will be more important. Sandbh agrees.
DS says patterns that exist only partially "cannot be admitted as foundational principles for the PT". He notes that such patterns are drawn on the PT, including by Rayner-Canham, only after the basic structure has already been erected by some other means, that by definition of periodicity must apply to all elements.

The popular form: Sc-Y-La-Ac

I (Sandbh) say La in group 3 is backed up by 100 years of chemistry practice, and that most new ideas are wrong
To some degree, resisting new ideas is healthy because most new ideas are wrong and established concepts are often backed up by lots of experiments and data. Scientists had a right to be skeptical, at first, of the ideas of Darwin and Mitchell. There were phenomena neither could explain and both of them got parts of the story wrong. As a result, it took about 17 years for Mitchell’s ideas and more than a half-century for Darwin’s ideas to become accepted.
DS notes that Lu in group 3 has history dating to the 1920s, too, and most chemists who seriously considered the group 3 question have supported it. It is not a new idea, and there is a lot of data supporting it.
DS says the fact the La form is the most popular does not make it right, citing how the myth of d orbital involvement in hypervalent main group compounds seems to be refusing to die even though it was refuted in the 1990s. At some point, the weight of evidence for a new idea becomes strong enough that the old idea has to be rejected, e.g. the end of phlogiston.

4f involvement in Lu

Sandbh says Lu has 4f bond strengthening involvement (p. 8); see footnote 3
Thus, excluding the 14 4f electrons of Lu makes the bond length too long i.e. the 4f electrons contribute to bond shortening or strengthening. The 5sp sub-shell also plays a (stronger) role here.
DS considers this to be a misunderstanding. In computational chemistry, many inner orbitals must be included to get quantitatively correct answers, but it doesn't mean they have significant contribution to the bonding. The fact that 4f here has an even weaker effect than the core 5s and 5p orbitals (part of the xenon core!) strongly suggests that 4f valence involvement in Lu is, for practical purposes, zero. Lu has no significant f involvement (not even to cohesively strengthen bonds like d in Zn). See footnote 4.

Differentiating electrons

Sandbh says the d/e concept is easily understood and has been used consistently by various authors since Ebel (AFAIK) first introduced the term in 1938
DS says they should be ignored as they cannot be defined consistently for cases like V 3d³4s² vs Cr 3d⁵4s¹, and are chemically irrelevant as within the energies of chemical bonds, many different electron configurations can exist, and depending on the chemical environment a chemically bound atom may exhibit any one of them. He also notes that the process involved in defining DE's, "add a proton and an electron to get the next element", is more the domain of nuclear physics than chemistry with the huge energies involved that will surely cleave all chemical bonds.

A continuum of properties

DS says the properties of the elements form a continuum and it isn't possible to draw dividing lines therein that will be relevant in all circumstances.
I (Sandbh) say the properties of the elements form a semi-continuum and that is possible to draw useful and informative dividing lines, as chemists have done since the time of Hinrichs (1869), including those that lie along group boundaries
DS does not dispute that dividing lines may be useful and informative, having drawn some of them himself with the caveats that depending on the context it may be valuable to draw them elsewhere. Sandbh agrees.
DS says that group divides, besides group 18 vs. group 1, are never very useful or informative in general (see footnote 5), and contends that generalisations of Fajans' rules (i.e. acidity increases as electronegativity and charge increase and atomic radius decreases) are more fruitful as a broad-strokes approach. When group divides appear, they are simply a result of a localised coincidence that is easily destroyed by expanding the boundaries to all significant chemistry (e.g. the group divide between group 3 and 4 disappears completely once we leave periods 4–6, or stop insisting on comparing +3 compounds to +4 compounds).
Such generalisations of Fajans' rules appear in the toolbox of chemists (e.g. Wulfsberg's Principles of Descriptive Inorganic Chemistry); group divides are at least significantly rarer due to their locality. DS thus refers back to his contention that the basic layout of the periodic table must be obtained through means that generalise to all elements.

Delayed start of filling of the 4f sub-shell.

Sandbh says the delayed start is widely if not universally recognised in chemistry and that e.g. it results in the double periodicity in the Ln, as first observed by Klemm (1929) and confirmed by the well-regarded Russian chemist Shchukarev (1974); the same double periodicity, to a weaker extent, is seen in the actinides
DS says this is not relevant to chemistry, just as that of 5f is not (no one doubts that Th, with zero 5f electrons in the ground state, is an f element). The delayed start of filling of 4f and 5f still allows La, Ac, and Th to display involvement of that subshell as a valence subshell for chemical purposes, resulting in La metal having the second-highest 4f involvement of all the lanthanides (Gschneidner): paradoxically, because the collapse is swift, elements before the start of filling are likely to show bigger involvement of that subshell than the ones after!
DS notes that a consistent reflexion of delayed collapses would anyway result in a "staggered" f block starting at Ce and Pa for its first and second rows, not a Sc-Y-La table; and it would also lead to an unsustainable situation once we open the 8th row, where calculations say 8p is first occupied at E121, followed by 7d at E122, followed by 6f at E123 or E124, and finally 5g only at E125!

Double periodicity.

DS notes that double periodicity of the Ln and An, from clear analogies of the stability of the +2 oxidation state to the 3d elements, supports Sc-Y-Lu. He quotes standard electrode potentials to support his point (see footnote 6).
Sandbh notes the special status of the half-filled and filled valence sub-shells in the cations, at Mn and Zn; and analogously at Gd and Lu.
DS contends that Sandbh's previous point is not supported by the data. Mn and Zn are local maxima, as expected: Mn and Zn reach a half- or fully-filled 3d subshell, so by high-school chemistry it must be more difficult to have electrons break free of those. Fe adds an electron on top of a half-filled 3d subshell, and the trend as expected goes down there. We expect the half- and fully-filled subshells in the f rows to also form maxima for the same reason, which appear at Eu/Am and Yb/No. By Ga, Lu, and Lr, the drowning of 3d/4f/5f into the core has gotten to the point that the new easily removed third electron must be coming from somewhere else.

__________
³ "Freezing the outer closed shells of Lu causes large errors in the bond lengths (too long) and bond energies (too small). The freezing of the outer 5s²5p⁶ Xe noble-gas semicore shell is more serious than the freezing of the inner 4f¹⁴ semivalence shell." (So apparently 5s and 5p show bigger involvement than 4f!)

__________
⁴ Droog Andrey, a computational chemist, offered as an example that for Ni complexes, only 1s, 2s, and 2p could be ignored as core electrons without significant consequences: in other words, at least the outermost core orbitals must be included, but that doesn't make them have significant valence involvement. A similar situation happens for the inclusion of d orbitals for hypervalent compounds, see Errol G. Lewars' Modeling Marvels (p. 59): "Including d functions in a basis set for calculations on hypercoordinate compounds may improve the accuracy of the results (this can easily be tested by comparison with known molecules), but this does not mean that physical d orbitals (whatever that may mean) are involved: the orbitals may merely be acting as polarization functions, skewing the s and p orbitals in more propitious directions".

__________
⁵ Take basicity of oxidation states for an example: witness how the maximum basic oxidation state moves from +1 in period 2, to +2 in period 3, to +3 in periods 4 through 6, to +5 in period 7, rather than having a group divide. One can see similar trends for example in the structures and degree of hydrolysis of chlorides in water, in which group divides are also absent. The appearance of a "group divide" in the specific situation when only d-block group oxidation states are considered stems from a coincidence in the d block only: the increased size going from 3d to 4d is partially counteracted by the fact that the EN doesn't go down very much (in fact it sometimes goes up), and there is no increased size going from 4d to 5d because of the Ln contraction (this added to an increase in electronegativity). Therefore, generalised Fajans' rules (acidity increases as electronegativity and charge increase and atomic radius decreases) predict that the group divide from 3d to 6d will move really slowly, as it in fact does: Sc³⁺ is amphoteric, its heavier congeners are basic; but the first basic group 4 cation is Rf⁴⁺. Once we get the EN drop and size increase back, we can go up to fantastic heights: Th⁴⁺ and Pa⁵⁺ are basic cations, as their EN is lower and their size is greater. And once the charge stops increasing, the group divide disappears: compare Sc³⁺, Ti³⁺, V³⁺, and we can see there isn't a significant difference (all three form chlorides that dissolve in water rather than hydrolyse, whereas the chlorides of Ti⁴⁺ and V⁴⁺ hydrolyse). And once we bring the size down to a minimum, we see already that BeCl₂ and BCl₃ are hydrolysing in water, even coming before the +3 vs +4 line, and the only reason CCl₄ is spared that fate is steric hindrance.

So let's apply the general theory to what happens in the early period 5 chlorides (EN_KK(Cl) = 3.06):

Rb (EN_KK = 0.77)	Sr (EN_KK = 1.05)	Y (EN_KK = 1.28)	Zr (EN_KK = 1.35)	Nb (EN_KK = 1.44)	Mo (EN_KK = 1.53)
RbCl	SrCl₂	YCl₃	ZrCl₄	NbCl₅	MoCl₆
3D ionic lattice, regular	3D ionic lattice, deformed rutile structure (undistorted rutile structure pictured, as I can't find a picture for the SrCl₂ structure)	layered 2D polymers like AlCl₃	linear 1D polymers	dimeric molecule	monomeric molecule
			ZrCl₃	NbCl₄	MoCl₅
			3D polymers	1D polymers	dimeric molecule
					MoCl₄
					1D polymers (diagram)
					MoCl₃
					layered 2D polymers like AlCl₃
					MoCl₂
					metal cluster structure

There's no group divide in sight, only a continuous trend where ionic character increases as electronegativity difference goes up and cationic charge goes down (which can be seen from the structures: as ionicity drops, we go from 3D lattices to 2D lattices to 1D lattices to "0D" lattices which are single molecules). (The initial reaction of ZrCl₃ in water is not due to hydrolysis, as a group 3-4 divide would suggest, but because Zr³⁺ and Cl⁻ are formed and the former reduces water. If you look at TiCl₃ vs. TiCl₄, you see the former behaves like a normal salt and the latter hydrolyses.)

__________
⁶ The data is as follows. Local maxima are bolded:

	M³⁺ + e⁻ ⇌ M²⁺	E° (V)	M³⁺ + e⁻ ⇌ M²⁺	E° (V)
0	Ca	(very high)^	Sr	(very high)^
1	Sc	−2.3	Y	−2.8 ^[n0]
2	Ti	−0.9	Zr
3	V	−0.255	Nb	−0.9 ^^
4	Cr	−0.42	Mo	−0.2
5	Mn	+1.56	Tc	+0.3
6	Fe	+0.771	Ru	+0.24
7	Co	+1.92	Rh	+0.7
8	Ni	+2.3	Pd
9	Cu	+2.4	Ag	+1.8
10	Zn	(very high)^	Cd	(very high)^
11	Ga	−0.8	In	−0.49

^ No doubt, since no one has ever made trivalent calcium, strontium, zinc, or cadmium

^^Nb³⁺/NbO

In these two tables, the more negative the electrode potential the harder is it to gain an electron; conversely, the more positive the potential the easier it is to gain an electron
Mn³⁺ d⁴ is quite desirous of gaining an electron to get to a half-filled sub-shell i.e. Mn²⁺ d⁵; +2 is in fact the most stable oxidation state of Mn
The +2 oxidation state becomes more stable towards the end of the series, only up to Zn; Ga falls off the trendline
The data we so far could gather for the 4d elements has lacunae at Zr and Pd, but there is enough to see that the double periodicity is still present (although weaker, as usual for later rows)
The 5d elements have not been included because of (1) contention regarding what should be under Y, which is the whole point of this, and (2) the fact that these elements are usually unhappy to form aqua cations (which is already a problem for the 4d elements)

	M³⁺ + e⁻ ⇌ M²⁺	E° (V)	M³⁺ + e⁻ ⇌ M²⁺	E° (V)
0	Ba	(very high)^	Ra	(very high)^
1	La	−3.1 ^[n1]	Ac	−4.9 ^[n2]
2	Ce	−3.2 ^[n1]	Th	−4.9 ^[n3]
3	Pr	−3.1	Pa	−5.0 ^[n4]
4	Nd	−2.7	U	−4.7 ^[n3]
5	Pm	−2.6	Np	−4.7 ^[n4]
6	Sm	−1.55	Pu	−3.5 ^[n4]
7	Eu	−0.35	Am	−2.3
8	Gd	−3.9	Cm	−3.7 ^[n2]
9	Tb	−3.7 ^[n5]	Bk	−2.8
10	Dy	−2.6	Cf	−1.6
11	Ho	−2.8	Es	−1.3
12	Er	−3.0	Fm	−1.1
13	Tm	−2.2	Md	−0.1
14	Yb	−1.05	No	+1.4
15	Lu	−2.7 ^[n6]	Lr	≤ −0.44

Notes: [0] [1]; [1] Cotton 2007, p. 22; [2] Wiberg 2001, p. 1761; [3] Wiberg 2001, p. 1764; [4] Wiberg 2001, p. 1763; [5] doi:10.1016/j.aca.2005.10.079; [6] doi:10.1021/ja403753j; otherwise NIST tables

^ No doubt, since no one has ever made trivalent barium or radium

Eu³⁺ f⁶ is the easiest of the Ln to gain an electron and become Eu²⁺ f⁷ even though, for Eu, this is a less stable state. As Eu is approached, the +2 state becomes more stable (Sm²⁺ f⁶ is well-known already).
Although the early An are all generally unhappy to show low oxidation states, we see that Am²⁺ f⁷ is the least unhappy of the lot by far
Gd³⁺ f⁷ is not very interested in gaining an electron since it would lose its half-filled sub-shell and become f⁷5d¹, analogous to Fe³⁺ d⁵ being rather ambivalent about becoming Fe²⁺ d⁶ (both states are common)
Yb³⁺ f¹³ is nearly as easy to gain an electron and become Yb²⁺ f¹⁴ even though, for Yb, this is a less stable state
The late An are generally increasingly happy to show low oxidation states; starting from Fm²⁺ f¹² they are stable in water, and at No²⁺ f¹⁴ it is even the predominant oxidation state.
The +2 oxidation state becomes more stable towards the end of the series, only up to Yb and No; Lu and Lr fall off the trendline

Closing statements

Limited to 400 words

Sandbh

I'm comfortable with my arguments for Sc-Y-La. They're well-supported by the literature.

Re Double sharp’s arguments, I have reservations about their presumptiveness and complexity. On several occasions my arguments were said to be a based on a misunderstanding or misinterpretation by the cited authors; history needing to be revisited; or were countered by introducing novel interpretations not supported by the literature. The complexity of Double sharp’s arguments speaks for itself.

There’s no silver bullet solution to the group 3 question. So we have to argue it out using qualitative or quantitative arguments.

Rather than dwelling upon the minutiae of the individual properties of La and Lu, I attempted to take more of a helicopter view. That meant examining the group in the context of its surrounds; the congruity of the f-block; patterns seen elsewhere in the periodic table; the periodic law; and global considerations. Along the way I entertained a few more detailed (ancillary) arguments where I felt these were required to provide context, were novel, or provide useful insights.

An interesting argument Double sharp raised with me, which I didn’t address, was that Lu below Y would result in a more homogenous d-block. That may be so. Yet the periodic table isn’t so much about striving for homogeneity as it is about periodic trends. And it’s these trends that result in the diversity we see among, for example, the transition metals, and the p-block with its mixture of metals, non-metals, including metalloids, halogens, and noble gases.

The funny thing about Lu under Y is that it looks nice—more symmetric or regular if you will—but it disrupts some cool chemistry-based patterns (as seen elsewhere in the periodic table) and introduces further irregularities of its own. Double sharp contends these patterns are too local or are that the irregularities are insignificant. I argue they are part of the rich texture of the periodic table, and that we here to draw and wonder at the periodic table as it is, not how we think it should appear

From a Platonic symmetry perspective and perhaps that of physics, and on some grounds of regularity but not on others, it can be argued that Lu is better placed under Y. But not from a chemistry perspective, or at least not as well.

My unqualified respect for Double sharp the person, and as a valued peer, stands.

--- Sandbh (talk) 04:13, 8 April 2020 (UTC)

Double sharp

“

Chemistry is not a heap of distinct conceptions standing apart alone, but rather interconnected system of conceptions based on experimental facts.

”

— Droog Andrey

No Sc-Y-La argument presented fulfills what a theory of chemistry underlying the periodic table must have: consistent applicability to every element.

Complexity is required to holistically understand why chemistry alone cannot solve the group 3 issue.

Shall we observe ScCl₃ vs TiCl₄, call it a fundamental group 3-4 divide, ignoring its disappearance for ScCl₃ vs TiCl₃, shifting past the +4 state in the 5f row, and before the +2 state for periods 2 and 3?

Exclude La³⁺ [Xe]4f⁰ from the Ln contraction, claiming predominant oxidation states, but let the scandide contraction start at Sc³⁺ [Ar]3d⁰?

Criticise water-reducing Yb²⁺, and equally use Th³⁺, Pa³⁺, and U³⁺ for the actinide contraction?

Insist half-filled subshells on the E⁰ trend give peaks in the d rows, but troughs in the f rows?

No! An end to "one argument here, one argument there, never the twain shall meet". Foundational periodicity must know no boundaries. Shall we be denied following Mendeleev, projecting into the unknown, where no boundaries are charted? Shall we holistically seek working generalisations, or argument barrages at each other's throats within milliseconds without artificial leashes?

Ever-reliable electronic structure, that solved formerly unsolvable Be-Mg-Zn and B-Al-Sc, truly is the "helicopter view": logically deriving continuous trends from theory, without artificial divides. The PT's rich structure is only derivable from holistic criteria. Locality is the next level!

We draw a first-order generalisation, not take one secondary relationship out of many strong ones, to honour as it never deserved!

Most textbooks still explain hypervalence with d-orbitals, though it was debunked decades ago. Why should we follow them if the literature knows better?

Shall we endlessly copy mistakes of a century ago, when electron filling wasn't understood, and 4f was a one-off interruption of the d block? Emphasise the ground-state delayed start of 4f/5f forever, when it means nothing for chemistry, their ends still happen at Yb/No, blinding ourselves to the reproachful counterexamples of thorium and the looming 8th row?

Or shall we progress and heed luminaries: Seaborg, Jensen, Schwarz, Wulfsberg, and Jørgensen, who long ago exposed the hollowness of ground-state DEs? Shall we deny the crown of useful generalisations to ideal configurations, given willingly to ideal gases, crystals, and solutions?

Respecting Sandbh, I support literature and logic, not debunked, self-contradicting tradition. Double sharp (talk) 07:43, 8 April 2020 (UTC)

What next?

Double sharp and Sandbh to conclude edits on immediate summary
Ask DePiep what he makes of it
Ask other members of our project what they make of the immediate summary
Hope for IUPAC project team report and recommendation this side of post-COVID-19 Xmas
WP:RFC by Double sharp in July?

Sandbh (talk) 12:46, 6 April 2020 (UTC)

@Sandbh: Seems like a good plan to me; yes, I plan an RFC in July. (I am taking a little bit of extra time only to finish this summary; after that, I think my work on convincing people from the literature should be done, and we will see what people think while I take my wikibreak.) That way, it should be possible for everyone to comment on this shrunken overview, instead of the original doorstopper. Double sharp (talk) 12:50, 6 April 2020 (UTC)

@Double sharp: Nice. Sandbh (talk) 12:53, 6 April 2020 (UTC)

The more I look at this, the more I think we should also ask for (separately, to avoid clouding the issue) group 12 to be coloured as TMs again, as direct d involvement stops mostly after group 12 instead of group 11 (doi:10.1016/0368-2048(75)80018-1; although there is a drop from group 11 to group 12, it is only at group 13 that d involvement becomes purely incomplete screening effects). The Zn group is not that far removed from the Cu group, chemically. But not in this RFC. Double sharp (talk) 05:42, 7 April 2020 (UTC)

Commentary

I still don't see a single La argument with a leg to stand on. Especially the point about sources who really consider the question mostly plumping for Lu tells me that an RFC is the right way to go here to correct the group 3 situation. (We can correct the group 2 situation and move helium there once we get the critical mass: right now I think we are in the equivalent situation as Jensen writing in 1982, with the advocacy of Grochala, Grandinetti, and the late Henry Bent.) Points 15 and 20 (in the right-hand column) are why I think an RFC is justified. Double sharp (talk) 16:47, 3 April 2020 (UTC)

As for how much of this is still active: mostly just the bottom of it at this point, from "Falsifiability" onwards, I guess. (I've just archived another big chunk into archive 42, which is now 1.3M...) Since Sandbh has recently stated that he won't address old ground, and the old ground is the key to our being in disagreement, I am not sure if there is anything new left that we need to finish addressing. I am also not sure how much inviting outsiders will help, because frankly the material required to tackle this subject is rather specialised, and unless your focus is rare earth chemistry (so these elements are the relevant ones, and even then it may not work so well because intraperiod resemblances must also be brought in) or the foundational aspects of general inorganic chemistry (i.e. regularities across the whole table, not just one region of it), it probably doesn't matter much to you. If we bring in an outsider, it should be one whose expertise is on one of these chemical branches.

So probably in the future an RFC should start, except that by mid-April I shall be a lot busier and therefore maybe the great big 2nd RFC to fix group 3 will have to be delayed until July. So perhaps what we should do is:

Tie up whatever loose ends we see fit to tie up from this thread within the next few days (that depends on what Sandbh wants to go over or address):
Archive the rest of it (I think, next week, since my reserve of free time for this should end very soon), so that we all have some time-out for passions about this to not flare so much:
And I'll be back later to start the giant RFC when my free time returns.

I still would like to thank Sandbh for the discussion, since it has definitely sharpened and greatly improved my approach to the periodic table. I still disagree with him, of course. ^_^ And I would also like to thank Droog Andrey for initially showing me the more advanced chemistry required to understand why the La table must be rejected. And also R8R, Dreigorich, and all other present and past participants in the group 3 debate, ranging all the way back those we cite who published about this in the last century. Double sharp (talk) 02:23, 3 April 2020 (UTC)

@DePiep, ComplexRational, Sandbh, R8R, Droog Andrey, and Дрейгорич: Pinging everybody. Double sharp (talk) 05:14, 3 April 2020 (UTC)

Responses etc

Heck, just reading this discussion improved my understanding of the theoretical structure of the periodic table, and how it ties in to the practical decisions that need to be made regarding chemical families. I talked a lot with Double sharp on my own talk page about the structure of the periodic table. I also agree that this has gone on for quite some time now. Thanks to everyone who attended this amazing not-quite-a-TED-Talk-but-it-might-as-well-have-been-one kind of thing. ― Дрейгорич / Dreigorich Talk 07:42, 3 April 2020 (UTC)

@Дрейгорич: Thank you!

There have been a few last posts to the discussion by both of us since your comment, but I think I've just written the last one I'll have time for in the near future. So, you know where to go if you want a group 3 archive binge (my sincerest apologies for linking to TV Tropes, which will certainly cause another one ^_^). ;) Double sharp (talk) 04:52, 5 April 2020 (UTC)

I’m a few responses behind recent posts. I’ll get to those shortly, and check for o/s threads. I don’t mind revisiting old ground as long as we don’t recycle it. I’ll see if I can extract the nub of these issues and address them that way or incorporate them into DS’ table. It’s good to be able to load our page without cacking my iPad. Sandbh (talk) 10:34, 3 April 2020 (UTC)

DS's table looks useful, then I strongly suggest we do not contunue arguing in this thread (so better ignore prose that starts I still don't see a single argument that .... This thread is *not* to settle an outcome. It is to give overview. -DePiep (talk) 11:46, 3 April 2020 (UTC)

OK, struck and replaced by an overview statement that points 15 and 20 (my column) are why I suggest an RFC to happen. Double sharp (talk) 16:47, 3 April 2020 (UTC)

@DePiep: Forgot to ping you, sorry. Double sharp (talk) 16:47, 3 April 2020 (UTC)

Thx. rereading me: sounding harsh, while trying to be clear & short... -DePiep (talk) 16:50, 3 April 2020 (UTC)

The #Main lines table, a great initiative and setup, is descending into a battle. Whatever the cost, I will not allow a 'shortened' repeat of the Grand discussion. Must I explain? Well here it goes: the #Main lines table shall not be a battlefield. Leave it to others. @Double sharp and Sandbh: -DePiep (talk) 18:06, 4 April 2020 (UTC)
- @DePiep: So far as I can see, there is nothing in the main lines table that has not been raised and discussed in the main thread already, so it is still a good summary. It just looks like a heated argument replay because it is summarising what already was a heated argument by quoting each side's arguments. Double sharp (talk) 02:34, 5 April 2020 (UTC)

Response to immediate summary

@DePiep, ComplexRational, R8R, Droog Andrey, Дрейгорич, YBG, 1.02 editor, Kpgjhpjm, UtopianPoyzin, and Paintspot:

Double sharp and I have provided an overview of the group 3 situation in a Background section (18 numbered bullets), a Current state of affairs section (39 numbered bullets), and closing statements (400 words each).

Your thoughts, if any, welcome. Sandbh (talk) 03:05, 9 April 2020 (UTC)

Can we have a TL;DR of the TL;DR? ― Дрейгорич / Dreigorich Talk 03:52, 9 April 2020 (UTC)

@Дрейгорич: Unfortunately, I start to doubt that it's possible to cut any further... Double sharp (talk) 04:05, 9 April 2020 (UTC)

TLDR of the TLDR

Double sharp

Although against my better judgement, here is a try:

Sandbh thinks the La table is backed up by a century of practice and notes, consistent with historical experience, that most new ideas are wrong; but I note that it has been challenged since almost the very beginning of that practice by authors supporting the Lu table.
I note most authors who seriously consider the situation end up supporting Lu; that the whole point of science is the ability to say "we were wrong" when new evidence comes in; and that textbooks are usually behind the latest literature by quite a while (just look at how many resources still give the d orbital explanation for 3p element hypervalence, refuted in the 1990s).
Sandbh thinks I'm being too complicated. I think that being less complicated won't fit the facts.
Sandbh thinks I'm choosing unrepresentative oxidation states like Yb²⁺. I say that by referring to the scandide and actinide contractions, he's implicitly doing so because there's no oxidation state that will be representative for all of Sc-Zn or all of Ac-Lr.
- Clarification: Reading this, one may get the impression that I don't use comparable standards. In fact, for the scandide contraction, we can use +2 since that is the only state common to all of them (aside from +1), and the most stable for six of ten of them. For the An, +3 is common to all of them and is the most stable state for 8 of 14 of them. Sandbh (talk) 01:35, 10 April 2020 (UTC)
  - Well, just look at 4d then. There's no such oxidation state to pick. Double sharp (talk) 03:13, 10 April 2020 (UTC)
    - Hey, you were the one to add the 4d metals to the table! Sure, there is no common oxidation state, yet +2 is the only one common to all of them (aside from +1). Like you said, the data that could be gathered for the 4d metals has gaps at Zr and Pd, but there is enough to see analogous periodicity is still present, although weaker (as usual) for later rows. I even somewhat support what you said re once we get rid of the s electrons we can at least see where the half-filled and filled states are. Sandbh (talk) 05:40, 10 April 2020 (UTC)
      - @Sandbh: Ah, but my whole point of picking +2 has nothing to do with common oxidation states. It has everything to do with getting rid of the s electrons only. That's why even for the lanthanides I insist on +2 and not +3; you want to get rid of the s electrons only to see where the half-filled and filled states are, like you agree in your last sentence. It's the only measure that is both fair and gets us to the point of what is going on. And I trust that my having added 4d is not a problem, since I'm sure you agree the 4d contraction runs Y through Cd, and we had better be able to use the same tools consistently to discover that. Double sharp (talk) 05:42, 10 April 2020 (UTC)
        @Double sharp: In the Ln you need to get rid of d¹s². 4d is awkward since effectively no-one talks about a 4d contraction occurring along the 4d metals per se, since they have no common, most stable oxidation state. Instead, the contraction is considered in terms of its knock-on consequences, from Cd or In onwards. Whereas with the Ln they have a common most stable oxidation state of +3 and you get to see the contraction as it occurs along the Ln trivalent cations, from Ce to Ln, as well as its knock-on impact starting with Hf(IV). Sandbh (talk) 06:01, 10 April 2020 (UTC)
        @Sandbh: You're almost getting it. ;) If you apply the logic "they have no common, most stable oxidation state", you will see immediately that the same is true for 3d and 5f. You can pluck out +2 and +3 that are the most stable for just over half of them only, but anyone can see that there is significant opposition for which it doesn't work (it's literally 6-4 and 8-6 respectively). So that confirms what I've been telling you: there is nothing comparable to the Ln contraction, because that's the only contraction for which both the direct and the knock-on effects are important.
        
        Now, for d¹s²: this assumes already that one d electron is hanging up and filling early. We both know that's not so, just look at the electron configurations. No, please don't tell me to look at the condensed-phase ones, because then we also have p occupancy filling early. And in chemical environments, configurations switch around, what matters is the number of electrons you can get and whether you can force them into a half-filled or fully-filled situation plus the s orbital. Then we can easily see that whole idea self-contradicts stability considerations, because a supposed half-filled f⁷d¹s² should be unstable because of that singly filled d orbital above. So we should be looking at f⁶d¹s² becoming stable f⁷d⁰s². So by this logic, the stable ones should be not half-filled and fully-filled subshells f⁷ and f¹⁴, but ideal f⁶ and f¹³ that can rearrange themselves into a more stable arrangement. Isn't this at the very least strange? Eu and Yb show all the signs of half- and fully-filledness in trends (they match the positions of Mn and Zn), but a Sc-Y-La table denies them that position and puts them as almost-half and almost-full shells which now get the special treatment. Well, by that logic we may also start each period in group 2 and end it at group 1. Double sharp (talk) 06:10, 10 April 2020 (UTC)

This is a level of complexity that isn't warranted or required. P occupancy is noise, compared to the main game. f⁷d¹s², as seen in metallic Gd, is very stable going by Klemm's crude analogy of Gd to a noble gas. There is no such thing as f⁶d¹s². There is instead f⁷s² in metallic Eu. Or, as you know, in it's most chemically stable +3 state, f⁶ [!] That's why trivalent Gd f⁷ gets the special treatment, not Eu. Sandbh (talk) 07:06, 10 April 2020 (UTC)

@Sandbh: p occupancy proves that condensed-phase band occupancy is too complicated to really use. You have to consider instead the number of electrons available. Metallic Gd has three electrons mostly delocalised, so the important thing is that you have basically a sea of Gd³⁺ [Xe]4f⁷ ions with three delocalised electrons per atom. For Eu you have a sea of Eu²⁺ [Xe]4f⁷ ions. We can clearly see that f⁷d¹s² isn't stable at all by itself until you get rid of that d electron. Whereas f⁷d⁰s² just needs the s electrons to be take care of. It's therefore absolutely clear that Eu f⁷d⁰s² is the one with the half-filled configuration just like Mn d⁵s² here: they just have an outer s shell, and a half filled inner shell that resists attempts to take more electrons out of it (though it is possible).

@Double sharp: Yes, agree on metallic Gd. For metallic Eu it's predominantly Eu²⁺ [Xe] 4f⁷ with some Eu³⁺ 4f⁶ which is weird but gives a hint as to what's going on. In actual chemistry, Eu³⁺ is the most stable cation with f⁶, quite unlike the most stable divalent form of Mn, which is d⁵. Here the analog to Mn is trivalent Gd as d⁵. Sandbh (talk) 10:21, 13 April 2020 (UTC)

@Sandbh: You keep focusing on most stable oxidation states. That is not the point. In actual chemistry, Tc²⁺ and Re²⁺ are not the most stable oxidation states, but that is not the point either. As we know because we have no qualms asserting that Tc and Re are the elements at the halfway point of the block. The point is just getting rid of the outer s subshell and creating equal terms for everybody. Because the s shell is the only covering shell that persists throughout, and we want the +2 state to ionise it away. Double sharp (talk) 10:24, 13 April 2020 (UTC)

BTW, you say there is no f⁶d¹s² (true), but if you consider d¹s² to be removed from each lanthanide, then you are implying that that and f¹³d¹s² are the ideal configurations of Eu and Yb respectively. Never mind that they, on trends, show exact analogies to Mn and Zn in 3d, not Cr and Cu. Double sharp (talk) 07:29, 10 April 2020 (UTC)

@Double sharp: I'm not implying anything. The most stable, chemistry-based configurations for Eu and Yb are trivalent f⁶ and f¹³, as you know. Sandbh (talk) 10:21, 13 April 2020 (UTC)

@Sandbh: As above. Double sharp (talk) 10:24, 13 April 2020 (UTC)

@Double sharp: Comparing ions with s² ionised away is one thing. We may observe that the ionic radius of divalent Ti is 0.86 and that of Zn is 0.74 and that therefore, on this valid basis, there is a 14% contraction from Ti to Zn. If you are going to persist with invalidly comparing the less stable divalent Eu and Yb states with the most stable divalent Mn, rather than using the most stable trivalent forms of Eu and Yb, we have nothing further to talk about, on this point. Sandbh (talk) 12:00, 13 April 2020 (UTC)

@Sandbh: The absolute stability of the +2 oxidation state is not the relevant issue here. Otherwise we will never be able to find the 4d and 5d contractions, and as I said below, you must erect the PT's structure through a means that encompasses every element. It is simply used because it corresponds to the removal of the s² electrons and exposes only the filling of the characteristic subshell. That's why I am only comparing relative stability of +3 vs. +2, knowing that reaching a half- or fully-filled subshell ought to stabilise +2 beyond what would linearly be expected. As I wrote four days ago: "As reiterated above, the point of using +2 everywhere is not because it's a common oxidation state (because it isn't), but because it corresponds to getting rid of the outer s subshell. So then you can look in isolation at the filling subshell and the stability of the half-filled one. If you want +3, that implies you have an outer 5d¹6s² all the time. Which obviously doesn't happen. ;)" (Nope, not even in the condensed phase, because of p occupancy.) Double sharp (talk) 13:03, 13 April 2020 (UTC)

M	Ca	Sc	Ti	V	Cr	Mn	Fe	Co	Ni	Cu	Zn	Ga	Ge
mp (°C)	842	1541	1668	1910	1907	1246	1538	1495	1455	1085	420	30	938
bp (°C)	1484	2836	3287	3407	2482	2061	2861	2927	2730	2562	907	2400	2833

M	Ba	La	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb	Lu	Hf
mp (°C)	727	920	795	935	1024	1042	1072	826	1312	1356	1407	1461	1529	1545	824	1652	2233
bp (°C)	1633	3464	3443	3130	3074	3000	1900	1529	3000	3123	2567	2600	2868	1950	1430	3402	4603

Double sharp (talk) 07:45, 10 April 2020 (UTC)

Let's focus on the chemically relevant properties.

Looking at the standard reduction potentials for the 3d and 4f metals, divalent Mn wants to hold on to its d⁵ configuration, as trivalent Gd wants to hold on to its f⁷ configuration:

3d	Ca	Sc	Ti	V	Cr	Mn	Fe	Co	Ni	Cu	Zn	Ga
M³⁺ + e⁻ ⇌ M²⁺	very high	−2.3	−0.9	−0.255	−0.42	1.56	0.771	1.92	2.3	2.4	very high	−0.8
M⁺²	d⁰	d¹	d²	d³	d⁴	d⁵	d⁶	d⁷	d⁸	d⁹	d¹⁰	d¹⁰s⁰4p¹
M	d⁰s²	0	0	0	0	d⁵s²	0	0	0	0	d¹⁰s²	0

4d	Sr	Y	Zr	Nb	Mo	Tc	Ru	Rh	Pd	Ag	Cd	In
M³⁺ + e⁻ ⇌ M²⁺	very high	−2.8		−0.9	−0.2	0.3	0.24	0.7		1.8	very high	−0.49

4f	Ba	La	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb	Lu
M³⁺ + e⁻ ⇌ M2+	very high	-3.1	-3.2	-3.1	-2.7	-2.6	-1.55	-0.35	-3.9	-3.7	-2.6	-2.8	-3	-2.2	-1.05	-2.7
M³⁺	4¹⁰5s²5p⁵	4f⁰	4f¹	4f²	4f³	4f⁴	4f⁵	4f⁶	4f⁷	4f⁸	4f⁹	4f¹⁰	4f¹¹	4f¹²	4f¹³	4f¹⁴
M⁺²	d⁰	0	0	0	0	0	0	4^f7	0	0	0	0	0	51	4f¹⁴	4f¹⁴5d¹
M	d⁰s²	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

5f	Ra	Ac	Th	Pa	U	Np	Pu	Am	Cm	Bk	Cf	Es	Fm	Md	No	Lr
M³⁺ + e⁻ ⇌ M²⁺	very high	-4.9	-4.9	-5	-4.7	-4.7	-3.5	-2.3	-3.7	-2.8	-1.6	-1.3	-1.1	-0.1	1.4	≤ −0.44

For the 4f metals, the most stable oxidation state is +3. Ostensibly +2 is the benchmark for the 3d metals since that is the only state common to all of them (aside from +1), and the most stable for six of ten of them. As you note, the data for the 4d metals has gaps at Zr and Pd, but there is enough to see double periodicity is still present although weaker, as usual, for later rows. For the 5f metals the +3 state is common to all of them and the most stable for 8 of 14.

It seems to me that had the 4f sub-shell started to fill at La rather than Ce, then it would have been Eu rather than Gd with the trivalent f⁷ configuration. For the 4f metals, I take the spikes at Gd and Lu to be a chemical consequence of the delayed start of filling of the 4f sub-shell. The further delayed start of filling of the 5f shell does not appear to have any additional chemical consequences.

The parallels between the d- and f-block metals are quite pleasing. Sandbh (talk) 07:52, 13 April 2020 (UTC)

@Sandbh: You only get the parallel by artificially shifting your boundaries. To quote Droog Andrey again: "you compare diactions with trications, so that's not a surprise you obtain analogies like Ca-Zn vs. La-Lu and Sr-Cd vs. Ac-Lr. So that's just an old "+3 state" argument. My point is that we should use equal terms for such a comparison." It must be the +2 state for everybody, that's the only sensible one because outer ns² are chemically speaking always ionised. It's not about whether that is a common oxidation state or not, it's purely about removing those s electrons and focusing on the characteristic subshell filling. Likewise, for the s and p blocks I would go for the 0 oxidation state, even if most elements don't want to be in it as free elements, simply because there is no covering subshell to get rid of there. It's a matter of electronic structure only. (And, besides, if 4f started in La, what you would expect is for Eu²⁺ to be 4f⁷ as it would be seven f electrons above [Ba] = [Xe]6s². Well, it actually is.)

Just look at the peaks and troughs of your chart. You say the parallels from the d block to the f block are quite pleasing. Well, they are: Mn/Tc and Zn/Cd show up as obvious peaks in the d block that end each half-series. And similarly Eu/Am and Yb/No show up as such in the f block. And yet you go and highlight the following elements instead and destroy the parallel. Well, let me paraphrase something from the old group 3 submission that I withdraw my support from: while I agree with the spirit of finding parallels, by that measure your support for Sc-Y-La is totally misguided, and the argument very strongly and elegantly supports Sc-Y-Lu. As is supported by absolutely every trend, when plotted, suggesting double periodicity as La-Eu and Gd-Yb families. Double sharp (talk) 10:17, 13 April 2020 (UTC)

@Double sharp: Headslap ^_^. There is no "artificial" shifting of boundaries. This is the doing of Nature, and the delayed start of filling of the f sub-shells. We should indeed use equal terms for the comparison just like all the authors I cited do. +2 is the most common stable state among the 3d metals. +3 is the uniformly mostly stable state among the Ln. Using a less stable state for Eu and Yb is not a level playing field. Next you will be telling me that alkali metals are nonmetals given they can form –1 anions, never mind their most common oxidation state is +1. OK, I'm exaggerating but the analogy is there. Many things become possible when we start referring to less stable oxidation states but we don't use these to make generalisations of the kind you are advancing.

Your bold assertion that, "as is supported by absolutely every trend, when plotted, suggesting double periodicity as La-Eu and Gd-Yb families" reminds me of Flat Earthers who explain a round Earth the same way they explain anything else that contradicts their narrative. They simply ignore or discredit or reinterpret any evidence of a round Earth. I'm not having a go at you, and I'm not annoyed. I find it quite funny that this happens to nearly everything I present, regardless of how many sources I provide. Praise be I still have my sense of humour. I hope you do to as we strive for common ground. Sandbh (talk) 10:44, 13 April 2020 (UTC)

For the 9001st time, there is no such thing as a delayed start of filling of the f subshells. It only comes about because of a double standard, in which the ability for thorium to show f involvement despite its [Rn]5f⁰6d²7s² ground-state gas-phase configuration is accepted to put it in the f block, and the ability for lanthanum to show it with [Xe]4f⁰5d¹6s² and actinium to show it with [Rn]5f⁰6d¹7s² is vociferously denied. Just like Jensen noted.

So, let's be consistent: we are talking about electronic filling, and stability of oxidation states is only a relative thing here that we do in order to look for the stabilising effect of a half-filled subshell. It does not matter one bit to me that +2 is not the most common stable state among the 4d metals: I use it anyway because it creates consistency and corresponds to the totally sensible removal of the s subshells. Common oxidation states are irrelevant for this problem precisely because they get us absolutely nowhere with 4d and 5d and we have to pick consistent criteria: you must erect the PT's structure through a means that encompasses every element. So we are just comparing the relative stability of the +3 and the +2 states, knowing that a half or fully filled subshell will increase the stability of the +2 state. The fact that Mn vs. Eu and Zn vs. Yb fits so well as an analogy makes it perverse to argue that instead we should have ds² hanging up instead, creating a totally unprecedented split block and destroying the nice pattern in favour of a shifted one. And the final nail in the coffin for that idea comes from plotting every single trend. Look at melting points. Look at boiling points. Look at densities. Look at phase transition temperatures. Look at standard reduction potentials. Look at electronegativity. There is no case at all where Eu and Yb match the positions of Cr and Cu, they always match those of Mn and Zn. That's all the confirmation you could ever ask for that the analogy of Sc-Zn to Ce-Lu is totally incorrect, and that the right analogy is Sc-Zn to La-Yb.

Let me quote Droog Andrey yet again: "You build a list of La arguments, a list of references, a list of authors who are wrong. But could you make a little analysis of what you have built?" Double sharp (talk) 13:03, 13 April 2020 (UTC)

You know, it is excellent that Droog Andrey has already addressed all of this, because it saves me time from drafting new responses that I need for RL:

“

"Eu and Yb are the outliers." Yes, and that's natural, because they end 7-element subfamilies La-Eu and Gd-Yb which have some correlations across. If one take Ce-Lu as 4f family, then Eu and Yb will be penultimate members of subfamilies which is just weird. ... the appearance of dips at penultimate members of subfamilies is weird. And that's not about the configurations, that's about chemistry. The comparison of d-block with f-block is valid simply because of the same number of outer-shell electrons.

You compare Eu and Yb with Cr and Cu, but that's just ridiculous. Look at the densities, phase transition temperatures, standard potentials, electronegativity, etc. along the atomic number, and you will see that. Actually neither Eu/Yb, nor Gd/Lu are "anomalous", the trends are smooth along the whole subfamilies La-Eu and Gd-Yb without any jumps, that's clearly seen from my chart.

Suppose we decided to start every period with group 2 element and end it with group 1 element. Your arguments will stand in that situation. Well, the periodicity is still here. The extreme properties of the penultimate elements of each period are just because of the filled p⁶ configuration, like d¹⁰ in Cu and Ag. All is clear, isn't it? ...

Again, the trends Sc-Y-La-Ac or Sc-Y-Lu-Lr are not at all about the configurations of neutral atoms, no matter gas phase or metal phase (BTW, there's no any physical sense in atomic configuration in condensed phase, because there's no pure atoms and no atomic wavefunctions). The trends are about real compounds and their properties. Boiling point trend of lanthanides definitely supports Sc-Y-Lu-Lr since it supports natural subfamilies La-Eu and Gd-Yb.

”

— Droog Andrey in Archive 33

Double sharp (talk) 07:53, 10 April 2020 (UTC)

@Double sharp: I've addressed Droog Andrey's arguments before. He isn't comparing like with like. The dips he is referring to as weird are an outcome of the delayed start of filling of the f sub-shells. This is seen in the gas phase, the metallic phase, and the ionic phase. The argument about starting every period with a group 2 element and ending it with a group 1 element is baseless, since their is no delayed start anywhere else (not yet, anyway). The trends are indeed about real compounds. The boiling points of the Ln have nothing significant to do with their chemistry, in the context of our huge thread. Sandbh (talk) 10:58, 13 April 2020 (UTC)

As I just wrote above: "For the 9001st time, there is no such thing as a delayed start of filling of the f subshells. It only comes about because of a double standard, in which the ability for thorium to show f involvement despite its [Rn]5f⁰6d²7s² ground-state gas-phase configuration is accepted to put it in the f block, and the ability for lanthanum to show it with [Xe]4f⁰5d¹6s² and actinium to show it with [Rn]5f⁰6d¹7s² is vociferously denied. Just like Jensen noted." So that whole argument collapses like a house of cards. There are only two consistent options here: either there is no delay (the chemically sound approach), and there's no reason for such strange dips; or there is a delay (the formal and irrelevant approach), in which case we note that the 4f row starts at Ce, but the 5f row starts at Pa. Well, the 5f increased delay explains the weird dips at antepenultimate members of the families Pa-Bk and Cf-Rf; everything is equally clear, isn't it?

And as I just wrote below: "I wonder why Greenwood & Earnshaw discuss melting points then, since their book is called Chemistry of the Elements? An explanation is, of course, not far off: what controls melting points is just the strength of bonds or intermolecular forces, which goes back to the electronic structure that underpins chemistry as well. There's not really a difference between how you explain melting and boiling points and how you explain chemical reactivity on this basis: they are both reflexions of the atomic structure and both are universally considered as periodic trends." That's exactly why bringing in physical properties is also important. Double sharp (talk) 13:07, 13 April 2020 (UTC)

@Double sharp: I'm puzzled as to why, on 9,001 occasions ^_^, you ignore the delayed start of filling phenomenon. It's widely discussed in chemistry and physics texbooks. It can be seen after La in period 6 and after Th in period 7. What is the issue with strange dips? There are plenty of other strange dips for Ln properties. Likewise, sometimes physical properties correlate with chemical properties, sometimes they don't. We're here to draw Nature as it is, not how we believe it should be. Sandbh (talk) 05:10, 14 April 2020 (UTC)

@Sandbh: Two reasons:

It has precisely zero impact on real chemistry. The end of 4f and 5f involvement as valence orbitals still happens at Yb and No, as expected if there was no delay. The elements that show up on the trends similarly to Mn and Zn in 3d are always Eu/Am and Yb/No, never Gd/Cm and Lu/Lr, as expected if there was no delay. La, Ac, and Th all can easily use low-lying 4f and 5f orbitals for hybridisation, as expected if there was no delay. And, actually, that last point is precisely why the delayed start of filling phenomenon is totally irrelevant. Because as has been widely discussed here already, backed up by the literature, the important thing is not which of many chemically relevant configurations lucks out into becoming the ground state in a gaseous atom by itself, but which ones are low enough in energy to be chemically relevant, and when you look at that there is no delayed start of filling phenomenon at all.
And even if it was important enough to reflect on the periodic table, it would not at all support a Sc-Y-La-Ac table. It would support a table where group 3 was Sc-Y-La-Ac and group 4 was Ti-Zr-Hf-Th. The first 5f electron appears in the ground state at Pa, so consistently reflecting the delayed start of filling (as irrelevant as it is) would mean that the f block has to be inserted between Th and Db. After all, Th has incumbency over Rf for the d²s² configuration.

So arguments for Sc-Y-La-Ac and nothing else based on delayed start of filling are not only focusing on an irrelevancy, they are even misguided. A real "delayed start" periodic table would have to look like

H                                                        He
Li Be                                     B  C  N  O  F  Ne
Na Mg                                     Al Si P  S  Cl Ar
K  Ca Sc    Ti    V  Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
Rb Sr Y     Zr    Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I  Xe
Cs Ba La *  Hf    Ta W  Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
Fr Ra Ac    Th ** Db Sg Bh Hs Mt Ds Rg Cn Nh Fl Mc Lv Ts Og

         *  Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
            ** Pa U  Np Pu Am Cm Bk Cf Es Fm Md No Lr Rf

which is evidently not the traditional Sc-Y-La-Ac layout. Well, it is certainly less symmetrical, and the f block no longer starts in a vertical column. But, as you say, "We're here to draw Nature as it is, not how we believe it should be." So why are you not consistently using this argument to support this table, since Nature gives us thorium with no 5f electrons, and you appear to believe that the delayed start of filling phenomenon is actually important? There's only two consistent options here: either argue with delayed starts and go for the table above, or drop them and go for something else. (But of course, dropping them for the good reason that they're chemically irrelevant immediately knocks out a lot of the arguments for Sc-Y-La.) Double sharp (talk) 06:46, 14 April 2020 (UTC)

I say the only constant oxidation states you can sensibly pick are 0 and +2, not +3, because you have to use identical standards for at least the d and f elements (transition elements). 0 is obvious; +2 at least ideally means removing the outer s electrons (that are almost always removed anyway chemically). Nothing else makes much chemical sense (otherwise, we can equally well say we have to draw the period break between groups 1 and 2, just looking at 2nd ionisation energies everywhere).
Sandbh thinks the Ln contraction should be measured from the filling of Ce³⁺ to Lu³⁺ as the 4f electrons fill from 4f¹ to 4f¹⁴.
- Clarification: That is a misrepresentation of what I say. The contraction starts with Ce³⁺ 4f¹ and finishes at Lu ³⁺ 4f¹⁴, having passed through Yb³⁺ 4f¹³. Of course, to measure the contraction in Ce, you have to compare it to La, which has no 4f contraction. Sandbh (talk) 01:35, 10 April 2020 (UTC)
  - My rebuttal still stands. Measuring contractions anywhere else requires bringing in weird oxidation states. You say below that you're relaxing it to oxidation states that at least the majority of the elements have as the most stable to allow +2 for 3d – very well, we still cannot find the start of the 4d or 5d contraction. That's why we need to use +2 everywhere because even if it's not stable, it takes away those s electrons and lets the stability of a half-filled or fully-filled subshell shine through. Double sharp (talk) 03:12, 10 April 2020 (UTC)
I say you can't find the start of any other contraction that way: Sc³⁺ has no d electron, Th⁴⁺ has no f electron, those are the usual oxidation states. You have to pick neutral atoms or +2 cations, and then Yb is the last one using its 4f electrons for anything.
Sandbh says the Ln contraction isn't a one-off, pointing to the scandide and actinide contractions as comparable
I note that they're only comparable electronically, not chemically, because there's no characteristic oxidation state to match across them.
Sandbh quotes a paper to support 4f involvement in Lu; I noted that the paper does not actually support that, as it suggests 4f involvement to be weaker than the involvement of the 5s and 5p orbitals (which are part of the [Xe] core).
- Clarification: It is nevertheless true that the paper supports 4f involvement in Lu, even if weaker than 5s and 5p. Sandbh (talk) 01:35, 10 April 2020 (UTC)
  - We are going to have involvement of every single orbital, speaking pedantically, because there is a non-zero chance a random 1s electron in a Lu atom somewhere on Earth is going to find itself far enough away from the nucleus to participate in bonding. There is also a non-zero chance that it appears on the Moon. Or on the planet Skyron in the Andromeda Galaxy, for that matter. It is just that at some point you have to draw a line because the chance ends up being ridiculously tiny. (After all, you refer to semi-continuums yourself, this is not a foreign concept.) And being lower than subshells which everyone agrees are in the core and not participating significantly is pretty damning. Double sharp (talk) 03:12, 10 April 2020 (UTC)
Sandbh wants to use local patterns like diagonal relationships or supposed group divides (that only exist if you look at just the right oxidation states); I say those only come after you've erected the PT's structure through a means that encompasses every element.
- Clarification: I agree with Double sharp's last sentence. Sandbh (talk) 01:35, 10 April 2020 (UTC)
  - So why refer to diagonal relationships to support Sc-Y-La? If you agree with my last sentence, then that means you have to erect the PT's structure first through global means, and then only then note that diagonal relationships (which are not global means, applying as they are only to 29 out of 118 elements) are cool. And since we agree that Al should not go over Sc even though that creates one more diagonal relationship Be-Al-Ti that Rayner-Canham has noted, consistency demands that diagonal relationships not be brought out to defend Sc-Y-La. We can only defend it through global means; the problem is that there aren't any such things that really defend Sc-Y-La if you look globally, as I note in my other points. Double sharp (talk) 03:27, 10 April 2020 (UTC)
Sandbh mentions DE's, and hence focuses on the delayed start of 4f; I say you can't define them (what is the DE between V 3d³4s² and Cr 3d⁵4s¹, anyway?), and that they're irrelevant (chemically bound atoms aren't usually in their ground-state gas-phase configurations)
- Clarification: The delayed start of 4f is seen in the free gas in a vacuum phase; the metallic phase, and the ionic state. Sandbh (talk) 01:35, 10 April 2020 (UTC)
  - Nope. Realistically speaking, free gas atoms don't matter one bit for chemistry. In the metallic phase, as already demonstrated, La has some f occupancy just like Th does. For ions, let me bring out another of Droog Andrey's old arguments; in practice you do not have a real +3 naked cation in a chemical environment, charge will be transferred and it will be closer to +2 on the La atom than +3. Now I just remark that promotion energy [Xe]5d¹ to [Xe]4f¹ for La²⁺ is only 0.9 eV. You can think of it as whether it's more profitable to attach an electron to La³⁺ 4f or 5d, and 5d is only barely preferred in a vacuum; chemical environments can easily provide the push to swing it to 4f. Meanwhile, promotion energy for Yb²⁺ 4f to 5d is 4.1 eV, and yet we are sure that 5d is doing something in Yb. There's no delayed 4f start in real chemistry. ;) Double sharp (talk) 03:12, 10 April 2020 (UTC)
I also note that by that logic, the start of the f block must be staggered (4f starts at Ce in the ground state, but 5f starts at Pa), and the 8th row becomes a horrific mess (we start occupying 8s at E119, 8p at E121, 7d at E122, 6f at E123 or E124, and 5g at E125), so you don't get a Sc-Y-La table anyway from this argument, just an unsustainable situation
I want to use the idealised electron configurations that match chemically active valence subshells; electronic considerations are the only thing that makes it possible to resolve the group II (Be-Mg-Ca or -Zn?) and III (B-Al-Sc or -Ga?) questions, and we should use them again here. (If we just look at chemical considerations, Al is actually closer to Sc than Ga!)
I claim (following Jensen) that there's a double standard in saying that Ac [Rn]6d¹7s² can't be an f element with the wrong configuration (which can be corrected in chemical environments, of course), but Th [Rn]6d²7s² can
Sandbh thinks that group divides can be useful, and that group 3 vs. 4 is one, and that that supports Sc-Y-La to make it match groups 1 and 2
- Clarification: No, I'm not saying a 3-4 divide "makes it match" anything. What I'm saying is the overall chemical behaviour of group 3 most closely resembles that of groups 1-2. Further, trends going down Sc-Y-La resemble those going down groups 1-2, whereas the trends going down Sc-Y-Lu most closely resemble those of groups 4-5+. There's nothing new here; it was noted by Jensen, and partly by Scerri. As the latter asserted, "Chemically similar groups should be close together, either as vertical groups or horizontal triads, with links between related elements clearly visible" (2004).
  - This is just my poor wording in an attempt to be concise, I think. What I meant to say is that I read you as saying that group 3 vs group 4 shows a group divide (viz. chemical difference), and therefore that groups 1-3 are more chemically similar and should be collocated, and so that group 3 should follow a trend like group 1 and 2 (i.e. Sc-Y-La). I think this is not too far from what you mean; if it's not, please correct me again.
  - Now, the statement about the trends is completely accurate. The only problem is that the overall chemical behaviour of group 3 does not closely resemble groups 1 and 2 alone. In actuality, most of those characteristic pre-transition properties are equally shared by the heavy group 4 and sometimes even group 5 elements: Zr, Hf, Rf, Nb, Ta, Db. They strongly prefer the group oxidation state, in which they are d⁰ and don't have transition properties to speak of. And the aqueous chemistry of Zr, Hf, and Rf strongly resembles that of the tetravalent actinides Th⁴⁺ through Pu⁴⁺ which have what is basically pre-transition chemistry, thanks to their high electropositivity. So, if we claim group 3 as trivalent versions of the group 1 and 2 metals, we can equally well claim group 4 from Zr onwards as their tetravalent version along with a bunch of actinides.
  - Meanwhile, the physical properties of Sc and Y are those of normal transition metals, more resembling group 4. This resemblance only works well if Lu and Lr go under Y, of course. Not to mention that the poor coordination chemistry of group 3 also resembles that of group 4, not only groups 1 and 2. So, there's still no group 3 vs. 4 divide, there's still no stronger resemblance of group 3 to group 2 vs. group 4, and so the rest of the argument crumbles. Double sharp (talk) 03:20, 10 April 2020 (UTC)
I say group divides are never useful (well, except noble gas to alkali metal that is the period divide) and that the real thing going on is generalised Fajans' rules (acidity and covalency increase as charge and electronegative increase and as radius decreases). As expected from those rules, such divides always disappear once we're not in periods 4-6, or if we stop insisting on group oxidation states. So we should ignore them.
Sandbh thinks the double periodicity of electrode potentials supports the f block starting at Ce, whereas I note that comparisons with the d block clearly show it must start at La.
Sandbh disputes this, arguing for +2 as a benchmark oxidation state for 3d (stable for a majority) and +3 for 4f. This, however, overlooks the inapplicability of this idea to 4d and 5d. By this logic, we cannot discover that Tc and Re are the "halfway" elements for 4d and 5, because for Tc, +2 isn't a common oxidation state. For Re, it's not even water-stable.
As reiterated above, the point of using +2 everywhere is not because it's a common oxidation state (because it isn't), but because it corresponds to getting rid of the outer s subshell. So then you can look in isolation at the filling subshell and the stability of the half-filled one. If you want +3, that implies you have an outer 5d¹6s² all the time. Which obviously doesn't happen. ;)

Detail about it can be found above and in the footnotes, but this should be a start that almost fits in one screen. Double sharp (talk) 04:16, 9 April 2020 (UTC)

Cool, thanks. This makes perfect sense. Well said. Team Lu for me! ― Дрейгорич / Dreigorich Talk 04:23, 9 April 2020 (UTC)

@Дрейгорич: You're welcome! I made a few little changes after you commented, but I don't think they change much. (Oh, and: DE = differentiating electron.)

Of course, this summary is dependent on whether Sandbh agrees if I have characterised his position accurately. Double sharp (talk) 04:26, 9 April 2020 (UTC)

May I suggest section title "... intermediate ...", as in: halfway the process? Thanks. -DePiep (talk) 05:29, 9 April 2020 (UTC)

Ye gods! A TLDR of a TLDR? Really? Head slap! Sandbh (talk) 09:38, 9 April 2020 (UTC)

@Дрейгорич: There have been some additions, in which Sandbh clarified his stand, and I rebut it again. Double sharp (talk) 03:20, 10 April 2020 (UTC)

Reread. ― Дрейгорич / Dreigorich Talk 08:33, 10 April 2020 (UTC)

Sandbh

Here it is, my TLDR of a TLDR, written with the benefit of having read Double sharp’s version.

Over the past 100 years a few arguments have been made for Lu. Jensen gave it a red hot go, with several arguments.

None of these went anywhere. Jensen's paper caused a frisson of excitement among a few authors. Not one of these authors, aside from Scerri (a world authority on the periodic table) looked critically at Jensen’s paper. Scerri concluded that Jensen was too selective and that his (Jensen's) arguments don’t cut the mustard. I agree.

A few people (not necessarily in this forum) feel that I sound like an old cloistered cleric, quoting chapter and verse, in order to defend the established tradition. In fact people familiar with me and my work know I can come up with, and promote, some far out ideas. So my support for La has nothing to do with defending the faith, so to speak.

As per Double sharp's quotation of Droog Andrey, arguments in support of La are mutually reinforcing, consistent with the nature of a periodic table as an integrated, complex structure whereas Lu in group 3 unravels this rich tapestry of chemical relationships.

One example is diagonal relationships. The classics are Li-Mg, Be-Al, and B-Si. Such relationships, which encompass another 20 elements (including La) are found in all blocks, and cut across 12 groups. Double sharp dismisses the relevance of such relationships. He says they only apply to 29 out of 118 elements, and don’t constitute a majority. Never mind their presence in all blocks and 12 groups! Extending this analogy we can say that nonmetals must be even more irrelevant since, according to us, there are only 17 of them, they cut across a mere four groups, and appear in just two blocks!

Another example is that I noted the special status of the half-filled and filled valence sub-shells in the cations, at Mn and Zn; and analogously at Gd and Lu (bullets 37–39, here). This analogy relies on +2 as the benchmark oxidation state for the 3d metals since that is the only state common to all of them (aside from +1), and the most stable for six of ten of them, including Mn and Zn. For the 4f metals, the most stable state is +3, and common to them all. Thus, Mn and Zn want to keep their +2 state, just like Gd and Lu want to keep their +3 states.

Double sharp responded by saying my argument is not supported by the data. He says, "We expect the half- and fully-filled subshells in the f rows to also form maxima…which appear at Eu/Am and Yb/No."

Now, Double sharp is happy to support divalent Mn and Zn as the relevant 3d metals since +2 is their most stable oxidation state, but when it comes to the 4f metals he supports divalent Eu and Yb even though +2 is not their most stable oxidation state! Thus, apples are comparable to oranges. Really?

Go figure, I say. Sandbh (talk) 01:53, 10 April 2020 (UTC)

@Sandbh: Added a rebuttal of the +2 vs +3 argument above to my TL;DR. Just look at 4d or 5d, there's no majority +2 state anymore, but we're still sure where the half- and fully-filled ones after we get rid of the s orbitals. Double sharp (talk) 03:02, 10 April 2020 (UTC)

@Double sharp: Same applies to the Ln once you get rid of their d¹s² electrons. We can see where the half- and fully-filled ones are, as per Klemm (1929), Endres (1932), Shchukarev (1974), Ternstrom (1976), Rokhlin (2003). Sandbh (talk) 05:48, 10 April 2020 (UTC)

@Sandbh: If you go by d¹s² as the covering subshell, you would expect a half-filled or fully-filled configuration (f⁷d¹s² or f¹⁴d¹s²) to be unstable still because of that unpaired d electron: it's not a closed shell, unlike what happens with Mn d⁵s² and Zn d¹⁰s². That is unlike anything else in the PT, and is another argument against this chemically weird idea that one d electron hangs up before the other nine get to fill.

There's no need to invoke d¹s² as the ideal configuration for the Ln to explain the +3 oxidation state. Chemically to get a +3 state you are taking something out of the f orbitals ideally, that's not a problem. It's totally analogous to what Fe does: Fe is d⁶s², to get +2 it gives away the s electrons to get d⁶s⁰, to get +3 it throws in a d electron to get d⁵s⁰. It's not the slightest problem to posit most of the lanthanides doing the exact same thing. Double sharp (talk) 05:51, 10 April 2020 (UTC)

@Double sharp: Well, I'm not invoking anything, aside from condensed and ionic configurations. You know the condensed configuration of e.g. Nd is 4f³5d¹6s² and that the ionic Nd³⁺ configuration is 4f³. There's no need to invoke or posit "throwing in" an f electron. Sandbh (talk) 06:42, 10 April 2020 (UTC)

@Sandbh: There is no integer occupancy of subshells in the condensed phase, all you have is electronic band structure. In chemical environments, configurations can switch around, what matters is the number of electrons you can get and whether you can force them into a half-filled or fully-filled situation plus the s orbital. You can absolutely have an f electron promoted, or not; depending on pressure, Eu and Yb will change their mind on whether to be divalent or trivalent in the metallic phase, for example. It's exactly what I've been saying about the interplay between 4fⁿ and 4f^n-1 configurations (which, as usual for most electronic features of the lanthanides, doesn't exist for Lu).

My explanation of Ln +3 is absolutely standard, see this resource from the Open University: there isn't a difference between how the 3d elements use their 3d electrons and how the 4f elements use their 4f ones. Once the atom is significantly ionised, it's no longer profitable to bring out more such electrons for bonding. That just happens sooner for 4f than 3d, probably because 4f ends up contracting quickly through an electron with higher electron density (4s+d+p instead of just 3s+p), and because 4f was already penetrating the [Xe] core quite a bit more than 3d was penetrating the [Ar] core. You can see that once radius increases for 5f (where there are radial nodes), we can get higher oxidation states.

So, that's precisely why the true analogy is from Mn (5 electrons plus an s-orbital) to Eu (7 electrons plus an s-orbital), similarly Zn to Yb. Just look at where the melting points drop drastically (Mn and Zn, same as Eu and Yb) when the half- and fully-filled subshell is more reluctant to be ionised. Double sharp (talk) 06:55, 10 April 2020 (UTC)

@Double sharp: And what does the melting point have to do with the actual chemistry of the elements involved, as per the comparative tables of standard reduction potentials I posted? And what does pressure have to do with our periodic table of the chemical elements in ambient conditions?

I've seen that unattributed and unsupported paper before. It strikes me as more complexity than is required, as if the author was unaware of the Ln configurations in the metallic phase. Why doesn't it apply to the metallic phase? Sandbh (talk) 12:12, 13 April 2020 (UTC)

@Sandbh: I wonder why Greenwood & Earnshaw discuss melting points then, since their book is called Chemistry of the Elements? An explanation is, of course, not far off: what controls melting points is just the strength of bonds or intermolecular forces, which goes back to the electronic structure that underpins chemistry as well. There's not really a difference between how you explain melting and boiling points and how you explain chemical reactivity on this basis: they are both reflexions of the atomic structure and both are universally considered as periodic trends.

Condensed-phase configurations are going to be mixtures of many configurations anyway and obviously don't fit your criterion of simplest sufficient complexity. Better to just consider the total occupancy of chemically active subshells, as that's the one thing that stays constant and easily explains the situation. Which supports a Lu table all over again. Double sharp (talk) 12:52, 13 April 2020 (UTC)

Triple TLDR: trying to get to the heart of the disagreement

So far as I can see, the points that Sandbh commented on reveal two major points of difference between us:

A significant argument line for Sc-Y-La appears to boil down to a supposed delayed start of the f orbital, to explain the otherwise weird deformations in trends from other blocks (Sc-Mn and Fe-Zn form double periodicities that look more like La-Eu and Gd-Yb respectively, than Ce-Gd and Tb-Lu with their weird dips at penultimate members of the family).
I assert that there is no such thing in real chemistry. Not unless you invoke a double standard that admits f involvement for Th [Rn]5f⁰6d²7s², and not for Ac [Rn]5f⁰6d¹7s² or La [Rn]4f⁰5d¹6s². Not to mention that a delayed start would also imply a delayed end, and 4f in Lu or 5f in Lr is none other than a core subshell.
Another significant argument for Sc-Y-La appears to boil down to the assertion that the group 3 metals (and the lanthanides) have chemistry most similar to groups 1 and 2, being basically trivalent versions of those metals; therefore, since Sc-Y-La gives a group-2-like trend, and Sc-Y-Lu gives a group-4-like trend, the former is to be preferred.
I note that Zr, Hf, Rf, and Th are essentially tetravalent versions of the group 1 and 2 metals, too. And we can draw analogies easily between the organometallic chemistries of Sc and Ti (where lower oxidation states are stabilised for both, and both organometallic chemistries are dominated by cyclopentadienyls). In general, we will have strongly pre-transition-like chemistry for not just the metallic s elements, but also the f elements, group 3, heavy group 4 (Zr-Rf), with heavy group 5 (Nb-Db) as a bridge to more transition-like chemistry.

As a clarification of my stand on the issue, I consider Sc-Y-La a valid piece of secondary periodicity, just like B-Al-Sc or Be-Mg-Zn; but I think that considering it primary periodicity to be reflected by the PT is inconsistent with the real principles underlying the PT, which are about idealised electronic structure, whose predicted numbers of valence electrons and types of valence subshells are retained in real chemistry. Double sharp (talk) 13:26, 13 April 2020 (UTC)

Thank you for the summary. Here's my perception.

I look for natural patterns and borderlines seen in the periodic table, as per the literature. Some of these borderlines are fuzzy. No matter; most borderlines in classification science have hard cases at the boundaries. The more important consideration is: do such dotted-lines provide an economy of description, a tool for structuring knowledge, and the possibility of leading to deeper understanding? If so there's no need to lose sleep over the hard cases.

In response, as I see it, Double sharp engages in one or more of the following:

Focuses on the hard cases at the boundaries.
Compares apples with oranges. Frex: We must focus on +2 for all metals never mind this is not the most stable oxidation state! Meanwhile, I focus on the most stable oxidation state common to as many of the metals involved as possible, which is what underpins the structure of chemistry.
Catastrophising. Frex: But if you do that, logic demands Be-Mg will have to be moved into group 12! Meanwhile I say I have no wish to take on the chemistry establishment in that matter. One step at a time. I. Group 3; II. He-Be; III. Be-Mg into group 12.
Tangentialising. That is, making irrelevant observations. Frex: Focussing on the physical aspects of double periodicity among the Ln, never mind the chemical aspects.
Flat-earthing. This encompasses ignoring, seeking to discredit, or reinterpreting my evidence.
Word-count bombardment. Double sharp's counter-responses to my evidence are generally five times as long. This is a classic sign of not having a strong response and needing to resort to multiple weak arguments and minutiae in order to shore up one's position.
Bolding text. This is a variation of word-count bombardment.

I note Double sharp's interest in the connection between idealised electronic structures and real chemistry.

When it comes to the astonishing relevance of electron affinity and orbital radius as a way of mapping real chemical relationships this is immediately dismissed, of course. Sandbh (talk) 07:22, 15 April 2020 (UTC)

I was earlier considering responding to the other points, but since I am once again being compared with flat-earthers, I see no point in doing so. I think I'll just go straight to drafting the RFC instead, since addressing any of those points will require repeating myself again and re-explaining basic logic and basic chemical facts and trends that I have already wasted too long doing over the past few months. Double sharp (talk) 09:35, 15 April 2020 (UTC)

Appendix I: MP, BP & standard reduction potentials

@Double sharp:

Too much importance is placed on gas phase configurations.

Here Mn is 3d⁵4s² and Eu is 4f⁷6s². Half-filled sub-shells all round.

We can see an associated phenomenon in the melting and boiling points (per your tables):

M	Ca	Sc	Ti	V	Cr	Mn	Fe	Co	Ni	Cu	Zn	Ga	Ge
mp (°C)	842	1541	1668	1910	1907	1246	1538	1495	1455	1085	420	30	938
bp (°C)	1484	2836	3287	3407	2482	2061	2861	2927	2730	2562	907	2400	2833

M	Ba	La	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb	Lu	Hf
mp (°C)	727	920	795	935	1024	1042	1072	826	1312	1356	1407	1461	1529	1545	824	1652	2233
bp (°C)	1633	3464	3443	3130	3074	3000	1900	1529	3000	3123	2567	2600	2868	1950	1430	3402	4603

Unlike the rest of the Ln, Eu and Yb delocalise only their two s electrons, so their MP and BP dip. The other metallic Ln delocalise three electrons.

So, due to the gas phase configurations and e.g. the MP and BP dips, people think just as 3d runs from Sc to Zn, so 4f must run from La to Yb.

Now, in aqueous solution—where real chemistry occures—Mn likes to be Mn²⁺ i.e. d⁵. And Eu likes to be Eu³⁺ i.e. d⁶. So the analogy is lost; it is rather Gd which likes to be d⁷, as Gd³⁺.

Why then does Eu²⁺ f⁷ with its half-filled sub-shell stability like to lose an electron and become Eu³⁺ f⁶? Has Eu gone mad?

No. Apparently the energy required to ionise Eu²⁺ f⁷ to Eu³⁺ f⁶ is more than offset by the gain in hydration energy.

As another example, Na could hypothetically become Na²⁺ and form NaCl². Theoretically such a compound would have a significantly larger lattice energy than NaCl. However, sodium's second ionisation energy is prohibitively large, which means it stays put in the +1 oxidation state.

So the chemistry-based analogy is Mn and Gd, with 3d going from Sc to Zn, and 4f going from Ce to Lu.

How do you see this? Sandbh (talk) 03:36, 15 April 2020 (UTC)

“

The characteristic tripositive oxidation state of the lanthanide elements is not related directly to the number of "valence electrons" outside the 4f subshell, but is the somewhat accidental result of a nearly constant small difference between large energy terms (ionization potentials on the one hand, and hydration and crystal energies on the other) which persists over an interval of fourteen atomic numbers.

”

— Glenn T. Seaborg

So it is a higher-order concern that is not directly relevant to the element's position in the table, which is based on valence orbitals. Double sharp (talk) 09:41, 15 April 2020 (UTC)

@Double sharp: Could we engage in a mutually respectful discussion to find out what is right? Not an argument about who is right.

Seaborg said he is of the view that the characteristic tripositive oxidation state of the lanthanide elements is related to a nearly constant small difference between large energy terms (ionization potentials on the one hand, and hydration and crystal energies on the other).

I said: "Apparently the energy required to ionise Eu²⁺ f⁷ to Eu³⁺ f⁶ is more than offset by the gain in hydration energy".

There appears to some truth there, or at least a commonality of observations. How do see this now? Sandbh (talk) 11:22, 15 April 2020 (UTC)

@Sandbh: Does comparing the other party to flat-earthers, as you did above, seem like something that is usually done in a mutually respectful discussion?

I agree that the stability of Eu +3 vs. +2 is related to such concerns. The I just don't think it has anything to do with the placement of elements. Well, just look at technetium and rhenium. They don't particularly like to be in the +2 oxidation state that corresponds to a d⁵ configuration either, does that mean the 4d and 5d boundaries must be shifted? Double sharp (talk) 12:11, 15 April 2020 (UTC)

@Double sharp: Comparing someone to a flat earther is not respectful. Could we hereafter engage in a mutually respectful discussion to find out what is right, or true if you will, and not an argument about who is right? That would be good, I'd expect. Sandbh (talk) 12:29, 15 April 2020 (UTC)

Looking back at the standard reduction tables I see we agreed that, "the 4d metals have gaps at Zr and Pd, but there is enough to see double periodicity is still present although weaker, as usual, for later rows." On Tc specifically we see that it has the highest potential of all the metals listed, bar Ag which we know is peculiar. For Re I know the higher oxidation states become more stable, for reasons I haven't researched. For the 5d metals +4 is the most common stable oxidation for 6 of 10 of them, so it's not clear to me what the relevance of +2 would be in this context. Nor have I looked to see if +2 potentials are available. I don't see any truth-value in your question about shifting the 4d and 5d boundaries.

There does seem to be truth in the stability of Eu +3 vs. +2 observation and explanation. It seems true that in this context there is a parallel between 3d, 4d, 4f and 5f. How am I going? Sandbh (talk) 12:47, 15 April 2020 (UTC)

@Sandbh: So you want to use +4 as the baseline state for 5d. Then I ask, how exactly are you going to determine which is the halfway element that prefers to form 5d⁵? Seems to have to be iridium with Ir⁴⁺ as a stable state, by this logic. And we even have Os⁴⁺ and Pt⁴⁺ next door to compare it with. I hope we agree that that's obviously not the correct outcome.

Well, choosing +3 as the baseline state for 4f and 5f is making the same mistake. As I've mentioned before: the important thing here is not picking the most stable state as a baseline. I pick the +2 state because these elements are usually dⁿs² and fⁿs², and that takes away the outer s electrons and lets the filling of the inner orbitals go normally. No, I don't care one bit that it's not always the most stable state. What matters is the relative stability of +3 vs. +2, which is trying to measure how much it is worth to get rid of another electron. Because basic high-school chemistry demands that reaching the halfway point should imply that +2 becomes more stable, so the M³⁺/M²⁺ potential should get a local maximum for the halfway element. (For the first two rows at least, when double periodicity is still strong enough.) That local maximum doesn't have to make it positive, it just has to make it higher than the surrounding elements. And we know from basic high-school chemistry that reaching the halfway point implies those electrons should be harder to delocalise, so the melting point should drop.

And the last point (physical properties) is why it doesn't work to say "oh, but we should take ds² as the covering shell for the lanthanides, so +3 should be the baseline to ionise away the outer s electrons, and use M⁴⁺/M³⁺ potentials". Taking melting point as an example, we know the halfway element should be a dip on the melting point trend by basic high-school chemistry. Which Eu is and Gd isn't. So that's one way we know the shell hanging up is not ds² but simply s², and thus that +2 should be our baseline for the f block too, not +3. Double sharp (talk) 14:09, 15 April 2020 (UTC)

@Double sharp: No, I don't wish to use +4 as the baseline state for 5d; I didn't say that. Rather, I observed +4 as the most stable state was common to 6 out of 10 5d metals. That's all. My line was, as you observed, that "the 4d metals have gaps at Zr and Pd, but there is enough to see double periodicity is still present although weaker, as usual, for later rows." That is to say, it becomes harder to observe the double periodicity in question. We agree this is right. We know a similar thing happens in going from 4f to 5f i.e. that double periodicity, while still present, is weaker.

We know the Ln are not usually fⁿs². We know they are usually fⁿd¹s². That is why +3 is used.

We know the high-school chemistry demand that reaching the halfway point should imply +2 becomes more stable, in a chemical property sense, is not right. We know this is because additional factors come into play, not generally taught at the high school chemistry level, namely hydration and lattice energies.

The standard reduction potential data for 3d, 4d, 4f and 5f, are right, within the limits of experimental or computational error. They show dips at Mn, Zn, Gd and Lu, Cm, and Lr. This corresponds with half-filled and filled d and f sub-shells for the cations of the metals in their most stable oxidation states. We know why, in the case of the 4f and 5f metals, there is a dip shift one place to the right.

Physically, the mp and bb trends are right. They show dips at Mn, Zn, Eu and Yb. This corresponds with half-filled and filled d and f sub-shells. Sandbh (talk) 01:33, 16 April 2020 (UTC)

@Sandbh: Your second paragraph is not correct. In the gas phase, the lanthanides are usually fⁿs²; in the condensed phase, we can't talk about such a situation because of all the hybridisation. There are no pure configurations in the condensed phase, only mixtures of many configurations, which for the lanthanides are going to generally involve both d and p orbitals. Which is exactly why they are too complicated to really use as a basis. So this is not a good justification for using +3 as the baseline, especially since all physical properties contradict it.

Your third paragraph is also not quite correct. A half-filled subshell certainly will increase the stability of +2. It may not make it the most stable state, because of course other factors such as hydration and lattice energies (which incidentally are considered at the high-school level when drawing energy cycles from Hess' law, IIRC) will be important, but it will certainly make the stability of +2 more than it was for the neighbouring elements. (Since the charges and radii are similar just comparing neighbouring elements, hydration and lattice energies are basically constant within the three-element range of interest around the putative halfway element.) And that's all that's needed to determine where the halfway mark is. Double sharp (talk) 03:44, 16 April 2020 (UTC)

Good. Yes, we know:

gas phase is fⁿs²
condensed phases are given as fⁿd¹s² or, if hybridisation is noted, fⁿ(ds)³
there can be contradictions between physical and metallic properties
chemically C is a non-metal yet physically it's electrical conductivity exceeds that of some metals
for most Ln:
- +2 does not correspond to an empty sub-shell or a half-filled sub-shell or an empty sub-shell
- +3 corresponds to an empty (ds)³ sub-shell, and that therefore +3 is preferred
- +3 corresponds to Gd f⁷ and Lu f¹⁴
for Eu and Yb:
- +3 further requires the "breaking" of the ordinarily stable half-full f⁷ or full f¹⁴ sub-shell
- the gain in hydration or lattice energy more than offsets the energy required to break the half-full (Eu) or full (Yb) sub-shell
- +3 Eu is f⁶ and +3 Yb is f¹³
- +3 is preferred
chemically, Gd³⁺ f⁷ denotes the halfway mark.

--- Sandbh (talk) 05:17, 16 April 2020 (UTC)

@Sandbh: Condensed phases are generally not so, as already shown in the Gschneidner article from before (doi:10.1016/0022-5088(71)90184-6). Instead they usually have non-integer occupancies for all of the 4f, 5d, 6s, and 6p subshells. There are about 3 electrons delocalised per metal, except for Eu and Yb which delocalise about 2; that's all we can say. It's certainly not enough to say that +3 should be our basic oxidation state because mostly in the transition metals there are more than 2 electrons delocalised per metal, too. The situation is more like what Wittig mentions in his article (doi:10.1007/BFb0108579):

“

In order to account for the anomalously high T_c and the other anomalous physical properties, such as the low Debye temperature and the low melting point (cf. Fig. 4), we once more propose that La should not be considered to be a plain (6s 5d)³ metal like Sc, Y, and Lu. We believe that it has an appreciable 4f-band occupation which must be responsible for the very high T_c at all pressures. We can write, perhaps, the electronic configuration in the metal in the form (6s 5d)^3-ε 4f^ε, the term 4f^ε denoting an at present undeterminable, however real and sizeable fraction of an electron, occupying the 4f band. We do not expect that pressure will change the term 4f^ε fundamentally, since we think it represents the screening charge of a 4f scattering resonance safeguarded deep in the interior of the lanthanum ion core (in agreement with our picture for Ce). It should be, therefore, a natural consequence of this model that the lanthanum ion introduces its inner 4f-scattering resonance into almost any metallic matrix, since the core potential should remain fairly unperturbed by the nature of the host. Practically, it will not always be easy to see the 4f virtual bound state on the La atom, since it has, in addition, a strong d resonance. Below we look briefly at three systems whose behavior seems to support our suggestion that a 4f resonance accompanies the La atom like a "name tag". It should be mentioned here that a similar model for the electronic structure of lanthanum (and the other rare earth metals) has been recently proposed by Gschneidner [41].

”

— Wittig, J. (1973). The pressure variable in solid state physics: What about 4f-band superconductors? Festkörperprobleme 13, 375–396. doi:10.1007/bfb0108579

He then goes on to mention some smoking guns, in which as usual La and Ce (preceding the collapse) show the largest 4f involvements. 4f involvement for every lanthanide is a non-integer, betraying some f contribution to the band (except for Lu where it is 0). Looking at the graphs in Gschneider's article, it seems plain that the only sensible way to consider La-Yb is simply as (fdsp)ⁿ⁺² elements in the condensed phase (because there are both localised and delocalised f electrons). So even if we insist on complicated condensed-phase configurations that give trouble elsewhere in the table, we still don't have fⁿds², because the f electron count is also a non-integer (crudely speaking, we can think about the interplay between promoting and not promoting an f electron, which is exactly my old argument about 4f^n-1 vs 4fⁿ being something that exists only for La through Yb). The notional order of subshell filling, with 4f beginning at La from the Madelung rule, and being a core subshell at Lu, is supported by the evidence; the case for the +3 state simply doesn't work because in the condensed phase you don't have only the d and s electrons delocalised, but contributions from 4f, 5d, 6s, and 6p. It's fundamentally clear that the f electron involvement is taking a dive at Eu and Yb, which is the smoking gun for the half- or fully-filled f subshell that resists delocalising its electrons.

Physical and chemical properties in this case are both relevant, because basic high-school chemistry implies the same effect is controlling both trends here: the occupancy of the 4f shell, and its resistance to delocalisation when a stable half- or fully-filled occupancy is reached. That explains the reduction potential trend just as surely as it explains the melting point trend. Double sharp (talk) 05:40, 16 April 2020 (UTC)

Jorgensen

P.S. Jørgensen agrees with me, BTW, though of course he goes into some deep theory that I don't actually understand ^_^ (doi:10.1524/ract.1983.32.13.1):

“

The relations between atomic spectroscopy and chemistry are also quite subtle. A major advance for the hypothesis that the 5f shell starts filling very soon after thorium was the assignment in 1946 of the ground state of the uranium atom (this, of course, has only very remote relations to the electronic structure of metallic uranium) to the configuration [86] 5f³6d7s². Contrary to the ideas of HUND [3] this fact does not make U(III) the most frequent oxidation state (any more than [54] 4f⁴6s² of the neodymium ground state [12] prevents Nd(II) from being far rarer than Nd(III), whereas atomic plutonium [86] 5f⁶7s² and samarium [54] 4f⁶6s² are now known to be isologous). Seen in hindsight, there have only been two significant arguments advanced before 1940 for the 5f group already starting among the known elements. GOLDSCHMIDT suggested from the stable fluorite-type M(IV) oxides (now known of nine M up to CfO₂) that thorium is followed by a series of predominantly quadrivalent thorides; and EPHRAIM [18] pointed out that the narrow absorption bands of green U(IV) salts indicate 5f² in analogy to 4f² of Pr(III). ...

Such evidence [J-levels of 4f and 5f], as well as calculated 4f and 5f radial functions, suggest that the electron affinity of the partly filled 4f shell is much smaller than the ionization energy. As first pointed out by CONNICK [31], this is the major reason [5, 32] why the lanthanides strongly prefer a constant oxidation state. There is no direct relation [2, 6] between the electron configuration of the monatomic entities containing 4f electrons, and the chemical fact that the preferred oxidation state is M(III). Going from the 3d to the 4d group [33,34] there is the same tendency as going from the 4f to the 5f group. In the beginning of the 4d and 5f groups, the oxidation states are more varying and, on the average, higher, as known from Mo(VI), Tc(VII), Ru(VIII) or from Pa(V), U(VI) and (the strongly oxidizing) Np(VII), whereas the last elements of the group are less readily oxidized. Much like Ag(II) is less stable than Cu(II), 5f¹³ Md(II) is less reducing than 4f¹³ Tm(II), and nobelium(II) is at least as difficult to oxidize to the ytterbium-homolog 5f¹³ No(III) as cerium(III) to Ce(IV), making Ζ = 102 much more similar to radium than to actinium [35].

The smooth variation of oxidizing character of M(III) or M(IV) going from zero to 13 electrons in the 4f or 5f shell is modified by the position of the lowest J-level below the average energy of the partly filled shell. In the 4f group representing a good approximation to Russell-Saunders coupling for the lower levels [22] this additional effect is proportional to parameters of interelectronic repulsion and expressed in the refined spin-pairing energy description originally introduced [36—38] for rationalizing electron transfer spectra. However, the same treatment can be applied to standard oxidation potentials of aqua ions [5,39] and to photo-electron spectra of metallic lanthanides and their solid compounds [32,40]. Taking the deviations from Russell-Saunders coupling into account, the spin-pairing energy theory also works in the 5f group [41]. It remains true that the lanthanides have a few characteristics not possessed by the 5f group. Thus, 4f⁷ europium(II) is more difficult to oxidize than 4f¹⁴ ytterbium(II) whereas it is very well-known that 3d⁵ Mn(II) is easier to oxidize than 3d¹⁰ Zn(II), and 5f⁷ Am (II) (now known in black but non-metallic AmI₂) much easier to oxidize than 5f¹⁴ No(II).

This explanation of varying standard oxidation potentials has renewed interest in the general question of hydration energies of gaseous ions [32, 33,42,43] allowing a certain understanding of which oxidation states are stable, at least in the form of aqua ions [44,45].

”

Just look at those analogies: Tm and Md compared with Cu and Ag (penultimate elements of the block), Eu and Am compared with Mn (halfway elements), and Yb and No compared with Zn (ultimate elements). Lu and Lr are clearly not f elements! As I've been saying, lawrencium's strong preference for the +3 state doesn't make any sense tacked on to the late actinide trend, where each element is more and more willing to avoid being oxidised that far than the previous one. Double sharp (talk) 05:48, 17 April 2020 (UTC)

@Double sharp: That is a lot to read and will take me a while to assess. Sandbh (talk) 08:02, 17 April 2020 (UTC)

@Sandbh: Well, did you get to it? It's a quote from the literature directly supporting what I say about analogies: Eu and Yb are analogous to Mn and Zn, not Cr and Cu. Double sharp (talk) 05:59, 3 May 2020 (UTC)

@Double sharp: First impression:

Per usual in an article of this kind only 14 rather than 15 f-block elements are in scope, making it hard to see what's going on at either end
- The fact that explicitly only 4f⁰ through 4f¹³ (La to Yb, in +3 compounds) are in scope strongly suggests that there is some reason why Lu is excluded. And one can easily see how the comparisons match perfectly with Yb at the end of the block and are nonsensical with Lu at the end of the block. Double sharp (talk) 12:23, 4 May 2020 (UTC)
Jørgensen:
- doesn't call them analogies; instead, he makes comparisons.
  - You may call them what you like: the fact remains that these are the examples he is using. Double sharp (talk) 12:23, 4 May 2020 (UTC)
- doesn't refer to Cu and Ag as the penultimate members of the block, presumably so as to not necessarily rope in Tm and Md under the same rubric.
  - Or maybe he thinks it's obvious. His statement that the "last members of the group [i.e. block] are less readily oxidized" on p. 2 is completely correct if you think the block ends at Yb-No and is completely wrong for Lu-Lr. Which suggests strongly that he doesn't think Lu and Lr are f elements. His Madelung-rule order for gaseous M²⁺ through M⁶⁺ ions on p. 1 even confirms it: starting at Li²⁺ with 1s, his shell filling order makes no provision for any idea of a 5d or 6d electron hanging up, and clearly implies a La-Yb 4f block and an Ac-No 5f block. Double sharp (talk) 12:23, 4 May 2020 (UTC)
mentions going from zero to 13 electrons in the 4f or 5f shell, which implies e.g. La to Yb
That's fine, but he doesn't consider the applicability of Ce to Lu.
- And anyone can see why: because the comparisons simply don't work if you do that. On page 2 he mentions, while talking about Pr(III) through Yb(III), "broad and intense electron transfer bands [21] due to one (or more) reducing ligands loosing an electron to a low-lying, empty or partly filled, d or f shell of an oxidizing transition-group ion". Lu cannot possibly do that; its 4f shell is always core-like and full. Whereas I've already given sources for La(III) doing the same thing (so, of course, Ce(III) certainly should be able to do it too). Double sharp (talk) 12:23, 4 May 2020 (UTC)

I'll have another look at this. Sandbh (talk) 11:42, 4 May 2020 (UTC)

Jørgensen (1988) has some good lines, doi:10.1016/S0168-1273(88)11007-6:

"Lob (1966) found the 4f → 5d transition in all M(III) from Ce to Lu (except M = Pm) in very low concentration in CaF₂, being transparent beyond 80 000 cm^-1 (or 10 eV, or 125 nm) and found excellent agreement with the refined spin-pairing energy treatment, as discussed in sections 3.3 and 3.5. McClure and Kiss (1963) had previously obtained comparable results for M(II) from La(II) to Yb(II) in CaF₂ (again excepting M = Pm). However, there are various problems for M = La, Ce, Gd and Tb. Apparently, lanthanum is a system with one 5d electron (as corroborated by gaseous La⁺² with this ground state followed by 4f at 7195 cm^-1 higher energy) and McClure and Kiss (1963) argued that cerium(II) in fluorite has 4f5d ground configuration, whereas gaseous Ce⁺² has the first J-level of 4f5d situated at 3277cm^-1 above the ground state belonging to 4f² "

"If there is a common z for the 3d group, like Ln(III), it is M(II) known from Sc to Zn, and V(II) to Zn(II) are all known as aqua ions." ^_^ "Redeemed"
- If there is. That is, it's difficult to find one in the first place. And just try for 4d or 5d. Double sharp (talk) 15:01, 4 May 2020 (UTC)

"The gaseous atom of thorium has the lowest configuration [Rn]6d²7s² and is as good a homolog to zirconium [Kr]4d²5s² as lanthanum [Xe]5d6s² is to scandium [Ar]3d4s²." ^_^ "Redeemed"
- @Sandbh: That's a redemption for me, not for you. He's saying that Th makes as much sense in group 4 as La in group 3: Zr-Th makes as much sense as Sc-La. Double sharp (talk) 15:01, 4 May 2020 (UTC)

"It is evident from the neutral atoms reviewed that 5f electrons play as minor a role in thorium as 4f do in lanthanum, but that 5f electrons are at least as important in uranium as in cerium."
- That's a fruit in my bin. ;) Allowing Th in the f-block and not allowing in La is a double standard. Double sharp (talk) 15:01, 4 May 2020 (UTC)

"The smaller ionic radius of zinc{II) compared to calcium(II), and the highly different chemistry, was ascribed by Goldschmidt to 3d-group contraction accompanied with 'imperfect screening'. In a sense, the 10 additional charges on the zinc nucleus 'shine through' the 3d shell, and if the argument is pursued to its (probably absurd) conclusion, the comparable ionic radii of Sc(III) and Zn(II) indicate that, on the average, the U(r) has an added contribution 1/r in zinc. The smaller ionic radius of Lu(III) compared with La(III) should be due to a similar 'imperfect screening' of the 14 additional charges on the lutetium nucleus. However, there has been some argumentation that part of the lanthanide contraction originates in relativistic effect. ^_^ "Redeemed"
- I agree that this is imperfect screening effect. Just like Hf(IV) or Ta(V), it's imperfect screening by corelike 4f electrons. So it doesn't redeem your point, as it works well for both of us. If I understand correctly, you'd like to ascribe Lu's better similarity to Y compared to La's just to second-order imperfect screening, whereas I claim that this imperfect screening is first-order. This is only resolved by looking at where the 4f activity starts. Which is lanthanum. Double sharp (talk) 15:01, 4 May 2020 (UTC)

"There is a recent trend (Fernelius 1986) to make rectangular versions with 18 columns, and though this is certainly better than 8, it may seem a little tough to put 15 'meta-elements' on the position of lanthanum, and even much more so to let Ac, Th, Pa, U, Np ..... share the same bed."

"There is not a tremendous difference between the chemical similarity of yttrium and lanthanum; or between sulfur and selenium… ^_^ "Redeemed"
- I never disputed that. If you just do comparative chemistry, Y-La looks all right. As does Y-Lu. As does Y-Gd. As does Y-Ho. So this is not really saying much. Also see page 266 for why it is not saying much: "When uranium was promoted to be a 5f element, it was also clear that some striking chemical differences occur between W and U, but after all, it was not worse than between tin and lead, or between antimony and bismuth". You can have strong chemical resemblances between two elements that don't belong in the same group. Sometimes it even looks better at first glance than the resemblances between the elements that are supposed to be in the same group. Just compare the pairs Mg-Zn and Mg-Ca. Double sharp (talk) 15:01, 4 May 2020 (UTC)

"As far as solid-state chemistry goes, the closed-shell cerium(IV) is not strikingly different from the slightly larger thorium(IV) or the somewhat smaller tin(IV)…"

--- Sandbh (talk) 12:51, 4 May 2020 (UTC)

Meanwhile, here are two of my favourite lines. I have taken the liberty of replacing his [54] with the more common [Xe]:

"The two major reasons why this series intended for gaseous atoms strongly bewilders chemists is that undue emphasis is made on irrelevant irregularities (such as the chromium, rhodium, palladium .... , atoms) and that the lowest level of two different configurations, such as [Xe]4f⁹6s² and [Xe]4f⁸5d¹6s² are only separated by 285 cm⁻¹ in the terbium atom, much less than 1% of the spreading of J-levels of each of the two configurations, and quite negligible for chemical purposes."

So, my attacks on the relevance ground-state electron configurations are completely supported by the literature. ;)

"The paradoxical side of 4f electrons is that they occupy an inner shell, but that they occur in compounds, having I(4f) comparable to the valence-shell MO."

As we can see, the idea that 4f is an inner orbital that is not being used much for chemistry is totally false. Double sharp (talk) 15:13, 4 May 2020 (UTC)

Appendix II: What is right (as we've agreed)

"Discussions are better than arguments, because an argument is to find out who is right, and a discussion is to find what is right."

Here's what we have agreed is right.

Philosophical
Chemistry is not a heap of distinct conceptions standing apart alone, but rather interconnected system of conceptions based on experimental facts.

An La table creates an irregularity that is absent from a Lu table.

Classification science
There are no sharp boundaries.

Electron configurations
We don't place Sc under Al due to the mismatch in configurations.

The 4f electrons in Lu are core like.

La clearly has more f character than Lu.

The uncontroversial nine 5d elements (Hf-Hg) all have core-like 4f electrons, which is something Lu has but La doesn't.

Sc and Y don't have any significant f character, which is something they have in common with Lu but not La.

I have added the ~~two~~ [one] indented points above, since I think ~~they are~~ it is probably uncontroversial; if you disagree ~~with them~~, or think ~~they're~~ [it's] not very important, we can discuss by commenting as I did on the points you raise that I disagreed with. Double sharp (talk) 05:16, 17 April 2020 (UTC)

@Double sharp: I don't agree with the first bullet. Still thinking about the second. Sandbh (talk) 07:56, 17 April 2020 (UTC)

@Sandbh: OK. For the purposes of understanding our disagreement, what part of my first bullet do you disagree with? I guess that Sc and Y have no significant f character should really be uncontroversial, so is it that you dispute that Lu has no significant f character, or that you consider the f character of La insignificant, or both? Double sharp (talk) 10:11, 17 April 2020 (UTC)

@Double sharp: I agree Sc and Y have no significant f character. I disagree this is something they have in common with Lu.

I'm OK with the second statement, and have adjusted its placement accordingly. Sandbh (talk) 03:33, 19 April 2020 (UTC)

@Sandbh: Well, we have agreed that the 4f electrons in Lu are core like. As they are for Hf through Hg. That means that the f electrons have no direct impact on chemistry, which is what I mean by "no significant f character". For sure there are incomplete shielding effects, but the f electrons are part of the core here. So, would you be fine with this if I rephrased it as "Sc and Y do not use the f orbitals as valence orbitals, which is something they have in common with Lu but not La"? Double sharp (talk) 04:38, 19 April 2020 (UTC)

@Double sharp: Yes, nearly. I'd like to make it clear that La has no 4f valence electrons of its own, as the concept of valence electrons is ordinarily understood. Sandbh (talk) 07:37, 22 April 2020 (UTC)

@Sandbh: OK, so this sheds a light on what the difference between our approaches is. See, the trouble is that I think this is unilluminating. Thorium has no 5f valence electron on its own, as ordinarily understood (looking at ground-state configurations). Yet it is not in serious doubt as a 5f element because of its obvious 5f character in chemical environments. So I would like to propose instead the following:

A valence electron is an outer shell electron of an atom, that can participate in the formation of a chemical bond

None of Sc, Y, La, and Lu have a valence f electron in the ground state

La has low-lying 4f orbitals that may be occupied in chemical environments, by partial hybridization or via ligand contribution (citations: here and doi:10.1103/PhysRevB.66.045106) which is something it has in common with Ce-Yb and not with Sc, Y, and Lu

This concept is more useful for transition and especially inner transition elements, with many configurations close in energy such that changes in the chemical environment can alter which one is preferred.

In this context, Th has no valence f electron in the ground state but shows some 5f chemistry in its Th³⁺ configuration

+3 is not a major oxidation state for thorium, which is almost always +4. So 5f occupancy for thorium will almost always be via partial hybridization and ligand contribution as well.

Therefore, we have a similar mismatch going from Y to La as the one going from Al to Sc, taking more relevant chemically active subshells rather than naïvely just using ground-state configurations.

That would supplant the two listed below, as they are saying the same thing. Double sharp (talk) 07:56, 22 April 2020 (UTC)

@Double sharp: I've edited and rendered the ones I agree with in fixed space font. The last one about a similar mismatch needs more work, since it jumbles the difference between Y-La as d elements whereas Al is p and Sc d. Sandbh (talk) 00:13, 23 April 2020 (UTC)

@Sandbh: It is absolutely accurate by the more relevant measure of chemically active subshells rather than naïvely just using ground-state configurations, as I've just explicitly added. Y is d, La is f. Double sharp (talk) 03:12, 23 April 2020 (UTC)

The important thing for real chemistry is not specific single configurations in isolation, but all configurations in totality that are accessible in isolation at reasonably low excitation energies: for these may become the ground state in specific chemical environments, and which one gets that honour will depend on which chemical environment it is.

~~Such configurations for La include those with 4f occupancy, so the same mismatch between Al and Sc happens from Y to La.~~

~~Added two more. Double sharp (talk) 11:56, 21 April 2020 (UTC)~~

Ionic to covalent
Ionic vs. covalent is gradual, from covalent to polar covalent to mildly ionic to strongly ionic, depending on the difference of electronegativity between the two elements.

Groups 3-4
Group 3 has predominantly main-group tendencies.

The same is true of Zr, Hf, and Rf in group 4.

Added this statement: same disclaimer as above. Double sharp (talk) 04:39, 19 April 2020 (UTC)

Ti is the first to show very serious transition properties that cannot be denied.

These transition properties come from the lower oxidation state +3, and titanium compounds in this state have more ionic character than in those in the +4 state.

Incipient transition metal properties can be seen in Ca, Ba, and Sr; Sc, Y, La or Lu; and Zr and Hf.

Lanthanides and transition metals
Lu is more similar to the other lanthanides than the transition metals. And so is La. Lu is closer to the TMs than La.

--- Sandbh (talk) 00:06, 16 April 2020 (UTC)

Appendix III: Thorium notes

This source gives the gaseous configurations of Th²⁺ as 5f¹6d¹ and Th³⁺ as 5^f1. I wonder what the configuration of Th is in its divalent compounds other than electrides like gold-coloured ThI₂? Wiberg (p. 1720) says Th⁺² is found in dilute solid solutions of the halides AnX₂ in alkaline earth metal halides MX₂, whatever that means.

This article refers to the formal existence of Th²⁺ and Th³⁺ complexes.

This article says "…it has been demonstrated that relativistic effects, along with the changing actinide orbital energies are responsible for the change from the bent cis- (d-character) to the linear trans- (f-character) geometry in the dioxide ions of Th and U, respectively". Unfortunately they cite the wrong source, and the source I think they meant to cite says nothing about ThO₂⁺.

@Sandbh: I guess they meant UO₂⁺ and isoelectronic ThO₂^-. Droog Andrey (talk) 06:10, 18 April 2020 (UTC)

Hmm. This book extract says ThO₂^- was expected to have the same structure as the ThO₂ molecule, which is bent: Th=O = 122°. This article reports a bent geometry doi:10.1063/1.5030142. Sandbh (talk) 04:07, 19 April 2020 (UTC)

Then again, this article refers to thermodynamic evidence for the participation of f orbitals in the bonding of ThO₂⁺. The same article says, "the structure obtained for ThO2+ is linear." And, "Although significant, the magnitude of the 5f orbital contribution to the OTh⁺-O bond dissociation energy is relatively weak, accounting for ∼13% of the measured BDE." Sandbh (talk) 04:25, 19 April 2020 (UTC)

@Droog Andrey and Double sharp: As above. Sandbh (talk) 04:28, 19 April 2020 (UTC)

--- Sandbh (talk) 02:41, 17 April 2020 (UTC)

Yes, thorium gets into the f block because it obviously displays f character in the metal and its compounds. But so does lanthanum, and probably actinium too (although there is little information there, the energies involved indicate that it's very likely; the promotion 7s→5f for Ac²⁺ is only 2.9 eV). Double sharp (talk) 02:51, 17 April 2020 (UTC)

Appendx IIIb: Actinium notes

Well, there seems to be 5f6d hybridisation in Ac metal about 10 eV above the Fermi level, but it seems to be negligible at the Fermi level where mostly d states contribute. (doi:10.1002/pssb.201451569). It seems that 5f in Ac has the same "pre-collapse" situation as we see in the lanthanides, noting doi:10.1103/PhysRevB.14.3265:

“

As noted earlier, the ξ entry (atomic correlation energy difference) for actinium in Table II is conspicuous because it is negative, implying that correlation effects are greater in the configuration with no, as opposed to one, 5f electron. There is an explanation for this in our HHF results. The 5f orbital calculated for a free actinium atom (5f6d7s configuration) is markedly distinct from the 5f orbitals of Th and the other actinides; most of its density is outside the f electron centripetal barrier and the 6d and 7s shells. Since the orbital is quite diffuse, little correlation is associated with the 5f electron, and ξ reverses sign. It is our intention to discuss other implications of this barrier-penetration behavior elsewhere.

”

Of course, these are all calculations, since the actual investigation of actinium metal would pose significant experimental challenges. The melting point arguments of Gschneidner would not work very well here, since no one seems to be terribly sure what the actual melting point of Ac is: Greenwood and Earnshaw give 817 °C, CRC and the Lange handbook give 1050 °C, while The Chemistry of the Actinide and Transactinide Elements gives 1227 °C. So I guess it is asking too much to expect a smoking gun, but the situation seems cautiously promising. Double sharp (talk) 05:35, 17 April 2020 (UTC)

@Droog Andrey: Do you have any sources on Ac? Double sharp (talk) 07:35, 17 April 2020 (UTC)

doi:10.1021/jp500215z may be of some interest, even if I don't really understand it. At least, they seem to be taking into account the state [Rn]5f¹ for Ac²⁺, and note that there may be cases when the high-lying [Rn]5f¹7s² state of neutral Ac may be important. So, I think this counts as a cautious "yes" to 5f involvement even for Ac, even if of course the delayed collapse means that 5f is pretty diffuse there.

And of course, 4f in La is certainly more than 5f in Ac, so if the latter seems to be pretty likely – well, we already have lots of sources for the former. It's certainly not peripheral, but a significant part of the chemistry of those elements. Much greater than the role of 4f and 5f in Lu and Lr respectively, which are respectively zero and zero. Double sharp (talk) 07:08, 21 April 2020 (UTC)

Appendix IV: Quarter-periodicity

G&E graph

On the topic of double periodicity I stumbled upon a mention of quarter- and three-quarter periodicity in G&E.

They plot the third IE of the Ln and say, "The sudden falls at Gd and Lu reflect the ease with which it is possible to remove the single electrons in excess of the stable 4f⁷ and 4f¹⁴ configurations." (p. 1235)

They add, "Explanations have been given for the smaller irregularities at the quarter- and three-quarter-shell stages, but require a careful consideration of isoelectronic repulsion, as well as exchange energy terms.^{(doi:10.1016/S0065-2792(08)60038-2)}"

I’ve added their plot here. Looking closely at where the quarter and three-quarter irregularities occur, the following pattern occurs.

Ce-xx-Pm-xx-Gd
1     4     7

Tb-xx-Er-xx-Lu
8     11    14

Here xx = two intervening Ln. The numbers under each set = the # of 4f electrons in the corresponding Ln³⁺ cation.

I’ve read elsewhere about such quarter- and three-quarter periodicity but never paid any attention.

I’ll have to read more now.

The 132 pp [!] reference given by G&E includes charts for other Ln properties showing the same pattern (pp. 25; 86; 96; 99; 104).

The graph is pleasing. --- Sandbh (talk) 02:53, 19 April 2020 (UTC)

@Sandbh: Everyone can see that the graph is more regular if you consider La–Eu and Gd–Yb to be the tranches. Greenwood and Earnshaw are right: the sudden fall at Gd reflects that it is one electron above the half-filled 4f shell that really occurs at Eu. Same thing going on with the fall in 3d at Fe. And the same for every property plotted on the magnificent p. 86 in that paper.

@Double sharp: I can't see how the graph is more regular if you consider La–Eu and Gd–Yb to be the tranches. That plot from p. 86 is annoying because Lu got left off. I've roughly added Lu on. The dips at Pm and Er are easily seen. Sandbh (talk) 05:10, 19 April 2020 (UTC)

@Sandbh: It's absolutely obvious. That way the huge dip is not part of a tranche, but separates the two tranches, as is expected once we get halfway.

The fact that Lu got left off in fact has a very good reason: since these properties involve divalent lanthanides, Lu does not make sense as part of the pattern as ionising it to +2 still leaves it above the 4f¹⁴ configuration. Double sharp (talk) 05:12, 19 April 2020 (UTC)

@Double sharp: OK. Let's discuss what is true from the chart. I see the highest line is the third ionisation energy. That is, Ln²⁺ to Ln³⁺. That will be relevant for La to Lu. What's left behind is f⁰ in La to f¹⁴ in Lu. That's a good start. Your turn. Sandbh (talk) 06:20, 19 April 2020 (UTC)

@Sandbh: No, it is only relevant for La to Yb. In almost all of these cases, we are ionising fⁿ⁺¹ to fⁿ. For La and Gd we are not, because the ground states of La²⁺ and Gd²⁺ are 5d and 4f⁷5d; however, the "correct" configurations are not far up (La²⁺ 4f is at 0.8881 eV, Gd²⁺ 4f⁸ is at 0.295 eV), and chemical environments can easily provide this energy. Comparing the difference between I₃ and I₃′ on the graph (that is due to this) shows that it does not do much violence to the final result.

Now, for Lu, there's no possibility of 4f¹⁵, even very high up, because an f shell cannot hold that many electrons. It is clearly something totally different. And Johnson correctly omitted it. Everything on the chart that Johnson presented (i.e., without the artificial addition of Lu that isn't comparable, and the addition of Ce-Gd and Tb-Lu tranches) is true; I simply disagree with your interpretation of it. Double sharp (talk) 06:29, 19 April 2020 (UTC)

@Double sharp: So, is it true the highest line is for the 3rd IE? And what is I₃′? Sandbh (talk) 23:35, 19 April 2020 (UTC)

@Sandbh: If you read the article that you cite, all those questions are answered: on p. 83 it is quite clearly stated that I₃′ denotes "a third ionization energy of the metal where the prime indicates that the electron is lost from a dipositive ion of configuration [Xe]4fⁿ⁺¹. Unusually careful specification of the configurations of the ions is necessary because in one or two cases which are considered in more detail later, the ground-state configurations of M²⁺ ions are not of the type [Xe]4fⁿ⁺¹." Whereas the highest line I₃ refers to "ionizations in which the ions are in their ground-state configurations". This matches I₃′ for all 4f elements, except La and Gd. (And not Lu, for which I₃′ makes no sense.) And chemical environments will easily change the ground state configuration, so that La and Gd are not even serious exceptions. Double sharp (talk) 02:51, 20 April 2020 (UTC)

@Double sharp: We know it is true that:

A discrete double periodicity pattern involving Ce-xx-Pm--xx-Gd, and Tb-xx-Er-xx-Lu is seen for at least five properties including 3rd ionisation energy. Sandbh (talk) 08:10, 22 April 2020 (UTC)

@Sandbh: I dispute this. The pattern is clearly more regular as La-xx-Nd-xx-Eu, Gd-xx-Ho-xx-Yb. This way, the huge drop Eu-Gd is placed between the two tranches, as should happen once the half-filled shell is passed (just like Sc-Mn, Fe-Zn). Quarter-periodicity is better observed this way, as for all those properties, we can see that the value for Nd is almost exactly the average of those of the pairs Pr-Pm, Ce-Sm, and La-Eu; and we can see that the value for Ho is almost exactly the average of those of the pairs Dy-Er, Tb-Tm, and Gd-Yb. All of this is lost in Ce-Gd / Tb-Lu tranches. Double sharp (talk) 08:13, 22 April 2020 (UTC)

@Double sharp: We know it is true that:

For G&E,the points of interest were "the smaller irregularities" (rather than "regularities")
Since Gd²⁺ has one electron above a half-filled 4f sub-shell, ditto Lu²⁺ with its full 4f sub-shell, we expect and observe dips or irregularities at Gd and Lu
In each tranche of Ce-Gd, and Tb to Lu, we can observe continuous bent wing formations, five Ln apiece, running from Pr-Eu, and from Dy-Yb, with no double ups, thus: Ce*Pr^Eu*Gd; and Tb*Dy^Yb*Lu
The axes of these bent wings are the quarter- and three-quarter irregularities originating at Pm and Er,

--- Sandbh (talk) 11:28, 22 April 2020 (UTC)

@Sandbh: The second point is exactly why the tranches should start at La and Gd. Just look at the 3d row: Fe²⁺ has one electron above a half-filled 3d sub-shell, and therefore it's the first element of the second tranche. The first tranche already finished at the previous element with Mn²⁺ 3d⁵. Similarly, the first 4f tranche should end at Eu²⁺ 4f⁷.

@Double sharp: We know:

3d	4f
A half-filled 3d sub-shell (d⁵) is attractive	A half-filled 4f sub-shell (f⁷) is attractive
The most stable oxidation state for: Mn is +2 i.e. d⁵ Fe is +3 i.e. d⁵ Zn is +2 i.e. d¹⁰ Cu is not impartial to +1 since this gives it d¹⁰.	The most stable oxidation state for the Ln is +3 Gd³⁺ is f⁷ and reluctant to be reduced to Gd Eu is also partial to Eu²⁺ since it attains f⁷ Even Sm is classically partial to Sm⁺² since this gets it closer to f⁷ Tb is also partial to Tb⁴⁺ since it likewise attains f⁷ Lu³⁺ is f¹⁴ and reluctant to be reduced to Lu Yb is partial to +2 since it attains f¹⁴
The first tranche thus finishes at Mn, as you say, which is position 5 of 10	Analogously the first tranche thus finishes at Gd, which is position 7 of 14

--- Sandbh (talk) 07:01, 26 April 2020 (UTC)

@Sandbh: You're still making the mistake of trying to use the most stable oxidation state as a baseline. By similar logic we will end up with +4 for 5d. Then we will find that Ir⁴⁺ is pretty stable and 5d⁵, rationalise that Os⁴⁺ and Pt⁴⁺ are stabilised by their proximity to that, and come out with the two tranches Ta-Ir and Pt-Pb. So, you cannot do this. The baseline state must be +2, because stabilisation of +2 corresponds to reluctance to dip into the characteristic subshell. Any higher oxidation states require doing that, +2 only needs to remove the s electrons. We see that at Mn and Zn in 3d, just as we see it at Eu and Yb in 4f, so those are the meaningful analogies. Double sharp (talk) 09:20, 26 April 2020 (UTC)

P.S. And even if we get into the not really relevant quagmire of the most stable oxidation state: I just remind that Eu²⁺ is only oxidised by water and oxygen slowly. (It can stay as it is for weeks, see Ronald Rich's Inorganic Reactions in Water, p. 54.) Double sharp (talk) 03:03, 29 April 2020 (UTC)

@Double sharp: We know:

much of chemistry is based on comparing the elements in their preferred oxidation states
the d-metals, where feasible, like to attain d⁰ d⁵ or d¹⁰
- the 4d metals Y-Tc like d⁰; Ru likes d⁵; and Ag-Cd like d¹⁰
- the 5d metals La-Re like d⁰; Ir likes d⁵; and (Au)-Hg like d¹⁰
- here we can see the tranches Y-Tc and Ru-Cd; and La-Re; and Os-Hg (for Os, it is odd to see that the trichloride is the most stable of the Os halides, or perhaps not so given the resulting d⁵ configuration, but why then is +4 the most stable oxidation state?)
Ce-Lu, where feasible, are drawn to f¹ f⁷ or f¹⁴, with some interest around f⁴ and f¹¹.

--- Sandbh (talk) 07:17, 29 April 2020 (UTC)

@Sandbh: But preferred oxidation states are not relevant for determining placement in the periodic table anymore. Just witness the difficulty Mendeleev had with the d block elements, with a "group VIII" that had literally two elements in it known to reach the +8 state (Ru and Os). What matters is the number and type of valence electrons and vacancies. Why is it so hard to understand that we have progressed past what Mendeleev could use? You have no problems appealing to electronic periodic tables to refute Be-Mg-Zn!

The d metals, in fact, have a bewildering variety of common and stable oxidation states, often differing by one oxidation unit, (for crying out loud, this is standard high-school chemistry). Half-filled and fully-filled subshell concerns have low relevance here; they are strongest for the 3d row, and are quite weak later. They only come into play when the oxidation state is forced to remain constant, which is the only way you can find them mostly. So, you need to ionise just the outer s² (force constant +2 state for everybody), and then the filling reveals itself: Sc-Mn d¹-d⁵, Fe-Zn d⁶-d¹⁰, Y-Tc d¹-d⁵, Ru-Cd d⁶-d¹⁰. (No, I don't care one bit that ground-state gaseous Ru is [Kr]4d⁷5s¹. What matters is getting rid of the outer s subshell, with low-lying excited states being completely fair game.) It's just the same in the f block: La-Eu f¹-f⁷, Gd-Yb f⁸-f¹⁴, Ac-Am f¹-f⁷, Cm-No f⁸-f¹⁴. Double sharp (talk) 08:29, 29 April 2020 (UTC)

If you insist on irregularities, then Droog Andrey has correctly identified that changes in slope happen at multiple places: within the La-Eu tranche they happen at Pr and Pm, within the Gd-Yb tranche they happen at Dy and Er. (Of course, using La-Eu and Gd-Yb tranches instead of artificial Ce-Gd and Tb-Lu ones mean there is one less slope change within a tranche). Those are more like 1/6-1/3-2/3-5/6 than 1/4-3/4, since there's then two breakpoints per half. Double sharp (talk) 13:06, 22 April 2020 (UTC)

@Double sharp: I haven't insisted on irregularities. Rather, I noted those mentioned by G&E. Sandbh (talk) 07:01, 26 April 2020 (UTC)

@Sandbh: And what irregularities? Let's see what G&E really say:

“

Explanations have been given for the smaller irregularities at the quarter- and three-quarter-shell stages, but require a careful consideration of interelectronic repulsion, as well as exchange energy, terms.

”

— Greenwood and Earnshaw, 2nd ed., p. 1235

No mention of what irregularities they might be. Well, we will have to find them for ourselves. That's OK, they are pretty obvious. But they're not 1/4 and 3/4, but more like 1/6-1/3-2/3-5/6: two irregular jump discontinuities in the derivative per tranche. And, as usual, only if the tranches are La-Eu and Gd-Yb. If you make them Ce-Gd and Tb-Lu, you create a third one for no reason by forcing apart the obviously correlated set Gd-Tb-Dy. Double sharp (talk) 16:35, 29 April 2020 (UTC)

@Sandbh: All these graphs are pretty regular. The first subfamily La-Eu shows three almost straight lines: La-Ce-Pr; Pr-Nd-Pm; Pm-Sm-Eu. The second subfamily Gd-Yb shows another three almost straight lines: Gd-Tb-Dy; Dy-Ho-Er; Er-Tm-Yb. Droog Andrey (talk) 14:35, 21 April 2020 (UTC)

@Droog Andrey: Thank you. Yes, they are pretty straight. I hesitate at the double counting ie, Pr and Pm, and Dy and Er, but can't think of a good reason right now why this could be of concern, other then Scerri's notion of "one element, one place". There is no double dipping with the other observation of Ce-xx-Pm--xx-Gd, and Tb-xx-Er-xx-Lu. That seems cleaner. Sandbh (talk) 08:02, 22 April 2020 (UTC)

@Droog Andrey and Double sharp: The irregularities are more meaningful, IMO. Slopes come with double counting baggage. Looking at the 3rd IE chart, the question to be asked is why are the values of Nd and Sm, and Ho and Tm "abnormal" compared to trend? Thus, each of these elements is adjacent to the quarter- and three-quarter anomalies occurring at Pm and Er. Sandbh (talk) 08:14, 26 April 2020 (UTC)

@Sandbh: There is no double-counting baggage. Just think of it as the graph of the function and observe what is basically a big jump discontinuity in the derivative. And there is nothing abnormal about Pm and Er, they continue the trends reasonably well from the previous elements on the graph. The real anomalous ones are Sm and Tm, where as Klemm's generalisation predicts the stabilities of the +2 state increase significantly. And that's because they are one element away from the half-filled and fully-filled subshells. Double sharp (talk) 09:22, 26 April 2020 (UTC)

@Double sharp: We know that:

Double counting occurs at Pr, Pm, Dy, and Er
G&E's chart shows abnormalities at Pm and Er
Klemm divided the Ln into Ce to Gd, and Tb to Lu
Remy:
- was a supporter of Klemm
- observed that Tb⁴⁺ attained the same configuration as Gd³⁺; that Eu²⁺ attains the same Gd³⁺ core; and that "samarium…shows a tendency at least to approximate to the Gd³⁺ structure by functioning as a dispositive element"
- associated Gd with the place of the noble gases.
Looking at this rare-earth metal long term air exposure test, bearing in mind Eu is the most reactive of the Ln, we can see where Remy was coming from (although Tb to Lu are much less reactive, so the group 17/18 analogy is not seen here. Sandbh (talk) 06:10, 29 April 2020 (UTC)

@Sandbh: Wrong. There is no double counting, as we have explained already. And there are also no abnormalities at Pm and Er, they continue the trend totally well. The abnormal ones are the next elements Sm and Tm, as Klemm noticed. No, I don't care if he thought Ce-Gd / Tb-Lu was the right way to split the lanthanides, because his own generalisation refutes it. The race to stability of +2 should happen as a half-filled subshell is approached, because it corresponds to a stable and hard-to-breach subshell. So it must be Eu and not Gd. Gd is hardly noble-gas-like at all in +2, it strongly wants to remove another electron. The better comparison is Eu to Mn, both are rather unhappy to go past +2 compared to their neighbours.

P.S. Reactivity means nothing, just look at the order of reactivity Mn > Cr > Fe. Here Mn is forming +2, Cr +3, Fe +2. It sure looks like Mn-Fe has a Eu-Gd analogy, since Mn is higher up on the reactivity series. And anyone can see that whatever effects the stability of half-filled subshells might be giving have been totally drowned out by everything else (including the different oxidation states involved). That's why you have to look at what look like chemically strange situations where oxidation state is forced to be constant (and, for the Ln, what looks like the wrong constant), or else double periodicity is going to be swamped by other factors. Double sharp (talk) 08:32, 29 April 2020 (UTC)

Tranches

If you focus on +2 vs. +3, the tranches are obviously La–Eu and Gd–Yb; only focusing on +3 vs. +4, as the author deals with more briefly on pp. 100ff., makes Ce–Gd and Tb–Lu look better. But I submit that it's clear that +2 vs. +3 is the more important one to look at, because of (1) consistency with the d metals; (2) that there's only an s shell hanging up, not a d electron too; (3) consistency with the variation of physical properties; and (4) +2 is known for every lanthanide, which cannot be said of +4. Double sharp (talk) 03:30, 19 April 2020 (UTC)

@Double sharp: Here is what we know:

comparative inorganic chemistry usually relies on comparing like with like
the most stable oxidation for the:

3d metals is +2 (for six of ten of them)
4f metals is +3 (for all of them)

there is no need to focus on Ln⁺⁴, which is stable for only 5 of 14 of them in any event, in order to show double, quarter- and three-quarter periodicty
the underlying core of the:

3d metals is reached by hanging up one or two s-electrons
4f metals is reached by hanging up two s-electrons and one d-electron

chemical properties are more important in chemistry than the physical properties of the elements
very few chemists work with the pure elemental metals
Nd in an La-Eu tranche and Ho in a Gd-Yb tranche do not exhibit comparable quarter and three-quarter periodicity

--- Sandbh (talk) 05:53, 19 April 2020 (UTC)

"Hanging up" meaning

This is false. As is quite clearly demonstrated in the article that you link, there is no such thing as "hanging up two s-electrons and one d-electron". (Not even in the condensed phase, because as I showed through quotes at the end of appendix I there is 4f contribution to the valence band, and anyway such a theory would prevent +2 from being a base state for the 3d metals since there is quite clearly significant 3d contribution to the valence band for most of them.) What happens is that the occupancy of the f subshell goes down by one as we ionise from +2 to +3. 4f is not a core subshell: the underlying core for the 4f metals is not [Xe]4fⁿ, but [Xe]. (Only for Lu is 4f¹⁴ part of the core.) That's also exactly why the tranches end at Eu and Yb: the end of a tranche ought to mean that we have gotten a half- or fully-filled subshell, so the next element should have a drop as it is one electron above a stable half- or fully-filled subshell. It doesn't make any sense to have such a drop inside a tranche.

I wonder how that argument against looking at the pure metals gels with how you've been quoting condensed-phase configurations of the pure metals, when similar logic would demand that we look mostly at configurations in chemical environments with other atoms around instead. In fact, just because the pure elemental metals are not the most commonly encountered thing in chemistry does not make their properties any less important, and I treat their properties equally to chemical properties of the elements in compounds. Except that, as demonstrated above, both support Sc-Y-Lu due to the total absence of any significant 4f involvement in the valence region of Lu metal and Lu compounds.

The f series has 14 elements, and you can't possibly make exact quarters out of that. So the fact that +2 state seems to markedly increase in stability only for the last two elements of each tranche in the Ln is immaterial, especially since we can see that the same trend goes one element later when looking at +3 vs. +4. Therefore, even if we insist on the La table as our basis, the effect still occurs mathematically after reaching 1/4 and 3/4: Sm-Eu / Tm-Yb looking at +2 vs. +3 (the Lu table idea with +2 as baseline), Eu-Gd / Yb-Lu looking at +3 vs. +4 (the La table idea with +3 as baseline). We must compare like with like indeed: but the important thing is the consistent baseline corresponding to the s electrons, not the fantasy of searching for the most stable oxidation state across the row which you are never going to find for 4d, 5d, or 5f. Double sharp (talk) 06:10, 19 April 2020 (UTC)

P.S. In fact, the electron configuration of the Ln has very little to do with their consistent +3 oxidation state. See the long quotes I gave at the end of Appendix I. The issue is simply lattice and hydration energies, which remain relatively consistent for the f orbitals because they are deeply buried and not so strongly influenced by ligand fields. When that fails to happen, such as for the early 3d or 5f elements, the situation is markedly different. So again, we see an example of why (as I have been saying for some time already) the Ln contraction is not comparable with any other one, because its direct effect on the elements involved is without parallel (at least, until we get to 5g, probably). Double sharp (talk) 06:33, 19 April 2020 (UTC)

@Double sharp: OK. I was interpreting the expression "hanging up", in the context of getting rid of the two s electrons from the 3d metals (exception: one s electron for Cr and Cu). In the case of the +2 cations of the 3d metals that leaves d¹ Sc to d¹⁰ Zn. Is that right? Hence my poorly chosen expression, "underlying core" i.e. of d electrons, which give rise to the characteristic properties of transition metals.

For the +2 cations of La to Yb, which each lose their two s electrons, that leaves d¹ in La; f¹d¹ in Ce; f³ to f⁷ from Pr to Eu; f⁷d¹ in Gd; and f⁹ to f¹³ from Tb to Yb. Is that right?

As we ionise from +2 to +3, La, Ce, and Gd lose d-electrons; whereas Pr to Eu and Tb to Yb lose one f electron apiece. This leaves La f⁰, and then Ce f¹ to Yb f¹³. Is that right?

@Sandbh: No, that's not right. As Johnson mentions in the article, the electron configuration of the Ln²⁺ ions is always [Xe]4fⁿ, except for La [Xe]5d¹ and Gd [Xe]4f⁷5d¹. (And even for these two, the regular configurations [Xe]4f¹ and [Xe]4f⁸ are very low-lying excited states, not even 1 eV above the ground state). So, notionally everyone is getting rid of two s electrons. (Things like Cr and Cu don't really matter because the regularised configurations are not far from the ground state anyway.)

So, as we ionise from +2 to +3, everyone loses an f electron. Except for La and Gd in their ground states. And note that due to ligand-to-metal charge transfer, a complexed La^III or Gd^III atom will have a charge closer to +2 than you would expect from the oxidation state, and chemical environments can easily favour occupying the f subshell instead.

Ergo, there is no d electron hanging up that we want to get rid of. To get to the +2 state we are universally removing s electrons from La through Yb; to get to the +3 state we are almost universally dipping into the f subshell, which by any sane measures must obviously be a valence subshell. (La and Gd are minor exceptions that can in chemical contexts stop being exceptions.) For Lu, no chemical context can ever stop it being an exception that removes a d electron instead. It clearly patterns with the d elements Hf through Hg. Double sharp (talk) 09:42, 19 April 2020 (UTC)

Excitation energies in eV for the Madelung exceptions, from the NIST tables:

Cr	Cu	Nb	Mo	Ru	Rh	Pd	Ag	Pt	Au
0.96097	1.38894	0.14169	1.35960	0.92778	???	3.11216	3.74957	0.10212	1.13584
La	Ce	Gd	Ac	Th	Pa	U	Np	Cm	Lr
1.88417	0.59050	1.35728	???	3.40455	1.61410	0.87046	???	0.15054	???

??? = no data found, but in those cases the tables are pretty spotty in their coverage (or nonexistent, for Lr). Every one is easily reachable in chemical environments, and that's why it doesn't matter that the ground state happens to be the "wrong" one. Double sharp (talk) 03:01, 20 April 2020 (UTC)

@Double sharp: Look-up configuration table follows:

M	La	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb	Lu
0(s)	4f⁰5d¹6s²	4f¹5d¹6s²	4f²5d¹6s²	4f³5d¹6s²	4f⁴5d¹6s²	4f⁵5d¹6s²	4f^~76s²	4f⁷5d¹6s²	4f⁸5d¹6s²	4f⁹5d¹6s²	4f¹⁰5d¹6s²	4f¹¹5d¹6s²	4f¹²5d¹6s²	4f^~146s²	4f¹⁴5d¹6s²
s to g	–	–	↓5d¹ ↑4f¹	↓5d¹ ↑4f¹	↓5d¹ ↑4f¹	↓5d¹ ↑4f¹	–	–	↓5d¹ ↑4f¹	↓5d¹ ↑4f¹	↓5d¹ ↑4f¹	↓5d¹ ↑4f¹	↓5d¹ ↑4f¹	–	–
0(g)	4f⁰5d¹6s²	4f¹5d¹6s²	4f³6s²	4f⁴6s²	4f⁵6s²	4f⁶6s²	4f⁷6s²	4f⁷5d¹6s²	4f⁹6s²	4f¹⁰6s²	4f¹¹6s²	4f¹²6s²	4f¹³6s²	4f¹⁴6s²	4f¹⁴5d¹6s²
0 to +1	↓6s² ↑5d¹	↓6s² ↑5d¹	↓6s¹ ↓5d¹ ↑4f¹	↓6s¹ ↓5d¹ ↑4f¹	↓6s¹ ↓5d¹ ↑4f¹	↓6s¹ ↓5d¹ ↑4f¹	↓6s¹	↓6s¹	↓6s¹ ↓5d¹ ↑4f¹	↓6s¹ ↓5d¹ ↑4f¹	↓6s¹ ↓5d¹ ↑4f¹	↓6s¹ ↓5d¹ ↑4f¹	↓6s¹ ↓5d¹ ↑4f¹	↓6s¹	↓5d¹
+1	4f⁰5d²	4f¹5d²	4f³6s¹	4f⁴6s¹	4f⁵6s¹	4f⁶6s¹	4f⁷6s¹	4f⁷5d¹6s¹	4f⁹6s¹	4f¹⁰6s¹	4f¹¹6s¹	4f¹²6s¹	4f¹³6s¹	4f¹⁴6s¹	4f¹⁴6s²
+1 to +2	↓5d¹	↓5d¹ ↑4f¹	↓6s¹	↓6s¹	↓6s¹	↓6s¹	↓6s¹	↓6s¹	↓6s¹	↓6s¹	↓6s¹	↓6s¹	↓6s¹	↓6s¹	↓6s¹
+2	4f⁰5d¹	4f²	4f³	4f⁴	4f⁵	4f⁶	4f⁷	4f⁷5d¹	4f⁹	4f¹⁰	4f¹¹	4f¹²	4f¹³	4f¹⁴	4f¹⁴6s¹
+2 to +3	↓5d¹	↓4f¹	↓4f¹	↓4f¹	↓4f¹	↓4f¹	↓4f¹	↓5d¹	↓4f¹	↓4f¹	↓4f¹	↓4f¹	↓4f¹	↓4f¹	↓6s¹
+3	4f⁰	4f¹	4f²	4f³	4f⁴	4f⁵	4f⁶	4f⁷	4f⁸	4f⁹	4f¹⁰	4f¹¹	4f¹²	4f¹³	4f¹⁴
0(s) to +3	↓5d¹6s²	↓5d¹6s²	↓5d¹6s²	↓5d¹6s²	↓5d¹6s²	↓5d¹6s²	↓6s²	↓5d¹6s²	↓5d¹6s²	↓5d¹6s²	↓5d¹6s²	↓5d¹6s²	↓5d¹6s²	↓6s²	↓5d¹6s²

OK, so what we know to be true is:

To get to +2, La loses 6s²; Ce-Sm each gain 4f¹ and lose 5d¹6s²; Eu-Gd each lose 6s²; Tb-Tm each gain 4f¹ and lose 5d¹6s²; Yb loses 6s²; Lu loses 5d¹6s¹
Ln²⁺ ions are 4fⁿ, except for La 5d¹ and Gd 4f⁷5d¹, and Lu 4f¹⁴6s¹
- For La²⁺ and Gd²⁺, 4f¹ and 4f⁸ are low-lying excited states, ≤ 1 eV above the ground state
- For Ce²⁺ and Tb²⁺, fⁿ⁻¹5d¹ and fⁿ are close in energy
- La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er, and Lu can also form 4fⁿ5d¹ divalent ions
As we ionise from +2 to +3, La and Gd lose d-electrons; whereas Ce-Eu and Tb-Yb lose one f electron apiece; and Lu loses an s electron
- This leaves La f⁰ and Ce f¹ to Yb f¹³
In ionising from Ln⁰(solid) to Ln³⁺, every Ln bar Eu and Yb loses 5d¹6s²
Ce³⁺ to Lu³⁺ are uniformly 4fⁿ (n = 1–14); La³⁺ is 4f⁰
Sc²⁺ to Zn²⁺ are uniformly dⁿ (n = 1 to 10); Ca²⁺ 3d⁰
In the progressive occupancy of the 4f sub-shell in Ln³⁺ ions, the half-filled sub-shell is reached at Gd f⁷ and the full sub-shell at Lu f¹⁴
The immediate neighbours of:
- Gd³⁺ f⁷ adopt its configuration too, i.e. as Eu²⁺ f⁷ and Tb⁴⁺ f⁷
- Lu³⁺ adopt its configuration too i.e. as Yb²⁺ f⁷ and Hf(IV) f¹⁴
The +2 state starts becoming classically more stable just after the quarter- (Pm) and three-quarter (Er) marks in the sequence Ce-xx-Pm-xx-Gd; and Tb-xx-Er-xx-Lu i.e. from Sm and Tm.

Sandbh (talk) 07:20, 20 April 2020 (UTC)

@Sandbh: You are focusing too much on minutiae. The exact occupancy in the gas phase configuration does not matter in chemical environments because the bond energies can easily be enough to favour one of those other states. Just look at cerium, within 1 eV you have not only 4f5d6s², but also 4f²6s² and 4f5d²6s. And as I have stated here ad nauseum, there is no sense in speaking of integer occupancies in condensed phase electron configurations, too many configurations are mixing. A more accurate description of what is going on is to say that the 4f elements La through Yb are [Xe] 4fⁿ⁻¹ 4f^ε (5d6s6p)^3−ε where n goes from 1 at La to 14 at Yb: there is some 4f contribution to the valence band. So can we please drop this idea of pure electron configurations in the condensed phase that is simply against reality?

The important thing is that in getting to +2, La through Yb are consistently [Xe]4fⁿ, either in the ground state or in some not-very-highly-excited state (below 1 eV). This is not true for Lu which makes no sense as part of that series. When we then ionise past +2, we are taking electrons out of the f shell. That's why the base line should be +2, same as it is for the d elements. The stability of a half-filled shell occurs at Eu and Yb. And the general stability of the +2 state follows the pattern of I₃′ on the graph, as Johnson notes on p. 87. Which lets us make better predictions about the stability of the +2 oxidation state than we would otherwise. Double sharp (talk) 07:43, 20 April 2020 (UTC)

@Double sharp: I compiled the look-up table as you made many statements and I was losing track of their basis. Could we drop the use of such words as "minutiae" and "ad nauseum" and jointly focus on establishing what is true?

Thus, it is not true that in getting to:

+3, everyone loses an f electron; here, Lu loses an s electron
+3, everyone loses an f electron, since we know that La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er, and Lu can also form 4fⁿ5d¹ divalent ions.

Thus, it is not true that:

Ergo, there is no d electron hanging up that we want to get rid of.

We know it is true that:

In 13 of 15 cases getting to +3 involves the net loss of 5d¹6s².

We know it is true that:

The indistinguishability of electrons implies that one can never state that a practical number of electrons are in any particular sub-shell, although it is frequently useful to make this approximation.
The independent-electron approximation, as it is known, represents one of the central paradigms in modern chemistry and physics.

--- Sandbh (talk) 08:07, 21 April 2020 (UTC)

@Sandbh: But you are focusing on things that are true but irrelevant chemically. "Minutiae" seems to be a perfect description of such things.

In fact, your second point is the most revealing because it actually shows the truth of what I have been saying. In chemical environments, these elements can form 4fⁿ5d divalent ions. But when isolated, they are usually 4fⁿ⁺¹. And they might also be that in different chemical environments. Ergo, both configurations need to be taken into account, as depending on the chemical environment of the Ln²⁺ ion it may prefer one configuration or the other. That's not only simply logical looking at the low excitation energies involved even as isolated cations, but also corroborated totally by the source you have given. And that's why your well-meant table is focusing on things that don't really matter.

So, what really is right is as follows:

To get from 0 to +3, 14 out of the 15 elements under consideration might be losing an f electron in a chemical environment, where they may be 4fⁿ or 4fⁿ⁺¹. TRUE!
Lutetium cannot possibly be doing that, there is no 4f¹⁵. TRUE!
Therefore, we can see that after 6s² is gotten rid of for everybody (notionally speaking; at least, Lu²⁺ [Xe]4f¹⁴5d¹ is probably not that high up anyway), La through Yb are starting to have 4f ionisable for chemistry. So only 6s² is the real preliminary; there is no 5d electron hanging up. And Lu is something totally different, as usual, that patterns more with Hf through Hg with its non-use of 4f.

The fact of the matter is that in any chemical environment, there is going to be orbital hybridisation and mixing of different configurations, and thinking of integer subshell occupancies valid for every possible use case is quickly going to get silly. Yes, La²⁺ might be 5d¹ in some situation, and it might equally be 4f¹ in some other situation. Picking either one alone will not get you anything general. Only in situations of chemical isolation can we talk about the one ground-state configuration, but then we are back to gas-phase configurations. And it should be obvious that mostly, we are not focused on situations of chemical isolation. Double sharp (talk) 08:18, 21 April 2020 (UTC)

@Double sharp: We know it is true that:

orbital hybridization occurs TRUE!
it is not always necessary to invoke hybridization in order to obtain useful generalistions
it is not necessary to think of integer subshell occupancies valid for every possible case. TRUE!

I've added TRUE! flags to some of your other contributions. --- Sandbh (talk) 07:32, 22 April 2020 (UTC)

@Sandbh: Thank you. I have repaid the favour by adding two such flags to yours above. ^_^ (For the last one: indeed, these are not necessary, because they don't exist outside hydrogen and helium.)

But I must protest the second one. Indeed, the bases for this protest are straight from the beginning of school chemistry. Why else is NH₃ trigonal pyramidal (basically tetrahedral, but with a lone pair as one pseudo-substituent), if the s orbital is different from the p one, and they don't mix? No, there's obviously something close to sp³ hybridisation going on, and it works well because 2s and 2p are so close in energy. So the molecular geometry is approximately tetrahedral with full symmetry; the only difference comes from the fact that one "substituent" is a lone pair, where by Bent's rule s character is concentrated (so the bonding electrons have more p character). (In CH₄, we have total symmetry and so basically ideal sp³.) Then once the sp energy gap starts rising for later periods, we can see that PH₃, AsH₃, SbH₃, and BiH₃ increasingly deviate from the ideal angle of the geometry, as s participation drops further and further. Simply put: you need hybridisation to explain anything beyond the chemistry of hydrogen and helium. That's why I insist that the important thing is the total number of valence electrons, because hybridisation in any chemical environment is going to make the occupancies change. What doesn't change is what orbitals they may occupy. Double sharp (talk) 07:44, 22 April 2020 (UTC)

@Double sharp: Hybridization is a tricky thing. You know, BiPh₄⁺ is tetrahedral, but with very tiny 6s contribution. In CH₄ there are one a1g and three t2u bonding orbitals, not four degenerate hybrid orbitals. There is a short guide :) Droog Andrey (talk) 10:09, 22 April 2020 (UTC)

@Droog Andrey: I guess you mean this?

Thanks for the article, BTW: I'm aware my general understanding of the details is mostly still high-school chemistry simplifications. (Which usually predict the right answer, though for the wrong reasons.) But I guess my point that there aren't pure orbitals stands. ^_^ Double sharp (talk) 10:22, 22 April 2020 (UTC)

@Double sharp: Right. How does it look now? --- Sandbh (talk) 11:32, 22 April 2020 (UTC)

@Sandbh: Now the middle point is not terribly relevant, because in the case being discussed here (the f elements), hybridisation and multiple configurations are absolutely needed. Double sharp (talk) 13:10, 22 April 2020 (UTC)

@Double sharp: Not in all cases, I'd say. Here, the second point was, "it is not always necessary to invoke hybridization in order to obtain useful generalisations." Hence, the caveat, "not always necessary".

@Sandbh: For heavy main-group elements like Bi with huge 6s-6p gaps, yes, we can argue that. For the 4f series, with so many configurations so close to each other, it is vital to consider hybridisation and multiple configurations to make any sense out of them. Double sharp (talk) 09:23, 26 April 2020 (UTC)

Fractions of 14

The expressions "quarter-" and "three-quarter" sub-shells come from the literature. Nobody I know of takes that to refer to exactly so filled sub-shells.

@Sandbh: Well, then what is standing in the way of considering Pm and Er as 1/4 and 3/4 anyway even in a La-Yb f block, if it doesn't have to be mathematically 1/4 and 3/4?

In fact, one can equally make a case for considering Nd and Ho as the 1/4 and 3/4 elements: if you take their data points as origins, then the graphs of the La-Eu and Gd-Yb tranches are approximately odd around them. Double sharp (talk) 09:43, 19 April 2020 (UTC)

@Double sharp: In an La table, the pattern becomes askew: La-xxx-Pm-x-Eu; Gd-xxx-Er-x-Yb. If you take Nd and Ho the pattern becomes balanced, as La-xx-Nd-xx-Eu; Gd-xx-Ho-xx-Yb, but misaligned with e.g. G&E's graph. Sandbh (talk) 07:27, 20 April 2020 (UTC)

@Sandbh: The alignment is better with Nd and Ho as middle elements of each tranche, La-Eu and Gd-Yb. Just look at the symmetry around it: the Nd value is roughly the average of those of Pr and Pm; Ce and Sm; and La and Eu. And the same analogously for Ho in the Gd-Yb tranche. This is totally lost in tranches beginning with Ce. Double sharp (talk) 07:31, 20 April 2020 (UTC)

@Double sharp: What values are you referring to?

@Sandbh: Look at any of the plots above. Double sharp (talk) 07:54, 20 April 2020 (UTC)

4d-5d and 5f common oxidation states

For the 4d series, +4 is the most common stable oxidation state (5 out of 10); 5d is +4 (6 out of 10); and for 5f, +3 is common to all of them and the most stable for 8 out of 14. Sandbh (talk) 08:02, 19 April 2020 (UTC)

@Sandbh: And in neither case do you get anything that makes any sense as a baseline. If you take +4 as your baseline for 4d, for instance, all the trends are going to end up going from Zr 4d⁰ to Sn 4d¹⁰. I trust we agree this is silly. So, this demonstrates that picking a baseline oxidation state from ionising outer shells should not have anything to do with the most common oxidation state: the fact that they coincide for 3d is a one-off coincidence that never repeats. Double sharp (talk) 09:42, 19 April 2020 (UTC)

@Double sharp: Yes. I was only responding to your observation that attempting to establish a common oxidation state for 4d, 5d, and 5f was a fantasy. Using these isn't necessarily silly, as long as you do so cautiously and with due caveats. Sandbh (talk) 07:41, 20 April 2020 (UTC)

@Sandbh: Such baselines are not useful unless you are focusing on just a few elements in the middle of the rows, not all of them. That's the sense in which I consider them a fantasy Where is +4 most stable in 4d? Apart from Zr, only Mo through Ru. Is that at least consistent with 5d? No, it isn't; apart from Hf, it's only most stable in Os through Pt. And, surely, the fact that Ir⁴⁺ happens to be 5d⁵ must be a coincidence, looking at this otherwise extremely wide spread. (And good luck finding any majority for 6d.) You're not going to get anything very reasonable attempting a 4f-style analysis of these elements based on generalising Klemm's rules about when the non-baseline oxidation states get stabilised (racing towards a stabilised configuration), you know. And even that doesn't work very well outside the most stable elements; just look at the stability trend from Dy(II) to Er(II), which goes towards being more rather than less unstable (Johnson, p. 87). Of course, idealised ionisation energies from pure-Madelung configurations explain that perfectly!

For the actinides, we see a very split behaviour between early and late actinides, so the reasonable thing to do is to consider each group separately. You'd be better off segregating Ac-Am (which have a d-like trend in oxidation states) from Cm-No (which act like La-Eu). Ah, but here the most reasonable groupings are again the ones following the Lu table. Because the split in behaviour is from Am to Cm; Am can reach transition-metal-like higher oxidation states past +4 through chemical means, Cm(VI) has only been prepared for sure radiometrically. Double sharp (talk) 07:53, 20 April 2020 (UTC)

4f sub-shell and +3 preference

On that PS, just check what you said there. That is:

"In fact, the electron configuration [filling of 4f sub-shell] of the Ln has very little to do with their consistent +3 oxidation state."
"The issue is simply lattice and hydration energies, which remain relatively consistent for the f orbitals [filling of the 4f sub-shell] because they are deeply buried and not so strongly influenced by ligand fields."

Nothing to with the electron configuration of the Ln, eh? Sandbh (talk) 08:22, 19 April 2020 (UTC)

@Sandbh: I didn't say "nothing", I said "very little", although I admit that this was poorly phrased. The point is that the extent of the relationship has only to do with the fact that 4f is the characteristic subshell, and not the details of occupancy of 4f and 5d.

Naïvely looking at the electron configurations of the Ln, which are usually [Xe]4fⁿ6s², would predict that they are usually divalent. That's clearly not what happens. The important thing to glean from the Ln's electron configurations is not naïvely counting outer electrons, but by noting that the characteristic subshell that is filling is 4f. That is deeply buried and not strongly influenced by ligand fields, as I said, and so lattice and hydration energies remain pretty constant throughout the 4f row as long as the elements involved are in the same oxidation state. So only the fact that 4f is chemically active matters; the details of occupancy of 4f and 5d do not really matter for the oxidation state. That's why I insist on chemically active subshells instead of just ground-state configurations. In the 5f row, we only see that once 5f shrinks into the core for the later actinides; same with the 3d row. Double sharp (talk) 09:42, 19 April 2020 (UTC)

@Double sharp: OK, yes. This a nice example of the potential hazards of gas phase configurations. Did you really mean to say, "that the characteristic sub-shell that is filling is 4f?" There goes La. Meanwhile we note the f¹³-f¹⁴ occupancy sequence in the trivalent cations of Yb and Lu, as their most stable oxidation states. The details of the occupancy of 4f and 5d matter in the case of the transition metal chemistry of the Ln. Sandbh (talk) 07:38, 20 April 2020 (UTC)

@Sandbh: Yes, I meant what I said. Lanthanum need not go anywhere, as it has a chemically accessible [Xe]4f¹6s² configuration at about 1.88 eV, and La²⁺ has a low-lying [Xe]4f¹ configuration at less than 1 eV. So it works as a member of the 4f series just as thorium works as a member of the 5f series (the same is likely true about actinium; it's just that there we have little information, because its radioactivity is a rather significant inconvenience). You'll never, on the other hand, find Lu with an f subshell contributing anything; that's the lanthanide that drops off. No, the most stable oxidation states do not matter for periodic table placement as I have explained 9001 times; as a simple counterexample, the 3d transition metals in their most stable oxidation states are d⁰ until vanadium (V^V has oxidising tendencies), and the 2s through 7s elements in their most stable oxidation states are always s⁰. What matters is whether the subshell is doing anything for chemistry, not arguing about most common oxidation states.

What I said is only that the exact occupancy does not matter for determining what the most stable oxidation state is. And if you actually analysed what you were reading (it's in the abstract already), you'll see this article exactly supports what I am saying: "These results indicate that the ground state of a lanthanide ion in a molecule can be changed by the ligand set, a previously unknown option with these metals due to the limited radial extension of the 4f orbitals." Precisely. That's why focusing on gas phase configurations only is as silly as focusing on condensed phase configurations only. Or ground states of cations only. You have to look at excited states within the range of possible chemical bond energies, because in chemical environments they might become the ground state. That's why I continually insist on the importance of 4f for lanthanum, and of 5f for actinium and thorium: in chemical environments they can become occupied preferentially, and their accidental emptiness in the gas-phase ground state is chemically meaningless. Just like 5s in palladium, or 6d in lawrencium.

So, what we have here is yet another golden example of interplay between 4fⁿ and 4fⁿ⁺¹ configurations for the 4f elements like I've been talking about: the point is not "what is the ground state", it's "let's look at different possible configurations". And yet again, lutetium is forbidden from joining the fun by mathematics. 4f in lutetium and 5f in lawrencium have zero valence involvement, all they cause are incomplete shielding effects. The same as what 4f does from hafnium to radon, and 5f does from rutherfordium to oganesson. There isn't any difference between Lu/Lr and Hf-Rn/Rf-Og here. Double sharp (talk) 08:02, 20 April 2020 (UTC)

Two excellent quotes from the very paper you linked:

“

Hence, the previous classification of +2 lanthanide ions into the traditional six 4fⁿ⁺¹ ions with Ln = Eu, Yb, Sm, Tm, Dy, and Nd and the nontraditional 4fⁿ5d¹ ions with Ln = La, Ce, Pr, Gd, Tb, Ho, Er, and Lu and 4d¹ Y must be modified in the sense that this dichotomy is apparently dependent on the ligand environment. In some coordination environments, specifically the (Cp′₃)³⁻ ligand set, Dy and Nd can adopt the 4f ⁿ 5d¹ electron configuration. With this (Cp′₃)³⁻ set of ligands, there are only four traditional 4fⁿ⁺¹ Ln²⁺ ions.

”

Exactly, dependent on the ligand environment. The 4f orbitals extend enough (although weakly) to be influenced by the ligands, that's why occupancy can change according to the ligands attached. For 3d the effect is yet stronger. Ergo, both configurations are chemically relevant, and that's how we know 4f is involved. But not for scandium, yttrium, and lutetium; because Sc and Y have no low-lying f orbitals, and Lu cannot cram in a fifteenth electron into its 4f orbitals.

And about Ln²⁺ trapped in alkaline earth halide matrices:

“

These data provide further support that the ligand field environment can affect the ground state electronic configuration of the Ln²⁺ ions. Since the ligand field splitting in a cubic environment lowers two d orbitals rather than a single d orbital as found for d_z² in the trigonal environment of the (Cp′₃)¹⁻ ligand set, the d orbital stabilization may not be sufficient to make d orbital population energetically competitive with f orbital population. Hence, the trapped Ln²⁺ ions adopt the traditional 4fⁿ⁺¹ configuration in this cubic coordination environment.

”

So the chemical environment can alter the relative stability of those two configurations. Why is this so difficult to understand? Droog Andrey has said it, I have said it, we have both pointed to many sources talking about the difference between configurations in isolation and in chemical environments, and now we have a paper outright saying what we've been saying. Double sharp (talk) 08:33, 21 April 2020 (UTC)

@Double sharp and Droog Andrey: This small discussion reminds me that I, or at least I think I do, put up relatively straightforward (s/f) observations about Sc-Y-La-Ac. My perception is that you (DS) respond with five times as many words setting out a counter-explanation/interpretation (5c/i). I don't know if this a named phenomenon. I can only think that, given a choice between a s/f argument and a 5c/i, all things being equal, the s/f argument is probably closer to the truth, or at least the 80/20 truth, that can form the basis for a good generalisation.

We know it to be true that:

The most stable oxidation state of the La to Lu is uniformly +3
In this chemically most important +3 ionic phase, the 4f sub-shell from Ce to Lu is progressively occupied with from 1 to 14 valence electrons
While La has no 4f valence electron of its own, its 4f sub-shell may be involved in limited hybridisation with its 5d and 6s sub-shells, and may feature ligand electron occupancy
Neither of these phenomena are pre-eminent characteristics of La
Th has no 5f valence electron of its own although 5f occupancy (~0.5) is known to influence its crystalline structure, and Th does have some 5f chemistry in its Th³⁺ form
Neither of these phenomena are pre-eminent characteristics of Th
Lu has 14f electrons in its sub-shell; these are not involved in chemical interactions aside from shorting bond lengths in Lu compounds

--- Sandbh (talk) 10:43, 22 April 2020 (UTC)

@Sandbh: It's only five times as many words because I'm quoting the sources. So, here is a completely straightforward statement without doing so.

The most stable oxidation state has nothing direct to do with the baseline oxidation state that we should be comparing against. (Justification: 4d, 5d).
The most important thing for real chemistry is a whole set of configurations within a certain energy range, because they may become the ground states depending on ligands.

It's that simple.

Now, your statements above exactly expose why I consider arguments about the lack of a 4f electron in the ground state of La to be a double standard. Because we can equally point that finger at thorium. So the only consistent choices are:

Either the lack of f involvement in La and Th is prohibitive for both in the f block:
Or it is prohibitive for neither.

A Sc-Y-La-Ac table has La excluded from the f block, but not Th, and is therefore plainly inconsistent. A Sc-Y-Lu-Lr table is consistent. And I'll follow it and take the non-ground-state 4f in La and 5f in Ac and Th any day over the corelike 4f/5f orbitals of Lu, Lr, and Rf, because it's silly to have elements of a block that don't use that orbital. (He 1s and Ne 2p are not exceptions, they control the instability of bonds to them.) Double sharp (talk) 12:04, 22 April 2020 (UTC)

@Double sharp: Ah well, I intended the "five times as many words" phenomenon as a general observation.

Anyway La and Th aren't directly comparable since Th³⁺ shows 4f chemistry with its own 4f electron, reliant on neither partial hybridization nor ligand donation. An Sc-Y-La-Ac table works in this sense. Of course it "fails" with Lu, which shows no 4f chemistry at all. So, I look to other truths. Perhaps, in my mind, this all goes back to the original notion of the Ln being Ce-Lu, rather than La-Lu. Nothing has happened since those days that warrants superseding it, as a better or superior treatment, as far as I can see. This has always been the case for the various arguments made in the literature for Lu-Lr. The cultural momentum (or inertia, if you like) of Battleship Sc-Y-La is too big to overcome in the absence of a staggering new development. That may suck, but that's the way it is in science. Sandbh (talk) 01:09, 23 April 2020 (UTC)

@Sandbh: Don't you realise how much this sounds like "oh no, Sc-Y-La fails on this count, so let me keep looking for other counts by which it looks slightly less bad"? And how exactly can that possibly qualify as "the way it is in science", in which by definition we're supposed to reject old theories once the evidence against them is overwhelming?

In actuality, Jensen's arguments really do demolish Sc-Y-La, at least once you understand the point of subshell filling and realise why "look at group 2" is not a counterargument. Although I think his strongest is the damning one he gave in his reply to Lavelle:

“

When it comes to the question of why La and Ac should remain in the d-block rather than being reassigned to the f-block, Lavelle offers no new chemical or physical evidence other than his constant reiteration of the fact that both elements contain d-electrons in their ground-state valence conﬁgurations, but no f-electrons. Yet in the cases of both Lu and Th, for which this is equally true, he proceeds to inconsistently argue that this fact is of no consequence when it comes to assigning them to the f-block. As with the case of the revised conﬁguration for Lr, which counts when it comes to not placing this element in the d-block but is irrelevant when it comes to placing it in the f-block, this arbitrary and naive use of electron conﬁgurations, to the exclusion of all other evidence, is logically inconsistent and leaves one with the impression that the only true argument that Lavelle has for the major premise of his diatribe is that La and Ac should remain in the d-block because that is where IUPAC places them in its official periodic table and therefore all rational discussion of other possibilities is strictly forbidden.

”

Replace "where IUPAC places them in its official periodic table" (because it doesn't) with "where they usually appear", and this is where your argument sounds like it's gone to me with its overlooking of the grrreat big nuclear bomb that torpedoes the battleship Sc-Y-La: minor irregularities in ground-state configurations have zero correlation with actual chemical behaviour, and the lack of an f electron in La, Ac, and Th is one of them. Do you think that's the way it is in science?

Since almost the beginning, Sc-Y-La has had a vocal minority protesting it and arguing for Sc-Y-Lu. Not only does this minority only increase, they have lots of good scientific arguments for it, and the majority of chemists who actually consider the group 3 issue support Sc-Y-Lu.

The fact that most textbooks have not followed suit is immaterial. The cultural momentum of the explanation of SF₆ by sp³d² hybridisation is still very strong despite what is pretty much slam-dunk evidence that 3d is not involved here. Are we going to support that too, instead of the less wrong description of resonance structures all obeying the octet rule and making up the deficit with partial ionic bonding? (*)

Finally: it does not matter whether the electron came from the ligand or not. The important thing is that the lanthanum atom in a chemical environment is likely to have a charge closer to +2 than to +3 even when it is notionally in the +3 oxidation state. We don't quibble about where the electrons are coming from in dative bonds because they are part of the bond and hence shared between the bonding atoms. And when its charge is closer to +2 its 4f orbital is likely to be partially occupied. That's the important thing, and I'm astonished I have to say this since this is middle-school chemistry. Thorium 5f presumably gets in on an absolutely similar basis (remember that +3 is not a major oxidation state for it). Double sharp (talk) 03:00, 23 April 2020 (UTC)

Clarify approach

@Double sharp: No, I've never said to myself, "oh no, Sc-Y-La fails on this count, so let me keep looking for other counts by which it looks slightly less bad". What I've done is look for observations that collectively support Sc-Y-La-Ac. Why? Because nobody else has done it. And there are lots of such arguments. Science does reject old theories once the evidence against them is overwhelming. The challenge is that none of the arguments for Lu are overwhelming. And there are plenty of new arguments supporting La. The vocal minority arguing for Lu, aside from Jensen, have done so on the basis of one-shot arguments. And they expect the battleship that is the chemistry establishment to take note of their pop-gun pronouncements? Tell 'em they're dreamin'. No, better, tell them they're deluded, and they have zero idea of how the chemistry establishment works, even if we think or feel that sucks. That's why their efforts came to naught. Jensen had a red hot go, but he came undone due to the selectivity of his arguments, as noted by Scerri. You have to work with 'em not ag'in' 'em which is why Scerri is running the project for them. Sandbh (talk) 08:13, 24 April 2020 (UTC)

An iconic rhetoric from Sandbh. Droog Andrey (talk) 08:56, 24 April 2020 (UTC)

Sandbh I found this comment rather interesting and this made me question one certain thing. You said you were looking for observations that collectively support -La-Ac. Do you think that this is a good objective in the first place? My normal understanding is that one should look for observations and then make a judgment: make observations, assess them, see what different combinations of them produce, and then, having done that, cast a judgment. I realize that your modus operandi sounds like you have a hypothesis, for which argumentation in support is sought; but how critical are you on it and what about argumentation against the hypothesis? Regardless, if my understanding I've just described is correct, then the hypothesis MO does not appear to be the right one, because this is not really an observation problem; this is a classification problem.

I have noted in the very beginning of this discussion, which started with an article you wrote, that it did not appear to me that pro-La-Ac and pro-Lu-Lr arguments were given the same weight, and I said, perhaps not as explicitly but to the same meaning, that it looked like this was done so deliberately so that one option is favored over the other. I am afraid that what I've read so far reinforces this thinking within me. Please correct me if my thinking here is wrong.--R8R (talk) 16:37, 26 April 2020 (UTC)

@R8R: +1

@R8R and Double sharp: That's right. To make my approach clearer, the start of the article now reads as follows:

“

Scope

My focus is intended to be philosophical or systemic rather than descriptive or theoretical. Along the way some more detailed ancillary arguments will be encountered where I feel these are required to provide context, are novel, or provide useful insights.

Arguments in support of Lu in Group 3 have been summarised by Scerri and Parsons (2018) and Scerri (2020, pp. 392–403).

I mention some recent arguments, in passing.

Stewart (2018a, p. 117) observed that an argument for Lu in group 3 was that the pth element in the f-block series, with the exception of Gd, has p f electrons. In contrast, Wulfsberg (2006, p. 3) opined that:

…valence electron configurations of atoms and ions are also important in predicting the periodicity of chemical properties. Since ions are more important than isolated gaseous atoms for nearly all atoms, and important ions have no anomalous electron configurations, there is little reason to worry students with anomalous electron configurations of atoms: we prefer to teach ‘characteristic’ electron configurations without anomalies in the occupancies of d and s orbitals in the transition elements or d, s, and f orbitals in the inner transition elements.

Thus, with La in group 3, the number of f electrons in the trivalent cations of the f-block metals corresponds perfectly with their position in that block. The series starts with Ce³⁺ as [Xe]4f¹ and concludes with Yb³⁺ [Xe]4f¹³ and Lu³⁺ [Xe]4f¹⁴. Likewise, Sobolev (2019, p. 715) observes that trivalent lanthanoid (Ln) cations, representing the normal valence of Ln, have no s or d valence electrons and contain only 4f electrons.

Scerri and Parsons (2018) proposed to resolve the issue by adding a third requirement to the two parts of the Madelung Rule. However, there are many pre-existing exceptions to the Madelung Rule, and the fact that the La form does not pass the new requirement is simply an outcome of the delayed filling of the 4f sub-shell. In this light, the merits of their proposal are not apparent.

Tsimmerman and Boyce (2019) argued for Lu in group 3 on the basis of the regularity of spin multiplicity, which is one of the three components of an element’s spectrographic term symbol. Unfortunately this argument introduces an anomaly in the overall regularity of term symbols.

Alvarez (2020) supports Lu on the basis of trends in atomic size, coordination number, and relative abundance of metal–oxygen bonds. However, the trends involved apply regardless of whether Lu is under Y or at the end of the f-block, after Yb.

Other than to provide necessary context, I will not further revisit Lu in Group 3 arguments.

”

I haven't received feedback from referees yet. Double sharp: As usual, I'm behind in responding to your comments.

--- Sandbh (talk) 05:00, 29 April 2020 (UTC)

@Sandbh: All I see is that Lu arguments are attacked and dismissed (sometimes on spurious grounds, e.g. Alvarez, where you ignore that the point is that La does not fit into any of those 5d trends at all), and the elephants in the room torpedoing the La arguments (i.e. they are totally local and cannot be applied anywhere else to give a coherent periodic system) are never mentioned. I insist: the only way to be fair is to start from the attitude "OK, tradition counts for nothing in science, we'll pretend we don't know what element should go under yttrium, and use what we know about the rest of the table to figure it out". If you're going to treat the Lu arguments like this and then not revisit them again, then R8R's criticism remains valid: your treatment is ~~unfair~~ unequal between the sides. And Droog Andrey's and my criticisms remain valid too: your arguments are logically flawed. Every La argument that has been addressed here either has false premises or is logically inconsistent. Double sharp (talk) 08:20, 29 April 2020 (UTC)

@Double sharp:Yes, that is why I asked for your views on the article. Sandbh (talk) 05:19, 2 May 2020 (UTC)

@Sandbh: Well, you have them: in my view, your arguments are logically flawed and your approach is not sound. Double sharp (talk) 05:22, 2 May 2020 (UTC)

@Double sharp: So noted. Sandbh (talk) 23:37, 2 May 2020 (UTC)

I'd like to clarify what I said and what I did not say. I said it looked like treatment of pro-La-Ac and pro-Lu-Lr arguments was not equal. I don't think this is fair or unfair, because that word implies some emotional attachment. I'd rather say it's unfortunate to emphasize how I think the thinking could be improved.

@R8R: So noted; changed it to "unequal between the sides". If that's still not a correct description of what you mean, just tell me and I'll change or remove it. Double sharp (talk) 05:24, 2 May 2020 (UTC)

The new version is good enough; I agree with that.--R8R (talk) 15:07, 2 May 2020 (UTC)

I was not rushing to accuse Sandbh of being unfair because I, while disagreeing, thought that this thinking is honest. I'm not saying this because that would make me look polite or because I'm afraid of confrontation: I mean what I said, even when I happen to disagree not just with the outcome, but also with the thinking itself. And I said before, Sandbh is trying his best, and one can only do so much in science. In that respect, I think similarly of Double sharp's thinking. I also think that not only I can disagree with someone, but I also find it important to remember that others can disagree with me, and their ideas are valuable in that case, too.

However, when I said that it looked like the two options were not judged equally, I got an upfront "that's right." I was expecting to hear something like, "I tried and this is just what it looks like," something that does not resemble what I said. I can only resort to that the quoted piece of introduction is up for interpretation. I am most certain Double sharp could write something like that but for -Lu-Lr. "Vernon (2020) notes that Ce³⁺ through Lu³⁺ have 1 through 14 f electrons, which is a good resemblance of a block. However, you look at atoms rather than ions elsewhere in the periodic table to define a block, and it remains unclear why this case should be an exception." And no agreement could ever be reached unless one side resigns from discussion, or unless the tactic is changed.

To resolve an argument, I'd propose first determining the criterion which allows us to say something is right or not. And if a solution is truly sought, I'd heartily propose establishing that common sense of criteria before applying it to both options. (Maybe that's been tried, please tell me if it has, this discussion is getting so out of hand with its size I couldn't possibly tell.)

What's the difference between an article that is set to put -La-Ac over -Lu-Lr and an article that is set to put phlongiston over oxygen burning? We wouldn't write a latter one today because we know that an equal approach would debunk the phlongiston concept. Is -La-Ac strong enough to stand a similar test from -Lu-Lr?--R8R (talk) 20:16, 29 April 2020 (UTC)

As for criteria, for me it is utterly simple: La and Ac have f involvement of the same kind as that of Th, therefore they have to all be in the f-block or all be out. Lu and Lr don't have any significant f involvement, they cannot be in the f block. That's just consistency and making the word "block" actually mean something. When I was arguing for Sc-Y-La, it was because my understanding then was that La and Ac did not have that, that Lu also had possible f involvement, and that chemical resemblances led to a break after group 3. If those were true, Sc-Y-La would indeed be preferred. Now I know all three of those are false, so I changed to Sc-Y-Lu. Double sharp (talk) 05:27, 2 May 2020 (UTC)

@Sandbh: Note, I suppose to some extent I come across as having the opposite bias towards Sc-Y-Lu. And certainly I have some such unconsciously even if I try not to let it come out. But I try to take the La arguments seriously. I don't brush them aside, I take them as they come and refute them logically. Either by noting that they are based on false premises (e.g. ionic vs. covalent or main-group vs. transition supposed dichotomies), or that they produce nonsense when asked to arbitrate other cases (e.g. Be-Mg-Ca or Zn, B-Al-Sc or Ga, the 4d or 5d elements).

This comment seems to imply, at least to me, that no matter how strong the Lu arguments are, they can always be brushed aside because of the inertia of the textbook literature. Well – as I have demonstrated, the d-orbital explanation of SF₆ is in the same situation: not taken seriously by any reliable sources, but often taught anyway (maybe as a lie to children to explain the difference between O and S, although there are honestly better explanations for that). Do we propose to plaster that refuted theory all over Wikipedia?

In science, tradition cannot count for anything if we learn something that refutes it. Well, probably the La table got there because of the old idea that the f block was a degenerate one-off branch of the d block and that the elements following Ra were normal transition elements. And then it got some more inertia because of wrong electron configurations. Both of those are wrong, so we cannot come to that conclusion that way. That's not to say that there are no conceivable strong arguments for the La table, but these are not among them. Neither are all the double-standard arguments that neglect f involvement in La and Ac because of their accidental gas-phase configurations, and then immediately backpedal on Th to say "oh, I guess that one has f involvement after all". You don't get to do that in science.

So far, I still don't see anything in the La table. Just look at the statements in appendices II and VII, even leaving out the ones we are arguing about and marked as contentious if you wish. Do you see a single one of them that actually supports La under Y? Double sharp (talk) 04:55, 27 April 2020 (UTC)

(*) @Droog Andrey: Thanks to you, I am aware that high-school-style hybridisation is not the final word here, and that MO theory gives a better explanation of SF₆. However, the ideas that the "average" S–F bond order is 2/3, that the bonding is thus electron-deficient, and that S 3d has basically zero involvement to the bonding are predicted by the resonance-structure explanation and are confirmed by more accurate MO theory (well, I do not really understand it, but thankfully this is a common example molecule and therefore I can at least Google what it predicts), so in this case my point should be borne out. Simplifications are all right for the basic level if they at least give the right predictions, in my opinion, and so I think it's miles better to teach high-school chemistry students the resonance octet-respecting explanation rather than the one that magically invokes d orbitals to expand the octet. ^_^ Double sharp (talk) 03:31, 23 April 2020 (UTC)

Meanwhile, arguments like Restrepo's are exactly also pop-gun one-shot pronouncements, but Sandbh does not make any notice of this. Note the complete analogy:

Restrepo: "According to our results, La appears in between two clusters, one of 11 lanthanoids and another of transition metals, namely {Y,Sc}. Lu is part of the clusters of 11 lanthanoids and the smallest cluster containing it is {Ho,Er,Lu}, which shows that Lu is more similar to lanthanoids than to transition metals, while La share similarities with lanthanoids and with transition metals. Therefore La must be the element located at the beginning of the third row of transition metals if chemical resemblances is what it is to be emphasized."

Merz and Ulmer (10.1016/0375-9601(67)90527-0): "This X-ray spectroscopic result shows clearly, that Lu, but not La, has the typical behavior of a transition metal in the structure of its conduction band. Arrangements of the periodic table, which ascribe Lu to the transition metals and not to the lanthanides, are therefore favored by this isochromat spectroscopic investigation."

Double standard to port, ahoy! Double sharp (talk) 16:47, 29 April 2020 (UTC)

@Double sharp: Double standard indeed! Pot calling the kettle black!

Here's the rest of what we said about Merz and Ulmer:

Analysis: We have no reason to question Merz and Ulmer's observation that La's conduction band does not have a typical d block like structure. This may be associated with the presence in La of a low-lying nonhydrogenic (unoccupied) f orbital. Even so, the significance of such an atypical structure is not clear to us since La still has the high density of states that are characteristic of transition metals (Goncharova & Il'ina 1984, p. 995). And while Lu may have a conduction band structure that is more characteristic of transition metals such as Hf, we do not think this is especially notable, given conduction band anomalies elsewhere in the periodic table. For example, the conduction bands of the heavy alkali metals exhibit anomalous behaviour due to the presence of empty d bands, whereas this is not the case for Li and Na (Smith et al. 1993). The conduction bands of the group 3–10 transition metals are characterised by complex interactions between s electrons and their partially filled d subshells whereas this is not the case for the group 11 coinage metals due to presence of a filled d subshell hence the latter metals exhibit high electrical and thermal conductivity (Russell & Lee 2005, p. 302). Bismuth, being a semimetal in the physics-based sense, has a conduction band structure atypical for other p-block metals. In the case at hand, while Sc, Y and Lu have similar conduction bands whereas La does not, this is not necessarily significant. Elsewhere in this submission we have questioned the non-critical application of shared properties as a determinant of group membership, for example with respect to the crystal structures, and we think this is another example (of an inconclusive argument).

At any rate, x-ray isochromats of Gd to Lu do not support Merz and Ulmer's conclusion that Lu is more favourably placed in group 3. Bergwall (1966) recorded these and found that they were rather constant, "which on account of the atomic configuration in these elements is expected." (p. 13) In other words, over half the lanthanides–not just lutetium—have conduction band structures that are more characteristic of transition metals such as hafnium. This means that there is nothing particularly unusual about Lu being positioned in the f block and it may be that the atypical conduction band structure of La is no more than a one-off outcome of the imminent 4f collapse that will happen one element later at Ce.

Merz and Ulmer = another pop gun! Sandbh (talk) 05:36, 2 May 2020 (UTC)

@Sandbh: Glad you quoted it. Because I agree with the first paragraph: this is not a very useful argument in the absence of explanations of why this might be a good way to test f orbital population and usage. La vs Lu is a question about blocks and therefore electronic structure, and it is not clear why this is relevant without such explanations. And as we pointed out with regard to group 11, there is even a case that it might not be. So I agree that there is a question mark hanging over this argument. It may work, but before using it there needs to be a strong case made for f orbitals being the culprit for La's conduction band structure.

But I strongly disagree now with the second paragraph. The point is that only La and Lu can possibly fit under Y. So we need to ask which one is more similar to the transition metals. Granting the relevance of this property for the sake of the argument, it would be Lu, and therefore the isochromats of Gd to Yb do not matter for this. In all arguments that consider properties of the 5d metals and show that Lu is more similar to them than La, it does not matter what the other late lanthanides do, as they are not candidates for the eka-Y position. The point is not the trend in the late lanthanides (which looks OK physically no matter what you do with it), it's about whether the group 3 trend looks anything like a normal d-block trend or not. So this is not a problem with the argument; only the first one is.

So, as you can see, I am still totally willing to poke holes in Sc-Y-Lu arguments that are logically incomplete. Before Merz and Ulmer's argument becomes ready for use, one would need to first establish whether f orbital usage is the culprit for La's conduction band structure. In general, when using these kinds of arguments that say "look, Lu is so much like a transition metal and La isn't", one must first argue from other means why the f block filling starts at La, in order to refute the objection that if 4f started after La, we would expect La-Hf to show a difference. I have taken that bull by the horns already, pointing to 4f involvement in La in a much more direct manner. That's how you argue for the group 3 issue; you recognise the point of it (it is an electronic issue) and use the facts of electronic structure to argue, and then argue that your way produces superior trends and is hence borne out. That's how you create something holistic instead of pop-gun one-shot pronouncements.

All this being said, you're missing the important point: if Merz and Ulmer is a pop-gun, then so is Restrepo. There is also no sense here of why this argument is relevant to electronic structure. Indeed, as I've mentioned before, it is even incomplete and will never find any resemblances that cut across valences. Why's his argument treated differently to Merz and Ulmer's? Double sharp (talk) 05:45, 2 May 2020 (UTC)

@Double sharp: Oh, well, I believe I applied the pop-gun label only to the Lu arguments in the literature, aside from Jensen's 1983 article. Restrepo is not quite in that league since he looked at all the elements, rather than just La or Lu. And then, as one observation among many, he noted that his results seemed to support La. Sandbh (talk) 23:45, 2 May 2020 (UTC)

@Sandbh: I know you applied it to only the Lu arguments. I'm saying that you should have realised that the same is true of most La arguments. Restrepo looked at all the elements indeed, but in the context of making a pronouncement on Sc-Y-La he saw fit to only consider La and Lu. So it's exactly the same. Of course, we know that his results are not adequate for addressing this situation, and that a real holistic comparison will always show Lu as closer to the indisputable 5d metals than La. But the point is that this is still a pop-gun pronouncement as well. You're not going to get out of that until you look holistically starting from your definition of a block since that is what is at stake here. Of course, once you do that with the real facts of chemistry, you will soon find it extraordinarily difficult to find a self-consistent way to get La under Y. ;) Double sharp (talk) 05:36, 3 May 2020 (UTC)

Y, La, Ln trifluorides

In this article the author observes (p. 715) that trivalent Ln (the normal valence for Ln) have no s and d valence electrons and contain only f electrons.

He also divides the trifluoride of the REM, having regard to f-electrons, into Ce-Gd, and Tb-Lu subsets, and then into the following sets:

La Ce-Nd|Pm-Gd
   Tb-Ho|Er-Lu Y
   ^^    ^^ ^^

The circumflexes are my own and correspond to the start, quarter, halfway, three-quarter, and full lines I drew on the G&E chart, thus:

La Ce-Nd Pm-Gd|Tb-Ho Er-Lu Y
   ^^    ^^ ^^ ^^    ^^ ^^
   1     4  7  8     11 14

--- Sandbh (talk) 05:39, 29 April 2020 (UTC)

@Sandbh: I see just the usual wrong statements here based on a misunderstanding on the significance of the 4f subshell of La. And what's especially funny is that the figure of periodicity does not give double periodicity so much as a separate "tetrad" effect: La-Nd, Pm-Gd, Tb-Ho, Er-Lu. What if anything this really has to do with double periodicity is not clear, given the mismatches and the slipperiness of the tetrad (Er can go with Tb-Ho sometimes, too). Double sharp (talk) 08:11, 29 April 2020 (UTC)

@Double sharp, R8R, and Droog Andrey: As a guiding principle, most scientists prefer to adopt the simplest valid explanation that fits observations. That's the approach I've been attempting. Sandbh (talk) 05:26, 2 May 2020 (UTC)

@Sandbh: The little problem with that is that Sc-Y-La does not fit these observations. There isn't a double periodicity here as it's been swamped by other factors. And when there is one, Sc-Y-Lu makes a more fitting double periodicity. Double sharp (talk) 05:28, 2 May 2020 (UTC)

I understand that this is your intent; it was when until I have understood this that I finally perfectly understood your general argument. I think, however, that Double sharp said a very smart thing during this discussion: it should be as simple as possible, but not simpler than that. I have gotten a few times these vibes that simplification at times becomes oversimplification at some moments and this negatively affects the thinking. (I can't bring up an example off the top of my head, but if I have to, I can look through the discussion and recall a few moments that gave me that feeling.) That's why I said I thought the thinking could be improved.

The question of what is oversimplification and at what point simplification becomes oversimplification is, naturally, a rather arbitrary one, as is the general question of whether La or Lu should be put under Y. If an answer is to be found, it will be a convention, not a secret truth uncovered, so there is some room for you to disagree with Double sharp and for Double sharp to disagree with you, and for neither being wrong. And of course, I am fully conscious that your thinking about your thinking could be different from mine, and that I'm not right by the mere virtue of it being me who thinks that. I don't think anybody is really right here at all (we're aiming for a convention, after all), and that includes me, but I'm trying to give a few hints for how a group of people could possibly come to a convention and agree to it.

From the quoted article, I see that making big conclusions based on it is not advisable. Let's look at the article critically. The article does claim that the La goes under Y and even devotes some room to discussion of classification of the REMs. However, it is only briefly explained that La is a d-block despite the obvious and noted violation of the Klechkovski's rule there and that most lanthanides don't have a 5d electron in the ground state. The only argument in favor of his conclusion is that trivalent ions show a progression from 1 to 14 from Ce to Lu. That's the observation you have referred to in the beginning of this level 4 section. I have always disliked this argument because it is used in this part of the periodic table only. How do we apply a uniform oxidation state to the preceding 6s series? Or the following 5d series? Or, in fact, any other series? Looks like a very ad hoc solution to me, and its credibility is seriously damaged by that. The article doesn't say a single word to comfort my concern. More importantly, Double sharp would surely say the same (though I'm eager to stand corrected on this if mistaken), and it's him that you're primarily having this discussion with; do you think that observation had any chance of changing his opinion?

(Yes, I would say the same. ^_^) Double sharp (talk) 13:20, 3 May 2020 (UTC)

But closer to the point. The author took that as a presupposition, even though he noted that "the REE classification (position of lanthanum) remains controversial." He got some results with that presupposition in mind. Now to have a proper comparison, we would also need to assume the "Lu goes under Y" presupposition and see what it gives us. The author did not do that, however, so no conclusion can be made just yet from his article alone.

So even if the author agrees with you or G&E or whomever, if a point has not been made properly, it has not been truly made, even if it can be made correctly; in that case, it should be made correctly. Even if the final result is correct, this solution would never be accepted; the same applies here.--R8R (talk) 15:05, 2 May 2020 (UTC)

@Double sharp, R8R, and Droog Andrey: In this paper, doi:10.1039/C3CP50717C the authors write:

"The Ln–F interaction is basically ionic (increasing with decreasing ionic radii) with some dative Ln³⁺ ← F^– bonding. The latter is of the Ln(5d)–F(2p) type with a rather constant bond order from La to Lu, with small Ln(5p) and very small Ln(4f) semi-core contributions decreasing from La to Lu. All these trends are rationalized.

"The Mayer bond orders indicate a rather constant Ln(5d)–F(2p) covalent contribution of about 0.15 and a smaller Ln(4f)–F(2p) contribution that decreases from La (0.06) to Lu (0.03). All other overlap populations are smaller."

Does this count as 4f involvement in La and Lu? Sandbh (talk) 06:20, 12 May 2020 (UTC)

@Sandbh: Only for La. I analysed this paper already at Wikipedia_talk:WikiProject_Elements#Some_wonderful_quotes_supporting_Sc-Y-Lu, so you can read that. Bear in mind that the M(4f)-F(2p) contribution is actually higher for IrF₃ than for LuF₃. XD Double sharp (talk) 06:23, 12 May 2020 (UTC)

Double periodicity

@Double sharp: A nice chart, showing much regularity:

steady increase followed by a divalency crash and +3 rebound in the two tranches Ce-Gd, Tb-Lu
double periodicity
outlier status of La and loss of double periodicity
consistent with Restrepo.

--- Sandbh (talk) 03:17, 5 May 2020 (UTC)

@Sandbh: I'd rather accept La in the tranche, deal with the slight outlier status (no doubt because the 4f collapse is in the middle of happening there), then force those huge gaps Eu-Gd and Yb-Lu into the tranches. One anomaly rather than two. Especially since everyone can see that a divalency crash ought to happen when the half- and fully-filled subshells are reached, because those are the stable ones that are hard to take another electron out of: just look at the 3d row. Having them at the penultimate members of families is nonsensical. The rebound does not belong in the tranches. Double sharp (talk) 03:33, 5 May 2020 (UTC)

@Double sharp: Well, there are no anomalies in the current chart. They're eminently understandable. The simplest valid explanation that fits the observations. If you accept La in the tranche than you have an anomaly. Your supposition is conjecture rather than explanation of what's going on. And you lose double periodicity, big time. And who says, and why is it, that the rebound does not belong in the tranches? --- Sandbh (talk) 08:13, 5 May 2020 (UTC)

@Sandbh: It's obvious why: I explained it already.

A divalency crash means that only the outer s² electrons are easily ionised. (Because it means that the energy needed to ionise the third electron is so high that it isn't compensated by the stronger metallic bonding that results if you do it.)
Which implies that the filling subshell below has reached a point that is hard to take more electrons out off, i.e. either halfway f⁷ or all the way f¹⁴. Because we know there is no d electron hanging up. Not unless you want half a p electron hanging up, too.
And that is the definition of where a tranche ought to end.
So, the double periodicity makes sense and is simply explained with tranches La-Eu and Gd-Yb: in both cases, the tranche ends sensibly with the divalency crash. Just like Sc-Mn and Fe-Zn.
Tranches Ce-Gd and Tb-Lu are simply nonsensical.
The La anomaly is a small one compared to this big one that makes the Ce-Gd and Tb-Lu tranches nonsensical. Therefore, La-Eu / Gd-Yb tranches are much better because they have one anomaly rather than the horribly big double anomaly of Ce-Gd / Tb-Lu, where we have a nonsensical rebound instead of a collapse at the end of each tranche.

4f as an explanation for La's anomaly is my conjecture indeed, but my tabulated data for the actinides below with an even slower 5f collapse makes it seem pretty plausible. Notice what happens past uranium when 5f and 6d become about the same level. You can also see that in the melting point trend of the 5f elements. ;) Double sharp (talk) 10:15, 5 May 2020 (UTC)

For reference, here are the bulk moduli of the d elements:

Sc	Ti	V	Cr	Mn	Fe	Co	Ni	Cu	Zn
57	110	160	160	120	170	180	180	140	70
Y	Zr	Nb	Mo	Tc	Ru	Rh	Pd	Ag	Cd
41	91	170	230	281	220	380?	180	100	42
Lu	Hf	Ta	W	Re	Os	Ir	Pt	Au	Hg
48	110	200	310	370	462	320	230	180	25

We see drops at the fully-filled subshell. And, for 3d where the double periodicity is strongest (it is weak for the other rows), also at the half-filled subshell. (If you insist on La, the value is 28 and as usual a worse fit with the other 5d metals.) The idea that a crash and rebound is "regularity" is nonsensical once you think about what the end of a tranche should mean.

(The value for Rh is doubtful, hence question-marked.) Double sharp (talk) 10:25, 5 May 2020 (UTC)

I was curious how the actinides looked. There the divalency crash only happens in full force at the end of the series, and we have a long period at the start where the 5f collapse only happens quite slowly. Mostly there is no data, but there are speculations for Young's modulus. When Young's modulus was unavailable, we use bulk modulus, as they are quite similar:

Ac	Th	Pa	U	Np	Pu	Am	Cm	Bk	Cf	Es	Fm	Md	No
~16	79	~116	208	~198	96	~45	~37	~20	~50	~15	~15	???	???

So, here we see the long drawn-out effects of a slow 5f collapse. And no, I didn't make up that explanation, here's a paper quoting 5f for what's going at Pu. The early actinides are very high as many electrons (even 5f) are in the valence band; then later we get to a situation more like Ce once 5f starts going below 6d. First we get hybridisation, and then we enter the regime where they are basically inactive and we're back to a La-Eu type trend. Only in this case the divalency collapse already happens at Es (I am not sure the Bk value is right, I would expect ~40. I guess these are hard to measure for obvious reasons.) No doubt trivalent Lr will look equally nonsensical at the end of the series, thus constituting yet another strong argument for the f-block to begin at La/Ac, absolutely not Ce/Th. Double sharp (talk) 03:42, 5 May 2020 (UTC)

@Double sharp: Here’s a literature extract illustrating simplest sufficient complexity:

“The justification of dividing lanthanides into two groups is confirmed by secondary periodicity. It consists in the fact that variations of properties in the first subgroup (from Ce to Gd inclusive) are repeated in the second (from Tb to Lu). Probably, the secondary periodicity is most vivid in changes of lanthanides of the first and second subgroups to manifestation of non-typical oxidation states. The elements of the second subgroup less tend to exhibit non-typical valences than the elements of the first one.

In the sixties knowledge about a more complex classification of lanthanides began developing from properties of their compounds. Three areas of the mentioned “crystallochemical instability” were singled out (Bandurkin I964; Bandurkin, Dzhurinskii, 1966), then came the “tetrad”-effect (Peppard, Mason, 1969) and later “W-effect” (Fidelis, Siekerski, 1971). These more detailed divisions of the lanthanide series, except exhibition of areas of “crystallographic instability " in LnF₃ were not significant, that is why such effects are not considered in this book.”

Sobolev BP 2000 The rare earth trifluorides: The high temperature chemistry of the rare earth trifluorides, vol. 1, Institut d'Estudis Catalans, Barcelona, pp. 44–45

Sobolev refers to these other divisions as being “more complex” and “more detailed”, and then moves on.

Just so Dr Sobolev.

PS: Supposedly, during the moon program, the US developed a ball point pen that could write upside down in a low gravity environment. The Soviets used pencils. Sandbh (talk) 12:57, 5 May 2020 (UTC)

@Sandbh: The problem with the first statement Sobolev makes is that the exact same thing is true with La-Eu and Gd-Yb as your tranches. Such tranches are just as simple and always work better.

P.S. That story is a myth. Originally both used pencils, but there is one little problem with them, to quote the article: "Pencils may not have been the best choice anyway. The tips flaked and broke off, drifting in microgravity where they could potentially harm an astronaut or equipment. And pencils are flammable--a quality NASA wanted to avoid in onboard objects after the Apollo 1 fire." So, later both the US and the Soviets used space pens. Remember what I said: as simple as possible, but not simpler! ;) Double sharp (talk) 13:52, 5 May 2020 (UTC)

@Double sharp: There is no issue with Sobolev's opening statement. If you make a decision about the the definition of where a tranche ought to end, fine. Another issue you'll have to contend with is no such definition of where a tranche should end is in the literature. Sobolev was only continuing the work of Klemm, Remy, and their successors (inc. C&W, G&E, and Wiberg). None of them said there was a fixed definition. Rather, they made their observations based on what looked s/f to them.

As to the simplicity of La-Eu, and Gd-Yb, I noted the La anomaly and the lack of double periodicity. Those things are absent in Ce-Gd, Dy-Lu. No explaining away required. No artificial definition required. No apologizing for a required anomaly. No need for hyperbole such as, "always work better". Only the simplest explanation for the observable facts, which may not work better in all cases as Sobolev observed, but works well enough.

The moon program anecdote, funny as it is, doesn't require deconstruction (the trees). The notion (the wood) it was illustrating is the key message. Sandbh (talk) 08:00, 6 May 2020 (UTC)

@Sandbh: Nope. I deconstructed it to give my key message: make everything as simple as possible, but not simpler. Well, La-Eu and Gd-Yb works well enough in almost everything, and when it doesn't quite work, there's a plausible reason. Whereas Ce-Gd and Tb-Lu has some serious explaining to do regarding why the supposedly stable half-filled subshell does not lead to a divalency crash like it should looking at Mn and Zn. That's the one that requires apologising, not La-Eu and Gd-Yb.

Do you think a tranche is just formalities? The whole point of drawing double periodicity tranches is that they ought to end at the half-filled and fully-filled elements. If you deny that definition, you're also denying whatever bearing this could possibly have on the group 3 question. ;) Double sharp (talk) 09:28, 6 May 2020 (UTC)

@Double sharp: This is just a difference of opinion, IMO ^_^ I say "simplest sufficient complexity". You say my simplest is too simple, never mind my additional qualifier of "sufficient". That's all it is. In the case of tranches ending at half-filled and fully-filled elements, this is what happens in the chart in question. Gd is the first Ln with 4f⁷; Lu is 4f¹⁴. Eu and Yb, in contrast are 4f^<7 and 4f^<14. In any event, we aren't really seeing the impact of a half-filled or filled sub-shell so much as we seeing, in the case of Eu and Yb, the assignment of only two electrons to bonding, hence the reductions in mechanical strength.

In the case of 3rd IE, we see the crash at Gd and Lu. In the case of 2nd IE for the 3d metals, we see the crash at Mn and Zn. Easily explainable; no La anomaly needing to be explained away.

Yes, the position of the dips will move around, depending on the property in question. Sandbh (talk) 03:27, 7 May 2020 (UTC)

@Sandbh: But that is not what happens. You say that Eu and Yb assign only two electrons to bonding, which is correct. Now, have you thought about why they do that? Very simple, it's because doing so leads to a half-filled or fully-filled subshell, and it's then not worth it to get rid of the third electron. Now, what does that remind you of: Cr and Cu, or Mn and Zn?

I insist: you must look at the 3rd IE for everybody. That's the only fair way, because it corresponds to getting rid of the outer s² electrons. There is no other covering shell. The lanthanides do not have a d-electron hanging up, they are getting their third electron by the 4fⁿ⁺¹-4fⁿ motif out of the 4f shell. There will always be some little anomalies after that, but I insist first on consistency to get rid of the great big anomalies that Eu and Yb are on your chart (in the wrong place, as I've just explained). Double sharp (talk) 03:55, 7 May 2020 (UTC)

@Double sharp: So, the position of the dips does not move around. Says who?

There is no need to ionise away the outer s² electrons. As I understand it, the s shell is only weakly occupied; it contributes only weakly to bonding, as in the other f-elements. There is no "big" anomaly here. The more important consideration is to compare like with like i.e. stable oxidation states. That is simple enough to be taught by textbooks in classrooms and realistic enough to be acceptable by practicing chemists. Sandbh (talk) 07:55, 9 May 2020 (UTC)

@Sandbh: Says the analogy. Well, do they move for 3d? No, it's always Mn and Zn that are the crashes for any physical property. And any natural chemical property using the most sensible +2 oxidation state, which is the only one that matches the physical properties. Funnily enough, in the 4f row only using +2 makes the crashes match the physical properties, never +3. XD

And of course, stable oxidation states are definitely like with like. So much so that they are almost always not the same for consecutive elements, let alone a whole row. And will never let you decide anything outside the 3d and 4f rows. XD Double sharp (talk) 09:44, 9 May 2020 (UTC)

@Double sharp: I cannot remember seeing +2 for 4d, aside from the 2nd IE. Yes, they do move around for 3d, depending on the the property. Sandbh (talk) 06:59, 11 May 2020 (UTC)

@Sandbh: Just plot any physical property along the 3d row, you'll always see crashes at Mn and Zn. And on 4f you'll always see them at Eu and Yb for physical properties.

You can make the gaps for chemical properties move indeed, but only by being unnatural about what state you pick. I can plot 2nd IE for all elements and say that the period divide should obviously be between group 1 and group 2. But you can obviously see that's completely unnatural by looking at the physical properties and seeing where the caesura obviously runs. Well, just do the same thing here, you'll see Mn-Eu and Zn-Yb analogies for physical properties all the time. Double sharp (talk) 07:17, 11 May 2020 (UTC)

Appendix V: Shielding effects

The end of a block should signify what orbital will be giving the incomplete shielding effect for the next elements, except for the s block (which sticks around as a chemically active valence subshell for the rest of the period – or almost there, for period 7).

For H and He, there is no preceding end-of-block element, so there is nothing between the valence electrons and the nucleus.

For Li-Ne, the preceding end-of-period element is He 1s², so the 1s electrons are doing the shielding. (And a very good job they do, too.) Normally the s electrons would hang up to the end of the period and keep being chemically active, not falling into the core (this is the symmetry break from pure n+l as shown in Charles Janet's table). But here they are the end of the period. The difference in shielding quality of 1s vs. nsnp is important enough to consider drawing He atop Be instead of Ne a sound approach.

For Na-Ar, the preceding end-of-period element is Ne 1s²2s²2p⁶; and for K-Zn it is Ar [Ne]3s²3p⁶. But then something interesting happens. For Cu and Zn, the 3d orbitals are chemically active. (Even for Zn they are clearly contributing as part of the valence band, as demonstrated above. In fact, there are predictions that oxidation states above +2 should be reachable even for Zn, see doi:10.1021/ic702384y.) But for Ga-Kr it forms part of the core, which is now [Ar]3d¹⁰. This follows the principle stated in the first paragraph: the d block is over, so for the following elements it gives only incomplete shielding effects as part of the core. The same kind of thing happens over the fifth period: the core is [Kr] until Cd, whereupon it becomes [Kr]4d¹⁰.

Now the test: the sixth period. In a Lu table, we expect from this that the 4f shell should be last active in Yb, and be an inactive core subshell for Lu-Rn that only gives incomplete shielding effects. In a La table, we would expect the 4f shell to be last active in Lu, and only become an inactive core subshell for Hf-Rn.

No prizes for guessing which one matches reality: the Lu table. The core sequence is [Xe] for Cs through Yb; then [Xe]4f¹⁴ for Lu through Hg; and then [Xe]4f¹⁴5d¹⁰ for Tl through Rn. The same thing happens in the seventh period, with the exception that due to relativistic effects, 7s doesn't last all the way to Og. But that doesn't really do much violence to the structure, as s was always the exception in the first place.

(Due to relativistic effects, I have intentionally not considered the 8th period very much. The reason is that we don't really know when the deadline beyond which 5g goes inactive probably is, and that we have a unique situation where the covering shells now include two types of spherical shell, that switch from 8s and 8p_1/2 at the beginning to 9s and 9p_1/2 at the end. The pattern still works approximately, however, with the same thing at least going on for when 6f, 7d, and the combined p subshell should become inactive.)

So, here we have another case where the flagrant irregularity created by the La table ends up destroying the relations between global considerations of periodicity, that are preserved by the Lu table. Double sharp (talk) 04:56, 19 April 2020 (UTC)

I basically agree, except for the unnecessary hyperbole regarding flagrant irregularity and the destruction of relations to do with global considerations of periodicity.

It is one way of interpreting the end of a block, as Droog Andrey noted with the pattern in electron affinity values. Thus, the very low EA values in group 2; Yb-No; group 12; and group 18. Is it the most chemically relevant? By no means, given the similarity of Lu to Ce to Yb. We can see this, for example, in the EA x orbital radius table, where the gap between La and Ce, and rest of the Ln is consistent with Restrepo (who supports La in group 3). Sandbh (talk) 08:15, 19 April 2020 (UTC)

Claiming that Lu is similar to Ce to Yb is true, but not the full story, as we said a lot in the old group 3 submission that I now entirely disagree with. Exactly the same could be said of La. Notice that in your table, both La and Ce are outliers, which surely weakens the idea that only La fits poorly with the lanthanides.

As everyone would have expected, since the properties of the lanthanides vary approximately linearly as long as their f occupancy isn't changing, La and Lu both stand out as the most extreme lanthanides in opposite ways. Lanthanum is the most reactive among the trivalent ones (the divalent ones meaning Eu and Yb, which are divalent as pure metals and hence not directly comparable); lutetium is the least. Lanthanum is the softest trivalent one, lutetium is the hardest. Lanthanum is the least dense among the trivalent ones, lutetium is the most dense. Lanthanum is the most basic, lutetium is the least. Lanthanum has the lowest atomic weight, lanthanum has the highest. Lanthanum forms the largest Ln³⁺ cation, lutetium forms the smallest. So no amount of looking at the lanthanides is ever going to tell you which one ought to be taken out of the 4f row, as they both continue the trends reasonably well. So you look at the 5d row as the next level of chemical and physical arbitration: which one has behaviour that better befits the 5d¹ position in the d block full of sturdy, hard, dense, usually pretty high-melting (leaving aside group 12), and not terribly reactive metals? The answer reveals itself immediately: lutetium fits better among the uncontroversial d metals than lanthanum in every way. Which is confirmed by the total lack of significant 4f valence activity in lutetium, and its presence for lanthanum. Double sharp (talk) 09:54, 19 April 2020 (UTC)

@Double sharp:. Restrepo noted Ce was a bit of an outlier too.

Yes, agree La and Lu are outliers. Lu is of course, closer to the 5d metals. This is due to the intervention of the 4f series. One can equally explain that is why La is not as close to the 5d metals, due to the intervention of the 4f series. In that sense, the 4f series does not favour either option. Of course, one then has to look at other means of chemical and physical arbitration. While 4f involvement may be present in La it's a relatively minor consideration, in my view of course. A tipping point argument as we said. Sandbh (talk) 08:15, 20 April 2020 (UTC)

@Sandbh: And of course cerium is an outlier because it is one of those with a common additional oxidation state. So is europium, for that matter. That's why I talked about the trivalent lanthanides above.

The first argument doesn't work precisely because 4f involvement is present in lanthanum. Ergo, the 4f series begins there. And we see Yb has finished filling the 4f shell, Lu doesn't use it anymore, so the 4f series ends at Yb. So it's already a slam-dunk for Lu purely from electronic considerations of the 4f series. I disagree that 4f in La is a minor consideration. In fact, it permeates all of lanthanum chemistry, as demonstrated ad nauseum above. It is in pretty much the same boat as 5f in thorium: not there in the ground state, but self-evidently low enough in energy to contribute chemically. There's no way you can exclude f involvement from lanthanum and actinium, and yet say that thorium has f involvement after all, without creating a double standard. Double sharp (talk) 09:43, 20 April 2020 (UTC)

@Double sharp: We know it is true that:

Restrepo:
- shows La and Ce as outliers
- does not show Eu as an outlier
Th has 4f¹ chemistry of its own as Th³⁺.

On La and Ac I'd be pleased to learn of a La compound in which it is attributed as having a 4f electron of its own. Sandbh (talk) 10:59, 22 April 2020 (UTC)

@Sandbh: Here you go: LaS and La-Ni intermetallics show telltale evidence of 4f hybridisation. And this one's even better for supporting what I've been saying: "For the metals and intermetallics it is due a charge fluctuation from 4f⁰ to 4f¹ occupation, while in the insulating compounds such oxides, halides and sulfides it arises from an electron transfer from the ligand to the lanthanum 4f state".

I find it rather surprising that Restrepo doesn't find europium to be an outlier. Because for one thing, his approach is based on stoichiometry, and therefore the significant stabilisation of Eu(II) ought to do something. And even his chart, incomplete as his approach is, neatly packages the traditional divalent lanthanides {Sm, Eu, Yb} together at one end of that great big pile of lanthanides. Not that we can count it for much, because {Pr, Tb} are oddly far away from the other Ln and put together with some actinides. (They have a significant +4 state, but then one wonders why Ce isn't moved away too.) ;) Double sharp (talk) 12:10, 22 April 2020 (UTC)

@Double sharp: Thank you. I was hoping to learn of a La compound in which La is attributed as having a 4f electron of its own, rather than via partial hybridization or ligand donation.

Yes, I'm waiting for Restrepo to publish some more research.

His similarity landscape for the Ln goes:

{Ce}, {La}, {Nd-Pm-Dy-Tm}, {Ho-Er-Lu-Gd}, {Eu-Yb-Sm}…{Tb-Pr}

Here's a table of the clusters:

Cluster/s	Notes
{Ce}, {La}	Plausible
{Nd, Pm, Dy, Tm}	Nd(60)-Pm(61) are atomic number neighbours, two places after Ce(58) Dy-Tm occupy analogous positions in the sequence Tb-xx-Er-xx-Lu
{Ho, Er, Lu, Gd}	Ho(67)-Er(68) are atomic number neighbours, two places after Tb(65) Ho-Er-Lu have almost identical production, purification, and fabrication details Lu-Gd is as expected, and occupy analogous positions in the sequences Ce-xx-Pm-xx-Gd and Tb-xx-Er-xx-Lu
{Eu-Yb-Sm}	Traditional divalent Ln
{Tb, Pr}	Tb is the first Ln (after Gd) having no 5d electron Pr is the first Ln (after Ce) having no 5d electron There must be something more to it than that, I suppose.

Sandbh (talk) 04:12, 23 April 2020 (UTC)

@Sandbh: The problem is that you are just not going to find any such thing, because the idea of "there are multiple configurations very close to each other" permeates the f elements. As it does the d elements. Neither are you going to find any such thing for thorium, for that matter, so using it to deny lanthanum f block membership is the same old double standard Jensen complained about.

Citations: one, two, three. Low-valent thorium compounds usually have 5f⁰ 6d¹ or 5f⁰ 6d² even though those are not quite the ground states of isolated Th³⁺ and Th²⁺ cations (which, as usual, supports what I say about having to consider what are excited states when the cation is alone, because in chemical environments they might become the ground state). Thorium's f character is solely based on hybridisation in real chemical environments. So I stand by what I've been saying: it is absolutely a double standard to let thorium in the f block and keep lanthanum and actinium out. Either all three are out, or all three are in. Given the complete lack of f involvement in Lu, Lr, and Rf, it's obvious that the second option is far more preferable, leading to Sc-Y-Lu. Sc-Y-La is just inconsistent. Double sharp (talk) 04:25, 23 April 2020 (UTC)

P.S. I bet any rare earth chemist will tell you that the main outliers among the Ln are the ones with common oxidation states that are not +3. That's mostly {Sm, Eu, Yb} with +2, and {Ce, (Pr), (Tb)} with +4. Double sharp (talk) 05:21, 23 April 2020 (UTC)

@Double sharp: I think I've been deluding myself about Th. I need to check the Wiberg reference.

There is doi:10.1039/C6DT01111J (2016), the authors of which write:

"Snijders and coworkers first predicted a 6d¹ configuration for an organometallic An complex and Bursten further corroborated these results with calculations, showing that the highest contribution to the a′₁ orbital in [Th(Cp)₃] arises from the 6d_z2 orbital (89%). The energy of the 6d_z2 orbital in these systems rises across the An series with a corresponding decrease in the 5f manifold (Fig. 2). The 6d_z2 orbital was found to be further stabilised in C_3v symmetry; however, coordination of a neutral Lewis base L to [Th(Cp)₃] on the z-axis would lead to destabilisation of the 6d_z2 a′₁ orbital. Therefore the hypothetical complexes [Th(Cp)₃(L)], in approximate C_3v symmetry, are predicted to exhibit 5f¹ valence configurations.^{doi:10.1021/ja00190a002}

-- Sandbh (talk) 12:00, 23 April 2020 (UTC)

Yet another paper supporting La 4f: "The ground state of the La³⁺ ion is a mixture of the eigenstates 4f⁰ and 4f¹L (where by 4f¹L we refer to the state with an additional 4f electron and a ligand-hole in the case of the two compounds, and to the state with charge fluctuation from 4f⁰ to 4f¹ occupation in the case of the metal)." Note, by "the metal" they mean metallic lanthanum. Well, there's some really slam-dunk 4f involvement in La. ^_^

And more: LaO has 4f hybridisation on La²⁺. With how low-lying the 4f¹ configuration is I'm confident that there'll be a complex somewhere which does exactly the right thing to make it the ground state. (Not that that's actually needed to make it important, it just scores rhetorical points by making it even harder to deny the omnipresent 4f involvement in La.) And, sure, it will probably be pretty weird, but then so will be any such thing for thorium.

You still can't include Th in the f block and exclude La without creating a double standard. Double sharp (talk) 12:50, 23 April 2020 (UTC)

Actually, on glancing at the above: how exactly do La and Lu count much as outliers? They both continue the trendline admirably well, they just happen to be at the ends of it. You know, if you had a sequence of numbers that went 0, 1, 2, 3, 4, 5, all the way up to 14, it is not sensible to say that the 0 and 14 happen to be outliers for that reason. The correlation is perfect. If any one of those numbers got suddenly replaced by 248790296, then you could speak about a huge outlier. So lanthanum is the most extreme lanthanide chemically one way, and lutetium is the most extreme one chemically the other way. Big deal! It also doesn't tell us anything about what goes below Y because every lanthanide with an uncontestedly dominant +3 oxidation state makes a reasonable eka-yttrium if you pretend no other lanthanides existed. La below Y? Sure, it chemically makes sense. Lu below Y? Yes, also. Gd below Y? Yes, also. Ho below Y? Yes, also! And there are many cases where elements with strong chemical resemblances belong in different groups, just compare tungsten with uranium or magnesium with zinc. And many cases where elements with weak chemical resemblances belong in the same group, just compare nitrogen and bismuth! So how is this argument worth anything?

In order to get anything useful, you have to recognise that descriptive chemistry alone will not cut it as a means of determining element placement on the periodic table. At the most it may serve as a confirmation that you are not producing obvious rubbish, but then again since everyone agrees that nitrogen and moscovium belong in the same group (even though Mc doesn't even have a +5 oxidation state, probably), that's an extremely low bar in terms of possible chemical resemblances.

First, one may look at intraperiod resemblances. Then we have some idea that La is not the one that belongs below Y, because if you look at the series Zr-Hf, Nb-Ta, we see the two heavier elements are pretty similar. Therefore, in order to stop group 3 from being too much of a d-block outlier, we want a late lanthanide as Y is closer to them. That, in itself, does not prove that Lu has to be the one, but it serves as some compelling evidence that if we have to choose between lanthanides it should not be La, as it is extreme in exactly the wrong direction.

For something conclusive you have to look at electronic structure, because we have made enough progress since Mendeleev to learn that that is what controls chemistry. Once you do that it becomes absolutely clear:

Lutetium with corelike f electrons and zero involvement of them that isn't just incomplete screening effects cannot be part of the f block. Not unless you want hafnium through radon in the f block as well, which are in exactly the same situation.
And lanthanum with 4f involvement should not be denied membership in the f block just because its 4f orbital usually gets occupied only from charge fluctuation and ligand-metal charge transfer. Not unless you want to force thorium into the d block, which is in exactly the same situation.
And differentiating electrons must be discarded because you cannot apply them consistently to all elements and because the process they represent has about nothing to do with chemistry, because the energy needed for it will cleave all chemical bonds a thousand times over.
And, for crying out loud, forming aqueous cations in water has never had anything to do with periodic table placement. Or else one starts to wonder if the noble metals have to all carry out a mass exodus to the right edge. Not to mention that the heavy group 4 metals form those cations anyway, thus blowing the whole argument about groups 1 to 3 being totally different from group 4 right out of the water.

So can we please have a moratorium on double standards? Double sharp (talk) 04:24, 6 May 2020 (UTC)

Appendix VI: Lavelle

1. I recall Lavelle's biggest objection to Lu Lr was that this would result in the only block in which both starting elements would have no valence electrons of their own consistent with that block.

2. Jensen partly responded by saying Lavelle was being hypocritical by ignoring the same thing happening with Lu Lr at the end of the f-block. And Jensen said Lavelle was also ignoring Th.

3. Jensen got the boot in too by saying the table was based on idealised rather than actual configurations.

What Lavelle said is true; that would be the case with La Ac starting the f-block.

Lavelle would say avoiding #1 is a more important consideration than #3 (this doesn't mean it's necessarily true, however). He would then probably say that after that, what happens at the end of block is not so important given the well-known irregularities seen in the d- and f-blocks, including the case of Th. So Lavelle is saying #3 is subject to #1, and the unavoidable irregularities.

I further suspect Lavelle's position needs to be seen in the context of these aforesaid truths:

The indistinguishability of electrons implies that one can never state that a practical number of electrons are in any particular sub-shell, although it is frequently useful to make this approximation.
The independent-electron approximation, as it is known, represents one of the central paradigms in modern chemistry and physics

Now, in a situation where no "proof" can be offered one way or the other i.e. for Lavelle (La) or Jensen (Lu), there will continue to be strong advocates for either position. Sandbh (talk) 04:05, 25 April 2020 (UTC)

@Sandbh: The proof is conclusive, because lanthanum's 4f involvement is of exactly the same kind as thorium's 5f involvement. The argument #1 fails precisely because it is inconsistent. It doesn't treat La, Ac, Th, Lu, and Lr the same way. That's not to say that there's no possibility for a strong La-Ac argument, but one such would need to be consistent in how it treats the cases of La and Th, and this does not do that.

In particular, it is not true to say that lanthanum has no 4f valence electrons. Not in the ground state, no, but in chemical environments 4f can have a positive average occupation and significant participation in the bonding. Otherwise thorium has no 5f valence electrons and it has to pack up and move into the d block too. Double sharp (talk) 09:31, 26 April 2020 (UTC)

@Double sharp: Even if you move La and Ac into the f-block you will still have two metals starting a block with no ground state f electrons of their own. Lavelle's argument still stands. Yes, Th has no ground state electron of its own. But that doesn't negate the Lavelle's argument, the equivalent of which is, essentially, that each block should start with the first appearance of the corresponding electron. Sandbh (talk) 05:48, 29 April 2020 (UTC)

@Sandbh: First, as demonstrated here many times, ground-state configurations and their anomalies are not relevant especially for the d and f elements. And secondly, even if you insist on ground-state configurations, the f block does not start with the first appearance of the corresponding electron: cerium has an f electron, but thorium doesn't. So it's still a double standard: why let Th into the f block, aside from a preconceived notion that the 5f block must start in an analogous position to the 4f one? Double sharp (talk) 06:16, 29 April 2020 (UTC)

P.S. 7p doesn't start with the first appearance of its corresponding electron, either. That doesn't mean Lr should go under Tl. Double sharp (talk) 06:26, 4 May 2020 (UTC)

Convention/s

@Double sharp: We know that:

the periodic table is organised around, among other things, the ground states of the elements i.e. as per Jensen's position allocation rules
there is no inconsistency with saying a block starts upon the first appearance of the applicable electron i.e. s at H; p at B; d at Sc; and f at Ce
there is a convention that the start of subsequent rows of a block line up accordingly
superceding an established convention requires an extraordinary development
most new ideas are wrong.

--- Sandbh (talk) 07:25, 29 April 2020 (UTC)

@Sandbh: That's wrong. As is quite clearly stated by Jensen, block assignment is "based on the kinds of available valence electrons and/or valence vacancies (i.e., s, p, d, f, etc.)" (my italics). La has valence f vacancies, so does Ac and Th. (In other words, in chemical environments their f subshells may be occupied.) Ground-state electron configuration anomalies mean nothing for the table anywhere else, as evidenced by how nobody bats an eyelid at the inconsistency of Ni [Ar]3d⁸4s² vs. Pd [Kr]4d¹⁰5s⁰ vs. Pt [Xe]4f¹⁴5d⁹6s¹. They are universally placed in the same group.

So – you have no argument for thorium but "convention". Which means nothing in science. There is quite clearly a double standard in how Th is treated vs how La and Ac are treated according to your and Lavelle's arguments. Which makes it wrong as it is logically inconsistent. Double sharp (talk) 08:08, 29 April 2020 (UTC)

@Double sharp: I was working from Jensen's 2008 article, where he referred only to "Assignment to a major block based on the kinds of available valence electrons". In his update article he actually cites this article to support himself. Sandbh (talk) 05:12, 2 May 2020 (UTC)

@Sandbh: Still no problem, as in compounds La can certainly have 4f occupation, and it counts as a valence electron. The fact that it just does not happen to have it in the ground state when alone is irrelevant. His later wording to include valence vacancies just makes it clearer. Double sharp (talk) 05:18, 2 May 2020 (UTC)

Old ideas wrong

P.S. Many old ideas are wrong, too. That's precisely why they are old ideas and not current ones. As we progress further, of course many ideas will keep falling out of the "current ideas" box into the "old ideas" box. It's just that for a long while they seem to retain a shadowy life-in-death when they are known to be wrong but most people still teach them anyway. ;) Double sharp (talk) 17:04, 29 April 2020 (UTC)

Most ideas are wrong, old or recent. And ideas often reemerge fundamentally the same even if they look different because of our desire to have them in certain way. The notion of archetypes is related to this. They say, all new is well overlooked old, which is a fine reflection of that. You may read Plato's Republic and see how those ancient ideas are so applicable to the present day, even if they weren't used all those years since Plato wrote them.

Among those wrong ideas is the notion that convention means nothing in science. It is debatable whether it is for the better or worse that convention has its value, but it most certainly does have some value.--R8R (talk) 17:54, 29 April 2020 (UTC)

@R8R: Philosophically, I agree. Scientifically I am not so sure. For one thing, I rather suspect that due to the ladder going up and up to more fundamental and more difficult understandings, most recent ideas in physics and chemistry simply could not have even been thought of in the past. (Electronic structure explaining chemistry postdates Mendeleev, doesn't it?)

For another thing, while a convention has some value, I would argue that what value it has does not come from its being a convention. Yes, Einstein in a sense supersedes Newton. But the reason we teach Newton first is not just a convention, it's also because it's pedagogically better to start there, and it's also an excellent approximation for nonrelativistic speeds (that's apparently because Newton's theory is indeed the limit of GR when c is taken to infinity; Einstein's equation just becomes Poisson's equation).

Now, does the Sc-Y-La table have actual pedagogical value? Not really, it creates a perturbation of the Madelung rule that results in hands being raised at the back of the classroom (and some confusion as to the profusion of variants here). Is it a good approximation of the facts at the basic level? Not at all, Lu is much more like a normal transition metal than La is. Does it at least visually suggest the right thing? No, it gives the idea that group 3 is somehow different from the other transition groups, when actually heavy group 4 (Zr, Hf, Rf) pretty much like the tetravalent version of group 3 with weak transition properties. Well, is it even right? No, it makes the statement "La is a d block element and Lu is an f block element". That's a falsifiable statement, so it's within the domain of science. And it is indeed false: La uses f orbitals just like thorium does, Lu doesn't have any significant f orbital usage at all. (And there's the "proof" you speak of in the first paragraph; electronic structure to sort out what is essentially an electronic-structure argument, since that's what blocks are supposed to represent.) So, what is the point of it? Double sharp (talk) 05:36, 2 May 2020 (UTC)

You're not wrong, but that is not to say that tradition doesn't have value in science (feel free to reprimand me for the double negative if you want to).

Consider Mendeleev, for instance, and his obsession with ether. He was truly obsessed by the idea and never let it go to the end of his days; he even thought the noble gases confirmed his thinking there. I don't know if he got the news from Einstein about the special theory of relativity, but not everyone immediately accepted it, either. Luminiferous_aether#Special_relativity says Lorentz was one such scientist who did not give up on ether when he heard from Einstein. Why did he not? Because he had already made his mind and was not convinced otherwise by the new data. And you may say that Lorentz was merely one scientist; my point is, science is made by such scientists. I did not say and did not mean to imply that conventions cannot be overturned (double negative again; is this really considered bad taste in English?); I opposed the idea that they had no value.

"La is a d block element and Lu is an f block element" is a falsifiable statement provided that you've clearly defined a block beforehand, which, as we have seen from this discussion, is not something everyone can quickly agree on.--R8R (talk) 15:40, 2 May 2020 (UTC)

Let's also say that, because the argument can cut both ways: if your focus is some idea in particular, you cannot just dismiss it by its age. That may be suggestive, but you are going to have to see if it stands up on its own merits. And that means looking at it dispassionately and really analysing it from the facts (and absolutely not the tradition), not saying "this is the idea of some naïve young upstart / out-of-touch old fogey and therefore cannot possibly have anything to it". Double sharp (talk) 06:48, 6 May 2020 (UTC)

@Double sharp: I agree. I did not in the slightest mean to say something like, "it's been decided once and for all and nothing can ever change it." My point is that it requires you some effort to overcome old conventions---because they have some value attached to them.

Facts are good, I'm not at all questioning the notion of their usefulness. The thing is, you can interpret them differently. Consider this: every scientific theory is a construct that more-or-less fits in all the facts known. (This is also why science will never be over: there will always be room for search of a fact that doesn't fit the current theory because what we will have at any point is just an approximation, however precise it may be.) However, how you build your construct is up to you. Then the thing come up in that once you've made a construct you like, you're not going to give it up easily (because you yourself have attached some value to it), even though the kind of perfect man of science you're trying to describe would do that. You will be more willing to think that the new information does not really question your theory the way the author thinks it does and think that your story (theory) still stands and you're still as scientific and reasonable as it gets. You can think of it as of a limitation of the human mind: indeed, if you change your opinion on things you hold precious and dear too often, that will bring mental instability. If you change your opinion on not so important things too often, it will still make you more likely to do the same during your next choice, because once a mind learn how you do things, it's willing to cheat to save the energy needed elsewhere in your organism and do the thing you always do. Do you want to say, "I'm not gonna do that, I'm better than that, I know how to be scientific"? If so, then I think it's highly likely that you'll end up doing that at some point without noticing it. Naturally, the same goes if you decide that you don't want to be a flik-flak and want to hold your opinion firmly: your mind will still at some point learn that this is the thing you do and it will try to keep you at an opinion you once established. It will still be a hard challenge to change from your normal stance, and not every time you do it is going to be perfect whatever you might think of it. I'm not in the slightest saying this to taunt you; we are all imperfect, and the same goes for all of us. (Nobody said this would be easy.) The best way to go forward is to be very mindful of that.

I will emphasize it to make what I'm saying perfectly clear: the tradition that holds is not in facts; facts, of course, overcome any tradition. The tradition that holds is in the interpretation of them.

I was going to say it myself at some point but Sandbh did it for me: there are simply different things you emphasize in your theories on group 3. You interpret the facts to have a construct named "group 3" the way you like. Sandbh does it to have it his way. You disagree because your interpretations differ. That is fine as long as you realize the validity of the other theory. The question really is, not what group 3 is (it is what you want it to be) but what vision of a "group 3" is better fit for purpose (and you can think of different purposes: teaching, analysis, etc.).--R8R (talk) 06:21, 7 May 2020 (UTC)

@R8R: I really don't think I interpret the facts to construct group 3 to have Lu in it. Rather, I decided on what I want to be important right from the beginning: that is, I wanted my blocks to be related to the chemically active subshells. Well, back in 2016 I thought La and Ac had a distinct lack of f involvement that was different from Th, and that f involvement for Lu was still possible, so I supported La in group 3. Now I know that La and Ac have f involvement in the same way that Th does, and that Lu has no significant f involvement, so I support Lu in group 3 from about 2019 onwards. Yes, it was hard to let go of an opinion that I put so much into supporting, which is why it took a year from when Droog Andrey gave his strong arguments in 2018 for me to really firmly let go of Sc-Y-La, but I did it. I really think the fact that I swapped positions when new evidence came in, but kept my criteria constant, should show clearly that my stake in the issue is not because I love one form especially above the other, but because I want to consistently find out and then strongly support the one that is right, whichever it turns out to be. That's why I have been on both sides of this dispute.

Maybe group 3 is what we want it to be, but I still insist that there is a most natural way for it to be, based on what controls chemistry: electrons and the orbitals they go into. Sandbh's approach has to handle everything case by case with lots of arguments that, when applied to something else like the position of Al, start to fight each other. My approach just builds up from this and is internally consistent. That's why I don't think Sc-Y-La is fit for any purpose: there is nothing it predicts better than Sc-Y-Lu and it is not easier to teach. Double sharp (talk) 06:30, 7 May 2020 (UTC)

I promise to give a thoughtful response some time later. I do, however, think that my words here have a lot to unpack, so I'm rather disheartened to see such a quick response, because I'm afraid that means you "ticked them off" in your head and won't revisit them. I'd love it if you tried to think of them more closely. I can't ask you to agree but a close consideration would be great, too.--R8R (talk) 07:00, 7 May 2020 (UTC)

@Double sharp: If there is one thing that I can be truly grateful to my mathematical education, it's that it has taught me not only to see how something follows or does not from a logical implication and, eventually, how to apply that to real-world problems. I am very far from saying by that you're interpreting it that it's somehow that it takes you some special effort of mental gymnastics to have it that way because the said way is so unnatural (quantitative). It does take you some effort, though, however little, because that interpretation does not exist in itself naturally (qualitative) but needs to be made.

I've said it a few times already, and I'll say it again. Did you consider that your interpretation of what group 3 is may not be the best one? I'm not saying it's not, but did you consider that? Because you're saying that you've held consistently on your criterion, even if recognizing it leads you to different outcomes. What if, say, there was a time in the periodic table when there were only 13 or 15 elements in an f-series in a certain sense, say, if lanthanum showed no f-involvement in bonding and that was how quantitative characteristics turned put to be? Consider the superheavy elements. It appears for now at least (although little research has been made) blocks, however you define them, look rather arbitrary in period 8 if you compare them against electronic configurations. What do we make of that? Could we even in principle have that in period 6; because if so, then we'd have to logically assume there are criteria other than what orbitals are involved in bonding?

There are different ways to answer that particular question, none of them "correct" by the virtue of me or you liking or not liking it; rather, they can be better suitable or not. What I am suggesting is that you consider that what you name to be your criterion doesn't have to be the choice that other people make, and they may have a good reason for choosing what they choose, too. I am not saying hereby that you should embrace Sandbh's point of view; what I'm afraid you're doing though is that you don't see how it could be seen as a legitimate point of view, without necessarily rendering itself absolutely unreasonable beyond repair in its own inconsistencies. I'm urging you to try that; that would lead to higher quality of the discussion itself and it would make you happier about it as a result. That path still allows you to take a stance in this dispute, but in a manner that is more fitting to the attempt to find the truth.--R8R (talk) 10:42, 9 May 2020 (UTC)

@R8R: I am also familiar enough with mathematics to understand logical implication. After all, I like real analysis, and that requires much prowess at manipulating quantifiers. XD

What if there were not 14 elements in the f-series – then my conclusion would be different, since reality would be different, and I would be starting from a different situation. What if there were more than 14 – same. (That is reality under pressure, with Cs and Ba becoming f-band superconductors and even yttrium showing a state with delocalised 4f bands; but that's not what we use to draw the table.) I suppose that if La and Lu both lacked f involvement, it would depend on what the trends were like in the lanthanides. If Gd and Lu in that hypothetical reality showed something similar to Mn and Zn (which they don't in this one), then sure, I'd support Sc-Y-La in such a universe. But that's not what we see in this universe, so I don't see how that should impact my stand here.

For period 8 – they don't look terribly arbitrary to me. Well, the s block is obvious, E119 and E120. The d block is pretty clearly E157 through E166, as E157 is when 6f stops being available (E155 and E156 are quite analogous to Md and No, just compare predicted ionisation potentials to see that 6f is probably still breachable there). The p block is equally obviously E167 through E172, these two cases are just like yttrium through xenon in period 5. So the hard cases are 5g and 6f which have no analogues. Well, let me quote Droog Andrey who analysed that back in 2016 at Talk:Extended periodic table/Archive 3:

“

Pekka Pyykkö's computations show that element 142 is the last one where 5g and 8s subshells are still open for chemical bonding. Although the neutral atoms of elements 143 and 144 has probably still unfinished 5g-subshell, it become 5g¹⁸ when atom is positively ionized (the reason was mentioned in the previous section: subshells with higher angular momentum are drowned deeper because of less screening). On the other hand, positive charge is the only way to reach 5g orbitals for (at least indirect) chemical bonding because of their small size. Therefore, element 142 is a good candidate for the end of g-block.

So, 6f series is probably started at element 143 since its 6f subshell has the highest angular momentum among valence subshells 6f, 7d and 8p_1/2. As for the right end of the 6f series, most of the authors agree that 6f become filled near element 156. Pekka Pyykkö shows that triple cation of element 155 has 6f¹⁴ and still may be chemically ionized further (the calculated ionization potential for Upp³⁺ is higher than for Tb³⁺, but lower than for Dy³⁺). Other authors predict a bit higher energy of 6f subshell in the vicinity of Z=156, but all of them agree that for Z=158 the 6f subshell is buried deep down together with 8p_1/2.

”

— Droog Andrey

So the only difficulty seems to be that the g block is too long: there's 22 elements with 5g involvement, not 18 (assuming E121-E124 have an analogous situation as pre-g elements). No problem, we just widen it to reflect that. So: s block E119-E120, g block E121-E142, f block E143-156, d block E157-E166, p block E167-E172. I don't see a great difficulty there. In principle it could have been different, but apparently in reality it isn't.

Sandbh's point of view – the trouble I find with it is that it either simply doesn't fit the facts or is illogical. Often it is about Lavelle's argument that La and Ac lack an f electron in the ground state, when the ground-state electron configuration has been already shown to be irrelevant. Or it is about misrepresenting my method as being overly complicated compared to his, when actually (1) his has weak explanatory power, tripping as it does consistently on thorium [Rn]5f⁰6d²7s² and tearing at its own throat regarding whether Al should go over Sc or not until he artificially sets down boundaries to stop that, and (2) mine literally simplifies his by saying "I don't care about anomalous ground-state configurations". Or it is about stuff that is chemically just not true and not widely accepted, like the idea that group 3 should not be treated as a transition metal group. (Sure, many people apologise for it having weak TM properties. Guess what, so do Zr, Hf, and Rf, and that's also well-established fact. And they still put group 3 with the TM's anyway for the most part.) So, I accept in principle that there may be better ways to determine a block than mine; but I think Sandbh's way will not cut it. And, since lanthanum has 4f involvement not less than that of thorium the undisputed f element, and lutetium has basically none at all, it's going to need a veritable nuclear explosion to come out with a better one reflecting reality that supports Sc-Y-La, IMHO. ^_^ Double sharp (talk) 12:02, 9 May 2020 (UTC)

I wasn't suggesting you were not familiar with logical implication or that you didn't understand it. The real challenge is to be able to apply it and to recognize that this is correct not only for mathematics. Many group mates of mine think that logical implication is for mathematics only, and life follows different rules. And that's not very difficult to think, since generally, how things work in life is that we look for what suits better, not what is correct. Yet I still find it important to understand logic very well, and I was stressing that it's still important in this case.

My particular specialty in mathematics is the optimal control theory. In such problems, you normally seek to maximize a criterion given the system behaves in a certain way but there is a parameter you can manipulate. I am again stressing that there in principle can be different criteria for each system. If you and Sandbh had agreed first and foremost on the criterion would be, then you could indeed discuss what suits that better. Without that or without a common way of trying to define that, you're essentially trying to shout each other down with your own flaw of thinking. It unsurprisingly has little effect on the other. I will leave it to you to decide how scientific the whole debate then is. (I will note that the end of the Transfermium Wars came with an arbiter who defined the criteria first and only then applied them, to give you one example. Even then it still didn't prevent the LBNL from rejecting the solution a couple of times, but it's clear enough that not only science was involved and scientifically, the way of resolving the conflict was picked correctly.)

I am, to be perfectly clear, not arguing in favor of Sandbh's position. I am arguing in favor of validity of it. It can be valid but still be decided against. (Speaking of implications, the ability to recognize this is also a part of that.)

Speaking of Pyykkö, he thinks that the f-block has 15 elements in each row. Pyykkö is very credible and he is certainly sharing the universe with us. What do we make of that? Do you say that he is wrong or do you say that you don't agree but his position has some merit? Not to mention that Pyykkö himself interpreted his own calculations in a different manner, one that does not give a 22-element g-block. And even if he did, I would most certainly not call that a "no problem" situation. Possible, yes, but definitely not "no problem," because that extra space for the 5g series comes at the expense of something else. Is Pyykkö here wrong as well or is there enough merit for the existence of this position?

Sandbh's criteria evidently include the simplicity of the explanation, at least the way he understands it. Imagine for a second that this was the view of all other scientists. What would we make of that? would they all be wrong or would there be room for accepting the other position as valid even while not agreeing with it and "agreeing to disagree"?

You know, there is one thing I particularly like about the English language and the people who speak it, and it's that there is a special custom in English to appear to listen to whomever you're talking to. This makes it much easier to start a discussion and get it going and that was what particularly attracted me to it back when I was actively learning the language. I hope you can pick up on that and try to see that there is a point in what Sandbh is suggesting, without necessarily making his point yours.--R8R (talk) 14:38, 9 May 2020 (UTC)

@R8R: Yes, that's why I asked him what for him would be sufficient evidence to overthrow Sc-Y-La. And I also, while I was at it, gave him what I would consider sufficient evidence to overthrow Sc-Y-Lu. In principle one could then start from there and thrash out some criteria we would both agree on. Or at least it would if he had not answered "I don't know. Not ruling it out but." You may also decide how scientific that is. I have asked him again, maybe I will get an answer this time.

Pyykkö certainly is in our reality, yes. And, he has a point that La-Lu is a natural grouping all together, so I can see where he is coming from. The only trouble is that Ac-Lr isn't quite so natural with the immense variety of behaviour (just compare U and No). That 4f situation is really quite singular for the reasons Seaborg mentioned; you're not likely to see it again outside 5g, and it had no precedents. He says, "To us the atomic ground state is less important than the chemical bonding, in the systems so far considered" – that's something I agree with, but it supports the Lu table if you look at the bonding orbitals. So, while I think he raises something with merit, and I can understand why he would come to his conclusion, it's only unarguable for the Ln and rather more strained for the An, and it's not generalisable to the rest of the table. It also gives a rather wrong idea that the f block is just a degenerate branch of the d block, which it is not (just look at the early actinides; better, look at the 4f involvement in La-Yb). I think it is preferable to look at other things here for that reason. And, anyway, the whole point of the IUPAC project is to come up with a definitive answer to the group 3 question, which itself assumes there is a right answer. I prefer to accept that assumption, that there should be an answer that is most natural, at least.

Simplest sufficient complexity as Sandbh continually refers to is actually something I agree with. Everything should be made as simple as possible, but not simpler. But that works against his own arguments. Well, if you go my route, you just look at chemical activity of the subshell, and ignore anomalies from the Madelung rule. Then you just apply it to everybody. If you go his route, you have to come up with some reason why the lack of an f electron in ground-state gas-phase La and Ac is absolutely prohibitive for them in the f block, and somehow for Th it becomes "oops, I guess some different sort of f involvement is fair game too". Or, at the worst it has become now, convention. I am prepared to agree with you that convention is not worth nothing. But I cannot accept that convention is a valid thing to refer to when the whole point of the discussion is the correctness of that very convention. And then you have to find some way to artificially stop the arguments from tearing at each others' throats when applying them to anything else. Simple, not quite. So, while I think this criterion of Sandbh's has great merit, I think it is actually inconsistent with his own position. To my mind that is even one step worse from what I think of Pyykkö's argument. Double sharp (talk) 15:04, 9 May 2020 (UTC)

@R8R: Actually, no. On reading Sandbh's statements from the previous three days, and checking back through the archives, I say: what Sandbh is suggesting has basically no point. It is simply riddled with a lack of understanding of basic chemistry (combined with an apparent mental block against my attempts to explain it to him, at least until in one brief shining case he found one of his own favourite sources saying the exact same thing), based on things that are not even true, and a basic lack of logic and a lack of understanding of the necessity for logic. While I agree that "things should be as simple as possible, but not simpler", I think he has no valid claim to a philosophical perspective without any of this. Just look at the following, all direct quotes from archive 42 and from here. (For exhibits A through G, since they're from the archives, I have had to resort to manual copy-pasting, so the formatting (including my bold) is gone. However, I think we can all see the point anyway.)

(@Дрейгорич: I hope you do not mind that I post these here too, as they were originally on your talk page.)

Exhibit A

“

There’s nothing particularly weird about group 3 acting more like groups 1 and 2. [Sandbh (talk) 00:06, 25 January 2020 (UTC)]

Indeed, since groups 4 and 5 also act more like groups 1 and 2 very often, so the argument does not amount to that much in hindsight. Double sharp (talk) 00:20, 25 January 2020 (UTC)

@Double sharp: That’s complete nonsense. I’m astonished to think you could post such rubbish. For the seven thousandth time, as per the literature, groups 1 to 3 have a predominately ionic chemistry. Groups 4 and 5 have a predominately covalent chemistry. End of story. The end. Period. Sandbh (talk) 06:48, 26 January 2020 (UTC)

Look, there is no such thing as a complete volte-face from ionic to covalent. It depends on what the counter-anion is. We go from ionic to metallic (which you're overlooking completely) across the series NaCl, Na₂O, Na₂S, Na₃P, Na₃As, Na₃Sb, Na₃Bi, Na. And that's in group 1, with an example taken straight from Greenwood & Earnshaw p. 81. Ionic vs. covalent is (1) gradual, from covalent to polar covalent to mildly ionic to strongly ionic, depending on the difference of electronegativity between the two elements; (2) not a complete dichotomy, because you overlook metallic bonding; and (3) not split by elements, but rather by electronegativity differences, which have a lot to do with oxidation state (just compare uranium chemistry as we jack the oxidation state up from +3 to +4 to +5 to +6). So I'm astonished to see you put so much weight on "ionic vs. covalent" as a false dichotomy. (And as I keep saying, the general thing across the periodic table is continuity, and the sharp dichotomies you like to point to have a distinct tendency to not exist.) The whole literature, when it sees fit to split "main group" from "transition", universally uses other criteria like "variable oxidation states", "coloured compounds from d–d transitions", "a wide variety of complexes", "formation of paramagnetic compounds". Ionic vs. covalent has nothing to do with it, and nobody uses that as a criterion in the literature for this divide. Respectfully, I put it to you that Zr, Hf, Nb, and Ta by this standards have weak credentials as transition metals, just as weak as Sc for that matter. Double sharp (talk) 10:32, 26 January 2020 (UTC)

[JUST OVER TWO MONTHS OF FUTILE ARGUING LATER]

The group 3 to 4 "divide"

@Double sharp: We’ve been discussing whether or not this exists.

We’ve argued about predominately ionic v predominately covalent. You’ll recall the extract from Rayner-Canham and Overton:

"For chemists…the most important feature of an element is its pattern of chemical behaviour, in particular, its tendency toward covalent bond formation (or its preference for cation formation)." (p. 29)

They add some nuance:

"The Ionic-Covalent Boundary

Unfortunately, there is no firm predictable boundary between ionic and covalent behaviour for solid compounds of metals and nonmetals. As predicted from Fajans’ first rule, increasing theoretical cation charge results in increasing charge density, which will favour covalent behaviour. However, as predicted by Fajans’ second rule, the anion also plays a role: thus as the metal oxidation state increases, the iodide is first likely to exhibit a low melting point, then the bromide, then the chloride, and finally the fluoride and oxide." (p. 99)

"…inorganic chemists see not a rigid ionic-covalent divide but a bonding continuum. Figure 5.11 shows electron density profiles for four points on this continuum: the pure covalent, a polar covalent bond, a polarised ionic bond, and a pure ionic bond. The ratio of ionic to covalent character can be defined as the difference in electronegativities…between the pairs of atoms. Thus, pairs of atoms with…[a difference] close to zero will possess essentially pure covalent bonds with equally shared electrons, whereas those…> 3.0 are regarded as purely ionic… (p. 109)"

They go on to refer to the Van Arkel-Ketelaar bond triangle with its "rough" division into metallic, ionic, and covalent “zones” and Laing’s extension of the triangle into a tetrahedron.

These kinds of divisions, while rough, are nevertheless valuable. As expressed by Nelson (2011):

"…care needs to be taken to remember that…[this classification scheme] is only an approximation, and can only be used as a rough guide to the properties of the elements. Provided that this is done, however, it constitutes a very useful classification, and although purists often despise it because of its approximate nature, the fact is that practising chemists make a great deal of use of it, if only subconsciously, in thinking of the chemistry of different elements. [Sandbh (talk) 09:46, 1 April 2020 (UTC)]

@Sandbh: Using those four categories is so much better than "predominantly ionic" or "predominantly covalent", so I'm glad we have come to some agreement on this. They are in fact the reason why I find "predominantly ionic" and "predominantly covalent" not useful: using those terms sweeps under the rug the very trend that is so clearly controlling it, that of electronegativity difference as Rayner-Canham and Overton are saying. Double sharp (talk) 13:09, 1 April 2020 (UTC)

@Double sharp: Quite so. Sandbh (talk) 01:08, 2 April 2020 (UTC)

@Sandbh: Well, I have been saying exactly that since January:

“Look, there is no such thing as a complete volte-face from ionic to covalent. It depends on what the counter-anion is. We go from ionic to metallic (which you're overlooking completely) across the series NaCl, Na₂O, Na₂S, Na₃P, Na₃As, Na₃Sb, Na₃Bi, Na. And that's in group 1, with an example taken straight from Greenwood & Earnshaw p. 81. Ionic vs. covalent is (1) gradual, from covalent to polar covalent to mildly ionic to strongly ionic, depending on the difference of electronegativity between the two elements; (2) not a complete dichotomy, because you overlook metallic bonding; and (3) not split by elements, but rather by electronegativity differences, which have a lot to do with oxidation state (just compare uranium chemistry as we jack the oxidation state up from +3 to +4 to +5 to +6). So I'm astonished to see you put so much weight on "ionic vs. covalent" as a false dichotomy. (And as I keep saying, the general thing across the periodic table is continuity, and the sharp dichotomies you like to point to have a distinct tendency to not exist.)”

But it looks like it's only admissible when Rayner-Canham and Overton say it, not when I say it, even if it is absolutely normal high school chemistry material (which I learnt too). Now, the same thing is going on for the supposed volte-face between group 3 and group 4 on the basis of aqueous chemistry: it doesn't exist, all you have is oxidation states, atomic radius, and electronegativity too, exactly like I remember from high school chemistry. Or do I have to quote Wulfsberg explicitly? ;) Here's a quote from p. 94 of his Principles Of Descriptive Inorganic Chemistry:

“Because the acidity of a cation rises rapidly with its charge, there are several d-block elements possessing several oxidation states (such as chromium) that have one or more oxides that show only basic properties (e.g. chromium(II) oxide, CrO), one or more oxides that are amphoteric (e.g. chromium(III) oxide, Cr₂O₃), and one or more oxides that possess only acidic properties (e.g. chromium(VI) oxide, CrO₃). Clearly, the higher the oxidation number of a given element, the more acidic the corresponding oxide will be.”

Zero mention of group divides in his whole section on periodic trends in acid-base and solubility properties of oxides. Which is because there is no such thing. Double sharp (talk) 14:04, 2 April 2020 (UTC)

”

And a brief appendix, in which he even somehow managed to come up with a list (supposedly "backed up" with quotes from the literature, oh my!) of some predominantly ionic and predominantly covalent elements(!!):

“

@Sandbh: The literature saying this has evidently never taken a moment to think about what they are saying. Exercise: based purely on the chemistry of these four elements, decide whether their chemistries are predominantly ionic or covalent.

Fluorine;
Caesium;
Uranium;
Thallium.
[optional] Carbon.

You are allowed to refer to the literature to see what the chemistry is like, but not just quote what they say about "predominantly ionic". You have to use the chemistry to decide for yourself if such a characterisation is warranted for any of these four elements. (Hint: it is not, as it varies too much on what the elements are bonded to, in what oxidation state they are in, and in what oxidation state the other element they are bonded to is in.) Double sharp (talk) 17:03, 5 February 2020 (UTC)h

@Double sharp: Here you are. I've indicated the most common oxidation state/s and whether the element in that state is predominately ionic or covalent. For added interest I added some commentary from the literature after each entry.

F (−1) ionic

"Fluorine's high electron affinity results in a preference for ionic bonding; when it forms covalent bonds, these are polar, and almost always single."

Cs (+1) ionic

"Cesium is the most electropositive and most alkaline element, and thus, more easily than all other elements, it loses its single valence electron and forms ionic bonds with nearly all the inorganic and organic anions"

U = (+6) covalent

"Because of the actinide contraction, uranium's chemistry is quite similar to that of molybdenum."

"The uranyl oxygen bonds are covalent in nature."

Tl (+1) ionic

As previously quoted

C = (±4) covalent

"In most organometallic compounds, the metal-carbon bond has predominantly covalent character…"

"Carbon chemistry is overwhelmingly covalent…" Sandbh (talk) 06:19, 6 February 2020 (UTC)

”

Exhibit B

“

Omnibus bombardment

For example, Double sharp wrote that:

"Shared chemistry supports Lu, DE's are chemically irrelevant, you misread the periodic law, your pattern is only graphic design, the 234 pattern is ungeneralisable, and isodiagonality supports Al in group 3. Your case for La convinces me about 0%. All it is is a bunch of one-off arguments glued together, with no hint as to which ones are the more important ones, and no heed to what nonsense they have to say for the rest of the periodic table. The only commonality with them is that they all support the La table in what IMHO are just increasingly desperate ways having less and less to do with actual chemistry. Since R8R and Droog Andrey have echoed some of my points, not to mention Jensen and Schwarz, I think the world would agree. At least I critically analyse and accept the tiny sparks of nonsense my single highest criterion appears to throw up (He in group 2, the ambiguous position of some s-block elements), and see that it is in fact not nonsense and has some chemical repercussions in the real world. So all is well."

There is a lot to unpack here. I see uncited opinions; fogging; selective quoting; unfounded undermining—the periodic table is "only" a graphic design; misattribution; more fogging, and myopia.

I've rec'd other respected external professional feedback on a summary of my article, and the response was, " I think you have presented a balanced description of the issue." Of course, DE's only shape the periodic table. And, as we know, Scerri observed, "…for the purpose of selecting an optimal periodic table we prefer to consider block membership as a global property in which we focus on the predominant differentiating electron." He must be wrong, of course. So much for d/e's. [Sandbh (talk) 04:17, 10 February 2020 (UTC)]

Yes, I agree. DE's are flawed and incomplete. Double sharp (talk) 07:59, 10 February 2020 (UTC)

I apply the periodic law in conjunction with the real aufbau process, not the misleading n+l approximation. Of course, the periodic table is only a graphic design, nothing more. The 234 pattern is not generalisable, and I never said it was; rather, I compared the two patterns in the La and Lu forms. That Al is isodiagonal with Sc does not undermine my argument. We addressed Jensen's contributions in our IUPAC submission. I've addressed Droog Andrey's major contribution which, to his credit, and as I said, stumped me for a while.

A good chemist is able to hold the three different perspectives in their head, and recognise they all have value depending on the context, rather than insisting there is one correct answer. Thus, I can appreciate the La form, the Lu form, and the IUPAC form, concurrently. (I’m not a chemist) It's a question of the right tool for the job rather than one size fits all. [Sandbh (talk) 04:17, 10 February 2020 (UTC)]

Well, do you think there is one correct answer for H, Be, Mg, and Al? Double sharp (talk) 12:18, 10 February 2020 (UTC)

@Double sharp: It's context dependent. Frex, Habishi's metallurgist's table in which Al is over Sc, but not B. Sandbh (talk) 23:11, 13 February 2020 (UTC)

@Sandbh: So how does that square with your statements "The world has moved on from the days of Be and Mg over Zn" and "Al in group 3 is a non-starter" on this very talk page? Double sharp (talk) 23:51, 13 February 2020 (UTC)

@Double sharp: Well, I haven't been talking about a metallurgy kind of table. I've been talking about the table that's near the middle of Scerri's continuum of tables, with the Platonic LST at one end and Rayner-Canham's unruly table at the other. Sandbh (talk) 04:55, 14 February 2020 (UTC)

@Sandbh: But how do you know that something near the middle of this continuum would not be better off reflecting the many ways in which Al is similar to group 3? Do you know that the pair Al-Sc shows more chemical similarities than the pair Al-Ga according to Rayner-Canham? Double sharp (talk) 11:59, 14 February 2020 (UTC)

@Double sharp: I don't. Sandbh (talk) 03:57, 17 February 2020 (UTC) [!!!]

@Sandbh: So you don't have a leg to stand on. All you have is an idea of something compromising between the boundaries, and what your most important criteria are seems to be what you feel like using at the moment in order to get your favourite arrangement of La and Ac under Y but not affecting anybody else. Contrast me: when I find that one criteria above any other really stands out as something that can make a great basis for the PT, but it has the side effect of insisting on He over Be, I am consistent and move it even if I thought at first that He-Be-Mg was chemically insane. (Now, of course, my trust in that criterion has been rewarded by predictions of He being like Be in its rare compounds, and in those graphs of periodic trends. Just like Mendeleev.) Double sharp (talk) 14:38, 17 February 2020 (UTC)

”

Exhibit C

“

@Double sharp: Regarding Th and reductio ad absurdum, and your assertion that, "Those arguments of yours about when a block begins, if applied consistently, lead to denying Th as an f-block element…" this misstates my position. From day 1, this has consistently been that a block starts upon the appearance of the first relevant electron. That is all. It stands alone: s at H; p at B; d at Sc; and f at Ce. If you choose to extend this argument beyond that, don't blame me. 01:44, 20 February 2020 (UTC)

@Sandbh: Chemistry is not a heap of distinct conceptions standing apart alone, but rather interconnected system of conceptions based on experimental facts. When Double sharp shows that your argument produces bullshit, you'd better learn what's wrong with the argument instead of continuously building artificial borderlines for its applicability. Droog Andrey (talk) 07:03, 20 February 2020 (UTC)

@Droog Andrey:@Double sharp: Hey, it's not my argument and not my BS! Repeat after me: Sandbh's argument is that a block starts upon the appearance of the relevant electron i.e. s at H; p at B; d at Sc; f at Ce. Sandbh's argument stops there. If DS wants to extend my argument such that it therefore needs to apply to the start of each row of a block thereafter, and then wishes to argue about an extended argument that I never signed up to, then he can knock himself out, as long as he leaves me out of it. Understand? What DS is arguing about is not my argument!! Why is this so hard to understand? Sandbh (talk) 11:32, 20 February 2020 (UTC)

@Sandbh: You don't understand logic.

I could equally well say that the f-block must end when the final f electron appears, i.e. at Yb. Say my argument stops there. If Sandbh wants to extend this argument such that it therefore needs to apply to every block, and notes that this is nonsense because it says the d-block ends at Cu, then I could equally well say that this is an extended argument that I never signed up to. But Sandbh has no problem using this refutation himself when I say (in a corrected version of this argument) that Lu is not an f-element because its f-electrons are core electrons, and give the argument without an f-block only restriction: [Double sharp (talk) 14:07, 20 February 2020 (UTC)]

@Double sharp: If you said, "the f-block must end when the final f electron appears, i.e. at Yb" I'd ask, "is this statement impacted by aufbau irregularities(?)"; and, "is it impacted by where the f-block then starts when the first f electron appears?" I wouldn't argue about the start of the second f-block row, since this not part of your argument. And I wouldn't argue about the d-block because that's not within the scope of your argument. Sandbh (talk) 22:59, 20 February 2020 (UTC)

@Sandbh: You should be arguing about the d-block if I said that. Because the natural scientific response to me going "oh, this is only valid for the f-block" is not "Great Scott! You're right, of course. Let me fight within the f-block only". It is "so what is the reason the f-block is categorically different from the other blocks that gives you a right to say so"? See the next few paragraphs. ;) And you should also argue what this criterion has to do with chemistry and physics, since it is not unheard of elsewhere that an already preemptively filled subshell is still valence later (see group 12 in the d-block), and it would be my burden to prove this doesn't happen for Lu. (Which Droog Andrey and I have done.) Double sharp (talk) 23:07, 20 February 2020 (UTC)

“ The line about "to the point where its characteristic electrons are core electrons" reminds me of group 12. Therefore we need to start the d-block in group 2! IUPAC will throw that one out. ”

— Sandbh

Of course, you don't even do it right, because as I demonstrated Zn 3d is demonstrably involved in the bonding of some Zn compounds!

Or I could say that only electrons in directly valent MOs matter for determining chemically active subshells in the s-, p-, and d-blocks. Say my argument stops there. (I don't say that, of course.) If Sandbh wants to extend this argument to note that it doesn't work in the f-block, then I can say the same thing. Of course, when I don't pose this artificial restriction, Sandbh has no problem coming up with such examples when attacking my statements about "chemically active subshell of highest angular momentum":

“ How does that work for e.g. Nd, which has a condensed phase configuration of 4f³d¹s², and which is not known in the +4 oxidation state? Time to move into the d block? ”

— Sandbh

And you don't do it right either, since Nd⁴⁺ is known.

So by Sandbh's logic, it appears that my arguments would become more convincing if I said "oh, that's for some elements only". The most convincing argument of all must surely be the one that says "this property is relevant for La only and the fact that literally every other element in the table contradicts it is irrelevant because I say so", then. Of course, the whole world begs to differ...

The point is: it's not enough to say: "This is my argument, and this is where it is applicable only. Lo! hearken to me for I have spoken. All ye shall only apply my argument where I say it is relevant. And all ye who proclaim that my argument is BS because it produces BS in regions I excluded it for are heretics. But I may do that myself when attacking your arguments, for I have special Divine Exemption from my side of this crusade." We are doing science, or at least I am doing science, so you have two requirements:

You have to justify why your argument should be the right one and not my artificially-concocted-to-be-BS ones above that happen to support Lu. (I have better Lu arguments than these, of course.) If you can't apply it everywhere, why should that inspire confidence in it as a foundational principle for the PT? And why is the next row not important? If you can't explain why a criterion is chosen to be relevant, then we should be throwing it in the garbage can. So: why is the first electron so much more important than all the others, and why does the next row of the block not matter?

You don't get to have your arguments in a vacuum. You say the criterion doesn't work somewhere. OK, what is the justification from Nature that says we are in a totally new regime there? Otherwise it is an artificial restriction to save face. As Droog Andrey says, "Chemistry is not a heap of distinct conceptions standing apart alone, but rather interconnected system of conceptions based on experimental facts." So is all of logic. You don't get to have mutually contradictory beliefs if you're arguing a stand. If you wish to claim that a clearly identified contradiction is not a problem because the argument cannot be applied there, then you'd better explain what is so categorically different that the argument cannot be applied there. Not should not. This is not a case of "Don't do it because I say so". Double sharp (talk) 14:07, 20 February 2020 (UTC)

”

Exhibit D

“

Th 5f involvement

@Double sharp: Why do you show Th as having potential 4f involvement and criticise me for mentioning this? Sandbh (talk) 22:17, 16 February 2020 (UTC)

@Sandbh: I criticise you for it because it exposes your inconsistency and double standard. You insist throughout on DE's being important, but they say that Th is not an f-element because 5f has not started filling. Instead you backpedal over it and say that, oh, actually, your rule of DE's and nothing else can be overturned specially for Th because of its really obvious 5f involvement. (That is when you're not claiming that Ce's 4f electron forces the rest of the 5f block by regularity aka symmetry to everybody else, while at the same time refusing to accept symmetry as a reason for the Lu table.) While I agree that chemically obvious 5f involvement for Th is more important, it is a double standard that shows that you are not consistently using your own criteria. You have two logically consistent options here: reject DEs, noting as Seaborg did that the actual DE does not really matter all that much, or somehow try to reject the chemical relevance of 5f in Th (good luck with that). Of course, you inconsistently do the first one for Th and Lr, but the second one for La and Ac! Double sharp (talk) 22:37, 16 February 2020 (UTC)

@Double sharp: Could you please desist from associating my arguments with symmetry in light of the fact that I don't give a rat's about symmetry or asymmetry, as I have stated before and you continue to ignore. I let Nature take its course. D/e's are important. So is aubau, and the periodic law, and regularity. I've unpacked my arguments several times, and your own critiques and have yet to see you find a single instance of a double standard. If that was really a wont of mine you would've found some good examples by now. Don't forget ceteris paribus. You seem not to know that one. If you find a double standard by me, I'll 'fess up. I don't try and evade my mistakes. I make them and will continue do so. You seem unable to acknowledge and learn from your own.

@Sandbh: I don't care how much you say that you don't care about symmetry, when your actions speak otherwise. Relabeling it as regularity does not make it stop being symmetry. I found many examples already, but you choose not to logically examine yourself.

Never mind the elephant in the room that La has valence 4f involvement and the best you can do for dredging up scraps of 4f involvement for Lu is (1) dragging out the core electrons and (2) misunderstanding computational chemistry, so we do not have a case of ceteris paribus here and Lu is clearly favoured as the d-block lanthanide. Double sharp (talk) 20:24, 17 February 2020 (UTC)

@Double sharp: Penrose tiling is another example of the difference between symmetry and regularity. Such tiling shows symmetry but not regularity. Despite my examples showing that symmetry and regularity are not necessarily the same thing, there is nothing I can do if you choose to continue to interpret my actions as speaking otherwise. I focus on regularity; if the outcome is symmetry that is fine. I have never relied on symmetry in my arguments. As you know from the draft of my article: [Sandbh (talk) 00:36, 18 February 2020 (UTC) ]

[and then some arguing from him that his "regularity-based arguments" are, somehow, not "symmetry-based"; I am curious what you think the difference between those two words is, as well as whether you think arguing that Th must go below Ce even in the absence of a 5f electron on Th in the ground state counts as XD]

@Sandbh: Penrose tilings show self-similarity. You've still not defined what exactly you claim the difference between symmetry and regularity to be, anyway. Double sharp (talk) 07:57, 18 February 2020 (UTC)

@Double sharp: From our own article: "A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and aperiodic means that shifting any tiling with these shapes by any finite distance, without rotation, cannot produce the same tiling. However, despite their lack of translational symmetry, Penrose tilings may have both reflection symmetry and fivefold rotational symmetry." Oh, and let us not forget, a square is regular and symmetric; a rectangle is irregular and symmetric." If you disagree, write a letter to Nature, and let the world know. Good luck with that. Sandbh (talk) 08:57, 18 February 2020 (UTC)

@Sandbh: More amazing equivocation. So for the latter "regular" can only be meant in the sense of regular polytope, which is obviously irrelevant to the PT. But this is even funnier, because do you know what the mathematical definition of regularity of a polytope or tiling is? Well, according to our article, it means that its symmetry group(!!!) is transitive on its flags! Double sharp (talk) 11:36, 18 February 2020 (UTC)

”

Exhibit E

“

Schukarev, SA

Here.

Russian, Soviet chemist, hydrologist, teacher, historian of the methodology of science.

Check out that bibliography. Sandbh (talk) 04:37, 21 February 2020 (UTC)

@Sandbh: And would you like to know the credentials of Landau and Lifschitz with their Lu argument? Not to mention that argument from authority proves nothing? Double sharp (talk) 07:57, 21 February 2020 (UTC)

”

Exhibit F

“

@Double sharp: One of the most important outcomes of GS electron configurations is the stable oxidation state or number of bonds that an atom can form to other atoms. For example Ni being 3d84s2 tells that it will probably be quite comfortable as Ni2+, which is in fact the case. With oxygen, Ni will form an oxide of composition NiO, with a bond order of two, which is in fact the case.

How do I tell this from your PT of significantly chemically active sub-shells? Sandbh (talk) 05:26, 23 February 2020 (UTC)

@Sandbh: I don't know, how do I tell from your PT that Fe is about equally happy in +2 and +3, whereas Os prefers higher states like +4 and +6, even though both are d6s2? Double sharp (talk) 09:44, 23 February 2020 (UTC)

@Double sharp: I start from the premise that about half the elements show some regularity between electron configuration and common oxidation states. For cases such as Fe and Os, I presume there must be other factors at work and I take it from there. Sandbh (talk) 12:20, 23 February 2020 (UTC)

@Sandbh: I get it, so if it happens to fit the ground-state electron configuration, that must be the reason, and if it doesn't happen to fit, there is another factor at work. What exactly makes you think then that ground-state electron configurations are relevant, and that it is not another factor working all the time instead even when the ground-state configuration coincidentally gives the right answer? Double sharp (talk) 12:31, 23 February 2020 (UTC)

@Sandbh: NiO is not molecular compound, but if you consider one molecule in gas phase, the bond order will be slightly larger than two because of O->Ni donation. As for oxidation states, Madelung-based electron configurations are better to predict the most stable states. For Ni we have 2 valence electrons in outer subshell and 8 more in inner subshell close to completion; that leads to the most stable +2 state (outer shell), possible +3 (one electron from inner subshell) and higher ones, and also 0 with 4s electrons displaced to 3d to complete it.

Another example is Cr: Madelung suggests 3d44s2, which corresponds to stable +2 (outer shell) and +3 (one d-electron), with higher states possible up to +6. The general trend of decreasing +3 stability from Cr to Ni is explained with 3d drowning, and the local stability of +2 for Mn is explained with symmetry of half-populated 3d. Real GSC 3d54s1 for Cr explains nothing but the highest oxidation state.

So it's better to use Madelung-based electron configurations for teaching, making a footnote that for single atoms in gas phase some of these configurations have not really the lowest energy, but are at least close to ground. Droog Andrey (talk) 05:05, 24 February 2020 (UTC)

”

Exhibit G

“

You can't do that

For example, "nobody uses that as a criterion in the literature for this divide". That may be so. And so what? That doesn't meant I can't put it forward as peer-reviewed (which it most certainly will be) OR. [Sandbh (talk) 00:43, 10 February 2020 (UTC) ]

@Sandbh: It's simply an observation that something serious chemists don't use is probably not terribly important. Double sharp (talk) 07:46, 10 February 2020 (UTC)

@Double sharp: I see. In your world there will never be OR, as serious chemists haven't used it therefore there will never be anything in OR. Sandbh (talk) 06:29, 16 February 2020 (UTC)

@Sandbh: It is possible to come up with useful OR here: for example, simply take what criteria serious chemists actually used and critically examine them. That's where I got Jensen's criteria and chemically active valence subshells from. (In particular, many who insist on blocks as the important basis is implicitly being inconsistent when considering helium. And many who put the standard n+l rule and a La table are also implicitly being inconsistent!) You must also critically examine your own criteria. Yes, it's possible that you have somehow come up with some fundamental basis that every single serious chemist missed. But realistically, they have probably as a whole thought about the problem far more than we have. And they have probably gotten all the simple arguments. So if a simple property fails to be used as something important in the literature for the whole PT and chemistry, then it is already quite suspect. We should try to find out why this is the case, and often the answer is not very far away: it produces nonsense when applied to other elements. Build on the literature, yes, but give them some credit! If something simple is absent there's probably a reason that a moment's thought will reveal. Double sharp (talk) 10:35, 16 February 2020 (UTC)

[JUST UNDER THREE MONTHS OF FUTILE ARGUING LATER]

The majority of those who actually focus on the controversy "stupidly" support the Sc-Y-Lu option on the basis of isolated pop-gun arguments (like I used to do, until Scerri opened my eyes). Same reason why its easier to find Lu tables. Publish or perish; don't do OR; parrot what others write etc, textbook errors etc; there'a a long history of this kind of thing. Sandbh (talk) 08:27, 6 May 2020 (UTC)

[And yet, Scerri supports Lu...]

@Sandbh: LOL. So if the Lu tables are in a minority, it's because no one took notice of the arguments for them. And if the Lu tables become more popular, it's because people are being stupid. Way to go putting Sc-Y-Lu into a no-win situation, compounded by shutting down cogent analyses of its flaws with "look at the chemistry establishment". That seems to be the definition of textbook errors, parroting what others write, and not doing OR. Funnily enough, the ones who focus on the controversy and support the minority option are by definition doing OR and not parroting what the chemistry establishment writes. Because if they were parroting what the chemistry establishment wrote, they would not be in the minority. ;) Double sharp (talk) 09:23, 6 May 2020 (UTC)

@Double sharp: Yes, that right. It suck's doesn't it? There are so many vectors out there in favour of La, and so few in favour of Lu. The ones who support the minority option do myopic OR. They think one-shot arguments will do, more fool them. Sandbh (talk) 05:58, 7 May 2020 (UTC)

@Sandbh: LOL. Make up your mind on how to criticise authors who come to the conclusion you don't like. Are the Lu authors doing OR, or not? Double sharp (talk) 06:07, 7 May 2020 (UTC)

@Double sharp: If you carefully read what I said, I said, "The ones who support the minority option do myopic OR. They think one-shot arguments will do, more fool them." Sandbh (talk) 07:00, 9 May 2020 (UTC)

@Sandbh: And yet above that you wrote "Same reason why its easier to find Lu tables. Publish or perish; don't do OR; parrot what others write etc". So do you actually read what you write? Double sharp (talk) 09:52, 9 May 2020 (UTC)

@Double sharp: Pot calling the kettle black! Do you actually read what I write? They think quick-fire one-shot arguments will do, without surveying the literature, and looking at both sides of the argument. They are more interested in getting their idea published, then putting in additional effort. Sandbh (talk) 05:40, 11 May 2020 (UTC)

@Sandbh: You consistently do not grapple with what I quote from you (bolding mine, everything else yours):

“ The ones who support the minority option do myopic OR. They think one-shot arguments will do, more fool them. Sandbh (talk) 05:58, 7 May 2020 (UTC)

Same reason why its easier to find Lu tables. Publish or perish; don't do OR; parrot what others write etc, textbook errors etc; there'a a long history of this kind of thing. Sandbh (talk) 08:27, 6 May 2020 (UTC)”

Can you explain this self-contradiction? Double sharp (talk) 06:43, 11 May 2020 (UTC)

”

Exhibit H

@Sandbh: First I would like to note something. In this discussion we have had five regular participants: Droog Andrey, me, Dreigorich, R8R, and you. Let's see what they think about the issue (we already know you support Sc-Y-La):

"Sc-Y-La delenda est" - me, on my userpage

"La arguments are totally local, while Lu arguments are pretty regular. That exactly matches Ptolemy vs. Copernicus. The history just repeats itself. Nothing more to say." - DA

"Cool, thanks. This makes perfect sense. Well said. Team Lu for me!" - Dreigorich

And let's see what even those with less harsh words against Sc-Y-La have to say:

"I have noted in the very beginning of this discussion, which started with an article you wrote, that it did not appear to me that pro-La-Ac and pro-Lu-Lr arguments were given the same weight, and I said, perhaps not as explicitly but to the same meaning, that it looked like this was done so deliberately so that one option is favored over the other. I am afraid that what I've read so far reinforces this thinking within me." - R8R

So let me make something clear: Sc-Y-La does not have a consensus. What we have is two users who would dearly love to kill it off and have cited zillions of scientific papers in support of why they think that's the best thing for WP, one who agrees that Lu is superior, and one who at least thinks your treatment is unequal between the sides. If I wanted to, I could go right now and switch WP totally to Sc-Y-Lu, and WP:CON would support what I was doing on the basis of this discussion. I have not done so out of respect for you and with the understanding that you may have something interesting scientifically in your arguments I can learn from.

However, the most recent statements from you about convention (forgetting, of course, that the important thing here for WP is sources that focus on the issue at hand, regardless of whether you like their arguments – never mind that your characterisation of their arguments applies much better to the Sc-Y-La ones) make me seriously question if that is the case. So, here are some serious questions that I would like answers for to determine if my continued participation in discussion is worthwhile:

A. What would it take to prove you wrong about Sc-Y-La?

You don't have to believe that it could happen. Please, just answer the question with something definitive that is not "I don't know". Because: "Refutability is one of the classic determinants of whether a theory can be called scientific" (Prof. Steve Dutch; nice quote, even if it is common knowledge anyway).

B. You often refer to convention. If Sc-Y-Lu had become standard, based on the arguments you now criticise, would you still be criticising those arguments?

Because nothing would have changed about the logical status of the arguments.

C. How do you resolve the double standard, in which La/Ac and Th have similar kinds of f involvement, but are treated so differently by the La table?

If I hear "convention" again, then shall I know indeed that this is not science. Never mind, of course, that a "convention" of sources who aren't focusing on the issue will always be less relevant than a "convention" of sources who are. And that "convention" is not a valid answer when the question is targeted at whether that very convention is correct or not. Double sharp (talk) 13:15, 9 May 2020 (UTC)

@Sandbh: Please answer the questions. If you lack the time, then please just answer question A, if you can. With a straightforward, well-defined, statement that can be verified or falsified by actual data. Certainly not "I don't know". Because that's the litmus test of whether your Sc-Y-La approach can be considered scientific or not. Double sharp (talk) 05:49, 10 May 2020 (UTC)

Pending. Sandbh (talk) 06:08, 10 May 2020 (UTC)

@Double sharp: I'd say there are two regular participants; you and me. Droog Andrey and R8R are semi-regular; Dreigorich is a very rare contributor.

I responded to R8R's earlier assessment. Since you posted R8R's contribution again, here is my response again:

That's right. To make my approach clearer, the start of the article now reads as follows:

“

Scope

My focus is intended to be philosophical or systemic rather than descriptive or theoretical. Along the way some more detailed ancillary arguments will be encountered where I feel these are required to provide context, are novel, or provide useful insights.

Arguments in support of Lu in Group 3 have been summarised by Scerri and Parsons (2018) and Scerri (2020, pp. 392–403).

I mention some recent arguments, in passing.

Stewart (2018a, p. 117) observed that an argument for Lu in group 3 was that the pth element in the f-block series, with the exception of Gd, has p f electrons. In contrast, Wulfsberg (2006, p. 3) opined that:

…valence electron configurations of atoms and ions are also important in predicting the periodicity of chemical properties. Since ions are more important than isolated gaseous atoms for nearly all atoms, and important ions have no anomalous electron configurations, there is little reason to worry students with anomalous electron configurations of atoms: we prefer to teach ‘characteristic’ electron configurations without anomalies in the occupancies of d and s orbitals in the transition elements or d, s, and f orbitals in the inner transition elements.

Thus, with La in group 3, the number of f electrons in the trivalent cations of the f-block metals corresponds perfectly with their position in that block. The series starts with Ce³⁺ as [Xe]4f¹ and concludes with Yb³⁺ [Xe]4f¹³ and Lu³⁺ [Xe]4f¹⁴. Likewise, Sobolev (2019, p. 715) observes that trivalent lanthanoid (Ln) cations, representing the normal valence of Ln, have no s or d valence electrons and contain only 4f electrons.

Scerri and Parsons (2018) proposed to resolve the issue by adding a third requirement to the two parts of the Madelung Rule. However, there are many pre-existing exceptions to the Madelung Rule, and the fact that the La form does not pass the new requirement is simply an outcome of the delayed filling of the 4f sub-shell. In this light, the merits of their proposal are not apparent.

Tsimmerman and Boyce (2019) argued for Lu in group 3 on the basis of the regularity of spin multiplicity, which is one of the three components of an element’s spectrographic term symbol. Unfortunately this argument introduces an anomaly in the overall regularity of term symbols.

Alvarez (2020) supports Lu on the basis of trends in atomic size, coordination number, and relative abundance of metal–oxygen bonds. However, the trends involved apply regardless of whether Lu is under Y or at the end of the f-block, after Yb.

Other than to provide necessary context, I will not further revisit Lu in Group 3 arguments.

”

Sc-Y-La has no consensus among our little subset of our Project. There has been no attempt to seek consensus among all Project members. We know IUPAC is considering the issue. We know the ratio in the literature is 4:1:1 La:Lu:* **. We know this establishes consensus in the literature by a wide margin, notwithstanding maybe two dozen(?) dissenters over the past 60 years, nearly all based on single property arguments. Against that there have been maybe a half-dozen or more supporters of La appearing in the literature, noting presumably a much larger silent majority as Lavelle put it. Thank you for your courtesy in raising this topic here, within our project. I appreciate that. It's been a learning experience for me too, which is perhaps what I enjoy the most, even when we get a bit tetchy in our responses.

A: I've switched back and forth between La and Lu. If IUPAC comes out for Lu that'd be fine by me. Would I've been wrong? No, I would've made a mistake, and would look forward to new learning. "Wrong" is negative, emotive, pejorative, baggage-like, and unhelpful.

B. If Sc-Y-Lu had become standard then no, I doubt I would've been criticizing this convention. Unless anti-Jensen had published an argument in favour of La. I supported Jensen, until Scerri (who supports Lu) opened my eyes to the limitations of Jensen's approach.

C. The thing about conventions is that they endure because they're useful, and nothing better has come along. It's a bit like the convention of the Madelung Rule. Even though it produces 20 errors, it works well enough. Nobody's come up with a better approximate with fewer errors, so even though the MR is "wrong" or only 80% or so accurate, people still use it.

On Th, this is only a question of degree, and bang-for-buck. Ce and Th are the first metals where we see a significant impact of f involvement. We don't see anything on that scale in La and Ac.

See also my response to your argument K. Sandbh (talk) 06:08, 10 May 2020 (UTC)

@Sandbh: You didn't answer my question A. Let me rephrase it, because you do not seem to like the word "wrong". What scientific possibility, as opposed to some pronouncement ex cathedra, would lead you to doubt Sc-Y-La?

You know, if IUPAC said "Sc-Y-La must be right, because lanthanum is not a lanthanide, it is exactly lanthanum", I bet you we will all consider this argument extremely stupid word-gaming. (Of course they won't do that, they have more sense than that, but this is hypothetical). And if IUPAC said "Sc-Y-Lu must be right, because that way La and Ac are in the f block together with the lanthanides and actinides", I bet you we will also consider this argument to be just as silly. (And of course they won't do that either.) In fact, probably so will the chemical community in both cases, who roundly still ignore their terminological pronouncements in favour of lanthanoid and actinoid instead of lanthanide and actinide. And if they end up using arguments I've also used, then what? Are you going to accept it just because IUPAC said so as opposed to me saying so, even though I got them all from the literature anyway? So there must be more to accepting a decision scientifically than "IUPAC / Jensen / Seaborg / Wulfsberg / Lavelle / Scerri / I / you / DA / Mendeleev might have / The Great Space Wombat said so". You have to ask: why did they say it?

Let me quote a philosopher of science, since you seem to want a philosophical perspective. Bold as in Wikiquote.

“

I may illustrate this by two very different examples of human behaviour: that of a man who pushes a child into the water with the intention of drowning it; and that of a man who sacrifices his life in an attempt to save the child. Each of these two cases can be explained with equal ease in Freudian and in Adlerian terms. According to Freud the first man suffered from repression (say, of some component of his Oedipus complex), while the second man had achieved sublimation. According to Adler the first man suffered from feelings of inferiority (producing perhaps the need to prove to himself that he dared to commit some crime), and so did the second man (whose need was to prove to himself that he dared to rescue the child). I could not think of any human behaviour which could not be interpreted in terms of either theory. It was precisely this fact — that they always fitted, that they were always confirmed — which in the eyes of their admirers constituted the strongest argument in favour of these theories. It began to dawn on me that this apparent strength was in fact their weakness.

”

— Karl Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (1963)

A theory, to be scientific, must be falsifiable. There must be some conceivable observation that would prove it mistaken. What is that, for your Sc-Y-La case?

Of course, your answer to B is revealing. It surely seems you have no argument for Sc-Y-La but "this is the convention". A convention based only on the sources who are not analysing the convention, of course, and many of whom I bet don't even cover group 3 significantly within their pages (the first-year textbooks). Among those who do focus on the issue, the consensus is for Sc-Y-Lu instead. That's the relevant consensus for WP: secondary sources focusing on a subject surely are more important here than tertiary sources for which the issue is completely peripheral and hardly addressed using any argumentation at all. See WP:PSTS.

And if this pseudo-convention was Sc-Y-Lu, but all the arguments were the same, you would apparently be supporting that. How's that scientific? And for C, all you have to go on is self-contradiction on whether Th has a significant impact of f involvement or not. Because to quote you further up on this page:

“

The concerns you raise about 4f involvement in La, (maybe) Ac, and Th, are valid, in a footnote or 20/80 kind of way. I'd not describe them as headline material.

”

Just as thorium without f involvement would be a normal hcp transition metal, so would be lanthanum and actinium. None of them are. There's a smoking gun for f involvement if I ever saw one.

So: you don't appear to have any arguments that are not based on an irrelevant pseudo-convention being a pseudo-convention, or that are not based on outright falsehoods that have been refuted over and over here.

Well! I can tell you that DA almost certainly agrees with what I've been saying, judging by what he wrote in Archive 42:

“

Having read all 700k+ of this discission, I've got the same feeling as Double sharp had:

"I'm tired of this endless double standard. You throw out a barrage of arguments that look like they might support the La table, and flip non-stop between them the moment one of them looks like it is in trouble. And then you selectively read the literature in order to not see refutations. And you never consider whether any of your criteria are truly fundamental by putting them to the test of the rest of the table, cloaking this masterpiece of inconsistency under the garment of minimising change. Which is more or less like taking the La table as an axiom and throwing out whatever you want to save it. All I can say is: this is not science. There is no way we can proceed if you refuse to follow scientific principles, actually put your theories to the test, and at least compare all possibly relevant criteria and no others equally regardless of whether they seem to favour La or Lu. If you don't do that, then I say: go ahead and get what you want published. But don't thank me for the critique in the acknowledgements, because I disagree with so much of your paper that I don't want it to look like I supported the final product."

Indeed, it seems that Sandbh lacks attention to patterns and general trends explained by Double sharp with great patience of job. As an experienced chemist, I insist that deep understanding of these interrelations is required to discuss the foundations of chemistry, even in the context of historical review. Otherwise this is not science to send an article, but conscience to withdraw it. Droog Andrey (talk) 07:51, 12 February 2020 (UTC)

”

And I have started writing a simplified form of my alphabet of Sc-Y-Lu arguments on Dreigorich's talk page. So far I am up to G, and he agrees with it all. He may correct me here if he does not.

So let me make something very clear: you do not have a consensus for Sc-Y-La. If I opened up a straw poll at the bottom of this page based on all the arguments set forth here, I am sure only you are going to support Sc-Y-La wholeheartedly. And for sure I and DA will be supporting Sc-Y-Lu extremely strongly. Maybe R8R would abstain from supporting Sc-Y-Lu outright on the grounds of the literature (although I have made a case that this is irrelevant, as the literature that focuses on the group 3 question skews towards Sc-Y-Lu and is miles more relevant than first-year textbooks for which group 3 is very far off the radar), but he has also criticised your argumentation. Well, we may summon him and ask him what he would do.

So: I have enjoyed this discussion indeed at the beginning of it, because it has certainly been helpful for clarifying my Sc-Y-Lu case. You did indeed make me think and I am grateful for that. But now that it is going in circles where the facts I bring forward with copious citations are never accepted, I am certainly not enjoying it anymore. So now's the time for the tough question: are you planning to be scientific, and provide a real falsifier criterion for your stand, or not? Double sharp (talk) 06:32, 10 May 2020 (UTC)

Pending. Sandbh (talk) 13:36, 11 May 2020 (UTC)

Best quote:

“

When it comes to the question of why La and Ac should remain in the d-block rather than being reassigned to the f-block, Lavelle offers no new chemical or physical evidence other than his constant reiteration of the fact that both elements contain d-electrons in their ground-state valence conﬁgurations, but no f-electrons. Yet in the cases of both Lu and Th, for which this is equally true, he proceeds to inconsistently argue that this fact is of no consequence when it comes to assigning them to the f-block. As with the case of the revised conﬁguration for Lr, which counts when it comes to not placing this element in the d-block but is irrelevant when it comes to placing it in the f-block, this arbitrary and naive use of electron conﬁgurations, to the exclusion of all other evidence, is logically inconsistent and leaves one with the impression that the only true argument that Lavelle has for the major premise of his diatribe is that La and Ac should remain in the d-block because that is where IUPAC places them in its official periodic table and therefore all rational discussion of other possibilities is strictly forbidden.

”

— William B. Jensen

Replace "Lavelle" with "Sandbh" and "where IUPAC places them in its official periodic table" with "where most textbooks who don't cover group 3 place them on their flyleaf periodic tables, except for when they really end up creating a Sc-Y-* form instead". Double sharp (talk) 07:35, 11 May 2020 (UTC)

@Sandbh: Well, you say above that you are two dozen pings behind. That's fine. Please answer this one. It is the most important one. What is the falsifier criterion for your Sc-Y-La stand? Double sharp (talk) 06:19, 11 May 2020 (UTC)

@Double sharp: Well, if Scerri, who is a great fan of Popper, knew the answer it would've been pens down. Likewise, I don't know the answer, honestly. But I'd know if I saw it; I haven't seen it yet. This is not a logical proof exercise. There is no logical provable answer. Chemistry, with its qualitative and quantitative aspects is like that: As Poliakoff (2011) said:

"In the end, I think that one should remember that Mendeleev devised the PT for a textbook to help rationalize the mass of facts in inorganic chemistry…For me, the PT remains a tool to help reduce the complexity, not a metaphysical truth that has a correct form yet to be discovered."

And there is this:

"Charles Perrin at the University of California, San Diego, who was not on the IUPAC committee, likes the fact that the bond can now be experimentally verified. “Chemistry has all sorts of fuzzy definitions,” he explains. At the same time, having several criteria allows for some much-needed wiggle room, he says." ---New Scientist 2011, on H bonding

To me, you and Droog Andrey don't appear understand that. For DA, this is is surprising. Chemistry is full of ambiguities and fuzzy boundaries. Logic doesn't apply in this case, only one's strength of arguments. Sandbh (talk) 11:01, 11 May 2020 (UTC)

@Sandbh: ROFL. And how do you plan on measuring "strength of arguments" if "logic doesn't apply"? At the very least, don't you think it's just a tiny bit ridiculous to keep going with an argument after its premises have been soundly debunked and the logical contradictions it leads to have been painstakingly detailed? Double sharp (talk) 12:16, 11 May 2020 (UTC)

@Double sharp: That's your problem, not mine! Why not ROTFL some more and see if that helps? No, it's not ridiculous, since, as I recall, we have uncovered new territory. Sandbh (talk) 12:28, 11 May 2020 (UTC)

@Droog Andrey, R8R, and Дрейгорич: This hilarious exchange presented without comment for all to see and judge how scientific it is. Double sharp (talk) 12:31, 11 May 2020 (UTC)

ROFL. Where is the "logic"? ― Дрейгорич / Dreigorich Talk 13:04, 11 May 2020 (UTC)

Actually: since evidently Sandbh claims that "logic doesn't apply" here, there is clearly no point to this discussion, as if logic is to be denied admission the possibility that he could change his mind in response to any evidence seems rather minuscule. Therefore I will (really this time) cease participation. (A good thing too, as I have more and more things to do and the only reason I can respond here so quickly is that we have gone round these bends so many times that I pretty much have all the plausible responses memorised.) Sandbh may write what he wants in response to my comments above, but responding to him would seem to be futile based on this comment (with one exception).

Any others who comment above will, of course, be replied to. I recall I had some unfinished discussion with R8R, for instance. But I think this unfalsifiability of Sandbh's approach already serves as quite an explanation for my stand on this argumentation.

Of course, my challenge to all who would like to refute the chemically-active-subshell theory stands. Since the presence of La 4f of the same type as Th 5f is by now unarguable with tons of papers supporting it, to do it you're going to have to find 4f involvement in Lu, or any subshell intervening where it doesn't belong. Go ahead and surprise me: my approach is open to falsification, hence scientific. This is the exception for which I will continue to reply to, as long as they are not reruns of already fully charted argument strands (defined by "would my reply consist of repeating something I've already said"). (Or Droog Andrey might, if he gets to it first, as he knows more chemistry than I do anyway.) Of course, my usual answer to attempts by him to debunk La 4f is going to be (writing it here, so I don't have to say it another 9001 times) a challenge to explain away the observations without La 4f, e.g. high T_c of La at all pressures, or cubic complexes of La.

Sandbh may, at any time, decide to actually give a criterion by which his approach may be falsified. It isn't terribly hard. Then we may resume subject to my time commitments IRL. But I'm not holding my breath anymore, since I've asked the same question over and over again and still not gotten a straight answer that can actually be falsified and cause him to change his mind about anything. And, as demonstrated above, there seems to be a dearth of criteria that will not lead to the La table shooting itself in the foot by arguing for Be-Mg-Zn, B-Al-Sc, Ti-Zr-Hf-Th, Ti-Zr-Ce-Th, or other such wondrous concoctions. Double sharp (talk) 17:11, 11 May 2020 (UTC)

It appears I will have to delay this disengagement by one more day, since even more funny quotes to summon everyone to look at are coming. XD Double sharp (talk) 04:40, 12 May 2020 (UTC)

@Double sharp: That's good to hear; I enjoy the funny quotes too. I've explained at some length all the other vectors operating within the chemical establishment, including IUPAC. For whatever reason you choose to myopically focus on logic, as if that is all that matters, and ignore all the other vectors. Yes, it's unpleasant or challenging that one has to grapple with political realties in science. But there it is. You can go with the flow or be run over by the locomotive. The alternative is to come up with a showstopper, which you haven't, IMHO. La works well enough. Lu doesn't offer enough enough bang for buck or ROI. As noted, chemistry is qualitative and quantitative. The latter you'll be fine with; the former is your stumbling block.

I see you've now come up with a convoluted argument for an RfC. Really? Never mind IUPAC has a project looking at the same question. WP is no more than encyclopedia, reflecting what the literature says, as I learnt lone ago. There is no consensus in the literature for Lu. Two dozen supporters in 100 years? I laugh at that, in a good-humoured manner. 100 frigging years? And you want to go to an RfC, ROTFLOL until my head falls off! When you get as old as me, you'll learn there is much more to the world than logic. Old age and wisdom beats youth and enthusiasm, as I learnt.

You keep asking for a falsifiable theory. There isn't one! Did you read what I said, "Well, if Scerri, who is a great fan of Popper, knew the answer it would've been pens down." What is it that hinders you from seemingly being incapable of grokking this? Sandbh (talk) 07:49, 12 May 2020 (UTC)

@Sandbh: I dunno, what is it that hinders you from understanding how the scientific method works? If you come up with a theory, there must be some sort of plausible observation that would falsify the theory. Otherwise it's no better than the psychoanalytical theories Popper critiques in the quotes above; they can explain everything, and that is their weakness. They have zero predictive power: when faced with any observation, you would get the answer "oh, this is exactly what you would expect from the theory". And when faced with even the exact opposite operation we would get that answer too. Scientific, not.

As our article scientific method states: "A scientific hypothesis must be falsifiable, implying that it is possible to identify a possible outcome of an experiment or observation that conflicts with predictions deduced from the hypothesis; otherwise, the hypothesis cannot be meaningfully tested." So, if you have some theory that predicts Sc-Y-La, it must make predictions about what should be observed about La and what should not be observed about La. You even implicitly seem to subconsciously accept this when you argue with me about 4f involvement in La, which is a fairly obvious tester for the Sc-Y-La hypothesis. But of course, here you don't give any possibility.

So far we've given lots of showstoppers for the La table and your arguments for it, pointing out its self-contradictions, its double standards, and its lack of alignment with the facts. All of which are well-supported by the literature, which is full of people arguing for the Lu table, and has not very many people arguing for the La table. (Yes, many people show it. While clearly not focusing on the issue at all. Or rather show inconsistent versions of it combined with Madelung rules that contradict it. With no analysis at all. Those are not arguments, and neither are they the relevant sources per WP:CONTEXTMATTERS.) Well, somehow everybody here finds them problematic for your theory but you. Which is why I think I was right yesterday; arguing with you really isn't productive because nothing I could possibly say would convince you. Of course, the difference between our approaches is that in principle you could say something that would convince me. It's just that nothing so far has done so.

My last words on this to you: if "there is much more to the world than logic", then why are you trying to use any arguments at all to support La? Arguments are logic, you know. Who's to say that someone couldn't just say "there is more to the world than logic" and say "Sc-Y-Lu because WP:ILIKEIT" instead? Oh wait, but I can't even point out the contradiction, because that involves logic! ROFL. Double sharp (talk) 07:51, 12 May 2020 (UTC)

@Droog Andrey, R8R, and Дрейгорич: For your amusement, as this really must be seen to be believed:

“

When you get as old as me, you'll learn there is much more to the world than logic.

You keep asking for a falsifiable theory. There isn't one!

”

— Sandbh, 07:49, 12 May 2020 (UTC)

Well, how scientific does that sound to you? Double sharp (talk) 08:02, 12 May 2020 (UTC)

Just one thing I'd like to say. inhales ROFLMAO! ― Дрейгорич / Dreigorich Talk 13:06, 12 May 2020 (UTC)

Read as few or as many of them as you like: I think my point is made. If you don't have time to read all eight, just read A, G, and H, as they're by far the funniest. (And if you need just one, just read G.) Maybe there are Sc-Y-La arguments that are not silly and self-contradictory, but Sandbh's are not among them. And given the obvious obstacle that thorium poses, you're going to have to work very hard to find any. Double sharp (talk) 06:50, 13 May 2020 (UTC)

@Sandbh: Courtesy ping. I have not changed a word above in what is quoted, except for the few things [in square brackets]: only the titles are mine, and they are totally backed up by what is in them. The facts of chemistry and basic understanding of logic, that are essential for a philosophical perspective, speak for themselves, as do our words. Double sharp (talk) 06:54, 13 May 2020 (UTC)

@Droog Andrey: Courtesy ping, since I also quoted you. Double sharp (talk) 06:57, 13 May 2020 (UTC)

@Double sharp: I will thank you to remove these defamatory titles including from Дрейгорич's talk page. It is one thing to engage in robust arguments and tetchy raconteur; it is quite another to engage in concentrated trumpeting to the world of your derogatory perceptions of another project member. You are of course free to reproduced my edits and comment on them. Sandbh (talk) 00:41, 15 May 2020 (UTC)

@Sandbh, Droog Andrey, Дрейгорич, and R8R: Sandbh: the titles are an exact statement of the situation, as backed up solidly by the quotes. (The only exception is "Double Standards" in Exhibit F, which I have removed as this one is indeed not so clear: while it is indeed not treating GS configurations fairly, because it essentially says "when it works it must be the reason, and when it doesn't work there must be some other reason why it doesn't work", that is not an explicit double standard, as it would be OK if there was some reason why we would expect the situations to be different, see my comments in Exhibit B. Of course there aren't, but I have removed those words from the title anyway. Thorium is a better example of your double standard.)

Take Exhibit A. Arguing for months about supposed predominancy of covalency or ionicity for a whole element's chemistry is simply not understanding first-year chemistry, for example. Explanations of this are so ubiquitous in basic chemistry textbooks that it cannot be considered to be only my perception. I am aware that you dropped that, once you found that even your own source was saying it to you. And I quoted that as well, so I have not portrayed you unfairly. But the mere fact that it took you that long to drop something this elementarily wrong, that you should have known already if you were going to argue about group 3, is still relevant.

I have not said anything in these titles that I or Droog Andrey have not already said. Which is that your arguments have showed a basic lack of understanding of first-year chemistry (except once you see your own source spell it out for you explicitly, in that single instance, which I quoted; now those supposed nonexistent group divides at least show a lack of understanding of a higher level only), inconsistency, a lack of understanding of logic and eventually disclaiming it altogether (while still producing arguments!), not understanding the word "symmetry", double standards, arguing from false premises, and self-contradiction about whether the sources who pick the option you dislike are doing OR or not. (Never mind the questionable relevance of that, since they are sources and WP:OR is only relevant for what is written on Wikipedia.) And this is not my perception, anyone looking at this discussion and applying logic and who understands chemistry will see it. Dreigorich is a participant in this discussion, and his talk page is just as much a publicly viewable forum as this project page. If this is "trumpeting to the world", then so has been this entire discussion.

“

Having read all 700k+ of this discission, I've got the same feeling as Double sharp had:

“

I'm tired of this endless double standard. You throw out a barrage of arguments that look like they might support the La table, and flip non-stop between them the moment one of them looks like it is in trouble. And then you selectively read the literature in order to not see refutations. And you never consider whether any of your criteria are truly fundamental by putting them to the test of the rest of the table, cloaking this masterpiece of inconsistency under the garment of minimising change. Which is more or less like taking the La table as an axiom and throwing out whatever you want to save it. All I can say is: this is not science. There is no way we can proceed if you refuse to follow scientific principles, actually put your theories to the test, and at least compare all possibly relevant criteria and no others equally regardless of whether they seem to favour La or Lu. If you don't do that, then I say: go ahead and get what you want published. But don't thank me for the critique in the acknowledgements, because I disagree with so much of your paper that I don't want it to look like I supported the final product.

”

Indeed, it seems that Sandbh lacks attention to patterns and general trends explained by Double sharp with great patience of job. As an experienced chemist, I insist that deep understanding of these interrelations is required to discuss the foundations of chemistry, even in the context of historical review. Otherwise this is not science to send an article, but conscience to withdraw it. Droog Andrey (talk) 07:51, 12 February 2020 (UTC)

”

Feel free to take it to WP:Dispute resolution or even WP:Administrator's noticeboard if you really want. (Although that would really be bringing the world in.) If the consensus there is that I have gone too far with these titles, I will remove them without complaint. Or ask Droog Andrey, Dreigorich, and R8R for their opinions of whether I have gone too far in these titles; if even one of them thinks I have, I will remove the titles. Although, I will note that I have certainly not gone farther than you who referred to my logical argumentation as "fogging", "flat-earthing"(!), and other charming epithets.

I am, in fact, very sorry that I have to say this. Let me just quote my conversation with Dreigorich on his talk page after I showed him Exhibit A:

“

There is so much OMG and ROFL here. Oi. ― Дрейгорич / Dreigorich Talk 14:54, 12 May 2020 (UTC)

Which sense of "oi" is that? ^_^ But enough is enough, I haven't got all the time in the world to spend on correcting such things. You will have to content yourself with the occasional archive binge. It probably gets funnier as you learn more chemistry! Double sharp (talk) 14:57, 12 May 2020 (UTC)

Oi in the sense of... how does an actual human argue this? ― Дрейгорич / Dreigorich Talk 14:59, 12 May 2020 (UTC)

Now, now, that's not very nice. Sandbh has already scolded me about civility, telling me on WT:ELEM that "As usual your bombastic sense of righteousness does you a civility disservice", and I don't want to go down to that level as it inevitably obscures your point. (Never mind that writing "I’m astonished to think you could post such rubbish", and that I'm engaging in "flat-earthing", does not seem to do him a civility service either.) So, patience it will be for me, even if I'm not going to keep responding to him. Perhaps we should ask instead: how does someone who evidently cares deeply about chemistry, enough to write long (even if they have some room for improvement) arguments for specific forms of the periodic table, and presumably should remember first-year chemistry classes, seriously argue this? I honestly thought he knew more than this when we were collaborating from 2011 onwards about metalloids, their classification on WP, and sooner or later the group 3 dispute. And when I was on the Sc-Y-La side, that was only because the information I had was not so good. And I progressed from that level; why this? I cannot help but feel greatly disappointed myself. These were not arguments worthy of what he was capable of when we started having these long discussions on WT:ELEM. Well, I guess I will have to consecrate a tear for how he could once argue in Archive 15. That feels so long ago now... Double sharp (talk) 15:06, 12 May 2020 (UTC)

To be fair, I've sort of given up on Sandbh at this point. You cannot argue with some people and convince them of your viewpoint. ― Дрейгорич / Dreigorich Talk 15:15, 12 May 2020 (UTC)

”

But, unfortunately, it is true, as I have demonstrated with quotes. What I say in the titles is exactly what has been said elsewhere here.

With continued respect for you as a person, Double sharp (talk) 03:37, 15 May 2020 (UTC)

As R8R has recommended so on the main talk page, I have removed the titles. Nonetheless, I point out that everything said in them has already been said elsewhere here. Double sharp (talk) 03:28, 16 May 2020 (UTC)

Philosophy

Almost forgot! You know how one important scientific degree is denoted by the letters Ph.D. Would you mind reminding me what that stands for? ;) --R8R (talk) 15:47, 2 May 2020 (UTC)

Why does that matter? Words are not defined by where they came from. This is language, there can be lots of old fossils in it, even if most scientists with that degree are not actually doing terribly much philosophy. Science is made by scientists, sure, but eventually the ideas that we find out are right get worked on, and the ideas that we find out are wrong die off. It takes a while, but it happens.

Yes, this is rather something I have found remarkable about this discussion. Because to me it is kind of obvious that an x-block element (x = s, p, d, f, g) is supposed to have some kind of involvement of the x-orbitals, otherwise the whole thing is just artificial. The fact that the blocks are normally explained as following the Madelung ordering supports that. When I was on the other side of this debate, it was because I was under the mistaken impression that Lu had some significant f-usage, and that La and Ac had a lack of f-involvement that was categorically different from Th. Now that we know that's totally false, there doesn't seem to be any sound basis for Sc-Y-La at all. But apparently, that will not stop the argument from raging in circles, with stuff I have already debunked appearing again and again. Double sharp (talk) 05:33, 3 May 2020 (UTC)

It's more than a fossil. Philosophy is a way to understand the world around us, just as science is. You may recall how Newton's magnum opus was titled Mathematical Principles of Natural Philosophy. In fact, natural sciences are very similar to natural philosophy, and philosophy lost a lot to science in the 19th century when branches of knowledge were reclassified from philosophy to science. (It was also around the same time when "scientist" became a profession, i.e., something you'd get money for, i.e., something someone would be willing to pay you for. The great ~~scientists~~philosophers of the Enlightenment, for instance, simply worked on their problems of interest in their spare time.) Also doing philosophy does not necessarily mean getting into a barrel and thinking about how civilization is retrograde or something. I recall Scerri, the chair of the IUPAC group 3 taskforce, has been described as a philosopher of science? Well, I am reading his book on the periodic table and I positively like how he tries to look into things and see why they were the way they were, and that is precisely philosophy. That's why it matters: I simply don't think the antithesis between "philosophically" and "scientifically" is a right one. It is right philosophically and, I would argue, it is right scientifically. Old ideas often don't die easily because they are already accepted by everyone. It is easy to get the idea that many old ideas have been identified as wrong and replaced, but that is because you know about how phlongiston or vitalism ended up but you're not exposed to ideas that have not been identified as wrong and you're not exposed to how advancements that might have been recognized have not been. And if you want to say that if ideas are right, they are posed to reemerge, then I'll note that that statement, at least in such generality, is not falsifiable. As I said, whether that tradition has a positive value is good or bad is up for debate, but whether that is the case at all is not.

Blocks are artificial

The whole idea of blocks is artificial however you look at it! But we create this artifact nonetheless because one may think it's easy/easier to have it, or because we can have it and feel smart about how we've created it (I'm serious, the desire to "feel smart" is a big part of science), or because there are certain points that people want to make. One such point is that there is a certain way of how scientific analysis should be done and one may want to apply it here as well and look at the result and declare it a success, whatever the actual result. (I think this describes both yourself and Sandbh; naturally, I'm not saying that's your only motivation, but do you see how that's a big part of it?)--R8R (talk) 10:51, 3 May 2020 (UTC)

Borders etc

I just remembered one example of such a "conventionally wrongly resolved" question that is similar to the question at hand. What is the precise geographical border between Europe and Asia? The answer to that question, like the group 3 question, is conventional: people need to decide where the border would be, there is no "natural way" of defining it. The general agreement is that the border on land goes along the Caucasus and the Ural Mountains; the problem is, the Urals doesn't end at the Caspian Sea but rather before it. The convention is to use the Ural River but the terrain on both sides of the river is very alike. The Russian Geographical Society launched an expedition into the area to define a more sensible border and here you can see what they came with. It is indeed better geographically, and the border is better defined geographically (the eastern slope of the Eastern European Plain) but that's not the border we'll follow because the idea has apparently been overlooked. The convention and/or tradition has remained in place.--R8R (talk) 12:48, 3 May 2020 (UTC)

Natural classes

@R8R: Is there really not a "natural way" to define group 3? I'd bet that if you showed most people who can recognise mathematical patterns the table from hydrogen to xenon, and asked them how they'd expect rows six and seven to go, they'll draw for you a Sc-Y-Lu table. That just continues the pattern in the obvious way. Well, we have a Madelung pattern that works perfectly from H to Xe: you're going to need a strong chemical argument to unseat that. That's why I have argued that it actually makes more sense to start from the assumption of Lu under Y as the "working hypothesis" if no strong arguments can be found one way or the other. We are supposed to be starting from what we now know about the elements, not what scientists in the 1920s knew. (Of course, IMHO this point is pretty moot because 4f involvement in La of the same order as 5f in Th is a strong argument already.) Maybe the fact that a tradition exists has some positive and some negative value, but if the whole point of the exercise is to determine if the tradition is right, like here, then it seems to me that the best way forward is to pretend that the tradition did not exist and see if it appears as a logical deduction from what we now know, as opposed to what we then thought we knew.

Seaborg example

Reading Sandbh's arguments, I get the impression that if we were (somehow, let's not think too hard about the technological issues involved) having this argument in the 1940s, I would be the fine 17-year-old upstart promoting Seaborg's actinide concept, and he would be equally fervently defending the old arrangement with Th, Pa, and U as transition metals. Well, that would be the unshakeable battleship shown by textbooks. Which turned out to be not so unshakeable after all, once Seaborg's team got in their stride synthesising actinide after actinide, with each new element past plutonium as a new death blow to that theory. Well, maybe a thoride series would start being argued for, instead. You know that MO₂ exist for Th through Cf and that Goldschmidt suggested a thoride series, too? And that the first 5f electron appears at protactinium? Well, even today we can make the case similarly to what Sandbh has done: thorium only has indirect 5f effects (causing the same fcc crystal structure as Ac), it doesn't usually have a 5f electron in any compounds. Thorium acts like a tetravalent main-group element forming Th⁴⁺ (King agrees with that), it is quite electropositive, and +4 is a reasonable baseline state for Th-Rf, being showed by Th-Cf and Rf. Yes, it makes a displeasing asymmetry, but we can again appeal to the old bromide about drawing Nature as She is rather than how we would like Her to be. And we have Bohr as a precedent, who thought that 5f would not start lined up with 4f! So Sandbh's very same arguments can also be used to undermine the position of thorium in the f block. Which makes me think, like Jensen, that the only real case for the Sc-Y-La table is "the textbooks have spoken". Never mind, of course, that the textbooks usually contradict their own tables within their texts, and often show tables that are clearly meant to be Sc-Y-La and really mean Sc-Y-*. Go figure. ;)

Geography, blocks and artificiality

Europe vs. Asia is at least partly a cultural divide and not solely a geographical one. I mean, you'd probably agree that the only sense in which Russia is significantly Asian is probably geographical. ;) Well, is Turkey European? Kazakhstan? Armenia? I'm not even sure there is a clear convention for some of these questions I just asked. ^_^ So I think this is not a comparable situation: we go for a convention here because there is not a natural answer and there is not a natural way to get an answer, it will move depending on what you are really interested in. For group 3: pedagogy supports Sc-Y-Lu, chemistry supports Sc-Y-Lu, physical properties support Sc-Y-Lu, now where is the point for Sc-Y-La? I only argued for it in the first place because I mistakenly thought that the chemistry and physics supported it, you know.

I don't think blocks are very artificial. Anyone may look at the chemistry of the elements and see the pattern of what subshells the elements use for chemistry. Once you do that, the periodicity becomes extremely clear, and the blocks pretty obvious. The only exception is the s block, which is the real symmetry break: it fraternises with the "wrong" n+l value. Double sharp (talk) 05:16, 4 May 2020 (UTC)

@Double sharp and R8R: I agree with you. Blocks are artificial in that the map is not the territory. At the same time, the blocks, or their broad contours, do appear to fall out quite naturally, allowing for some seeming fuzziness at the margins. As with the metalloids I feel the fuziness does not necessarily prevent us from drawing useful boundaries, acknowledging these can change according to the properties of interest. I recognise the validity of the La, Lu and 15 Ln forms, depending on your bent. I feel the Lu form requires too much work to be worth the effort. There isn't enough puff in it to capsize BB Chemical Establishment. That doesn't mean it's wrong (it's quite interesting, in fact). Sandbh (talk) 06:53, 6 May 2020 (UTC)

@Sandbh: OK, we are basically in agreement regarding the blocks. We drew the little rectangles, nonetheless they are certainly pretty obvious from the data. However, I do not see how the Lu form requires any significant extra work. Indeed, part of it involves not doing some work: it basically says "let's ignore Madelung anomalies because they seem to not mean anything for real chemistry". And, indeed, the real facts support that, with 4f valence involvement for La and no such thing for Lu. And, because it's now clear that the third electron is actually coming from 4f rather than 5d, the Lu table gets rid of the misapprehension that the 4f electrons are not doing anything much for the lanthanides. So it seems totally worth the effort; you get a better understanding of the role of 4f orbitals, from a simpler starting point and a more symmetric table. Why would anyone go for the La table in this scenario, which is less symmetrical and gives a worse understanding? Double sharp (talk) 06:59, 6 May 2020 (UTC)

Natural classes II

Is there really not a "natural way"? Well, a natural way is one that everyone can easily agree on, that feels simple and natural to everyone, as simple as that, and from this discussion we can see that this problem is not the case. You may have an opinion, I don't think it's too unreasonable, Sandbh has an opinion, I don't think it's too unreasonable, either. By the way, if you ask many people a question, you are far from guaranteed to get a correct answer: just yesterday, I discovered this headline. (The word "British" can be safely removed without any loss of accuracy.) This in part has to do with that not everyone having an opinion thinks the reduction of the problem to that of a mathematical sequence is correct.

Tradition and its place

For one, I think that Sandbh overemphasizes the importance of tradition whereas you neglect it. I don't particularly agree with either approach. That is, however, not to say that I'm going to say that either of you is wrong. First and foremost, I don't think that I'm right on the merit of me being me: other people have their ideas. I recall what is emphasized in that headline from the last para: most ideas people have are wrong; mine could be wrong, too, and I'm mindful of that however I may like my arguments. I always try to "try on" somebody's shoes if I am to argue with them and see why they argue the way they argue and how their opinion could be in principle changed. (There would be a point when I could say I have collected enough data to know the real answer for certain, but as I said before, this is not a question of that kind that has a "right" or "wrong" answer.) And another reason is that if I'm at all about to change somebody's opinion, then telling straight away that they're wrong isn't going to help; it'll do the opposite if anything. I can't say I always handle my arguments well, but I am making an effort to get better at it, and I think it's working. What I find important in this kind of discussion is that neither side sees the need to go defensive and thus deaf to the arguments of the other side. That would be the kind of climate where arguments lead to birth of the truth. (Now, there are arguments where you are not looking for the truth, for one, where you are looking to prove your opponent wrong. Political debates are one notable example among many. The opponent is not going to recognize it, of course, whatever the facts, and all side show off before an audience rather than each other.)

As for Europe and Asia, I'll try not to go too off-topic here. The point that I was making, however, has to do with a, quote, "precise geographical border"---that can be defined without any reference to culture (or even worse, contemporary politics). Cyprus is undoubtedly a part of the European cultural space and is just as undoubtedly not European geographically. Please re-read that part with this consideration in mind.

Re "I don't think blocks are very artificial": depends. Not very artificial indeed, it does make sense to make the decision to have them. However, my point was that it was not quantitatively artificial, but qualitatively. Blocks have been first thought of, after all, in a deliberate manner. Quantitative allows for more diversity, i.e. more room for disagreement. That includes your disagreement with Sandbh about how blocks, particularly, group 3, should be drawn. You can say that you find the other ways than yours artificial: well, following that logic, someone is sure going to say the same about yours. I'm suggesting to not call others' opinions inferior, in this case, "unnatural."

I was going to write that in a separate response to Sandbh, but as it comes down to it, I want to mention it here too, so I'll do it here. (courtesy notification for Sandbh) What I found really interesting in what Sandbh says is that he thought the arguments starting with the symmetry of the -Lu-Lr blocks were flawed by their nature, and that he tried to go the other way. I am thankful for this explanation. As a thinking principle, I think that is very reasonable to try, and gives me a better incentive as to why Sandbh argues the way he does (remember the bit about shoes). I also notice that you said that symmetry is not totally wrong-headed... I noticed that "totally" there, so it partially could be? I'd take that as a recognition of how Sandbh, or anyone in principle, could be not entirely satisfied with that argument and might want to try the other way. And I think it's up to you how to handle it from there and whether to lock Sandbh there in a defensive stance.

My most sincere recommendation is to revisit the "If a scientist makes an error in judgment, he must recognize it or else he is not being scientific" attitude. (Let's say you think that Sandbh is mistaken on this issue. You effectively said that a million times yourself, so that's hardly an assumption.) Science is a human enterprise, run by humans with their virtues and flaws. Is it humanly to point that out so much and so vigorously, without giving a way to save face? More importantly, could it possibly be that some of your own arguments are flawed? Questions like that is something that I'm trying to keep in mind. I have not participated in this discussion very actively in great part because I needed time to write a good response that would be reflect my mindfulness of those concerns and by the time I'd figured out what precisely to say, they discussion had long moved past that point, so I thought it was too late for me to pitch in. I think that given its speed, it's no surprise you say the argument is "raging in circles."--R8R (talk) 12:13, 4 May 2020 (UTC)

Balanced view of convention

@Double sharp and R8R: R8R, I like your balanced view opposing the notion that conventions have no value, and the observation about not being able to falsify a statement referring to blocks, without defining what you mean by a block. Here are some of the conventions at play, which seem as good as any:

scientific information should be communicated according to accepted scientific conventions
electronic configurations are based on those in the gas phase since these are relatively easy to measure
the s, d, and p blocks start with the first appearance of the applicable electron
Bohr observed/started(?) this convention; he started 4f at Ce
the start of subsequent rows of a block line up accordingly
Scerri refers to blocks according to the predominant differentiating electron
white P is the standard state of P never mind it's the most unstable form, in complete contrast to all other elements—talk about classroom confusion; now that black P can easily be produced I look forward to the end of the WP convention.

@Sandbh: So, you are looking forward to the end of the white-phosphorus convention, which is there because it is easy to study even if it lacks general relevance. And you are not looking forward to an end of the gas-phase convention, which is likewise only common to see because it is easy to study even if it lacks general relevance. ;)

Bohr thought 5f started after uranium, too. Well, he was wrong: he clearly did not have empirical configurations to draw a table from. And probably he thought that the trivalence of the Ln had to imply they had three valence electrons outside a [Xe]4fⁿ core. Well, that's totally false, so why are we referring to what he drew? And why is he a valid precedent for delaying the start of the 4f block, but not for misaligning the start of the 5f block?

Differentiating electrons are not well-defined throughout the whole table. Why are they still being referred to?

You criticise Sc-Y-Lu as appealing to symmetry when the facts of chemistry supposedly disagree (the relevant ones don't, this is just obsessing over ground-state configurations), and then ask for the start of subsequent rows of a block to line up accordingly to take care of thorium, which is exactly symmetry when the same irrelevant facts disagree. Double standard, ahoy. ;)

Everything I am saying in this comment, and in my reply to your recast of your summary (which has every point either wrong or just inconsistent), has been said by me before here. Sometimes a few months ago. But it seems to go in one ear and out the other. ;)

I trust everyone else can see the different levels of self-consistency here. ;) Double sharp (talk) 05:27, 3 May 2020 (UTC)

Refresh understanding

@Double sharp and R8R: This is interesting. There may be some old ground here but I'll see if I can refresh our understandings.

I'm looking forward to the end of the WP convention since BP is easy to prepare, and easier to study, and will enable a comparison of like-with-like in terms of thermodynamic stability, rather than the myths associated with WP e.g. that P is quite "reactive. No, it isn't.
I have no views about gas phase configurations other than they are relatively easy to determine, and study, and they provide the simplest valid explanation that fits observations, and form the foundation of the arrangement of the PT, by convention.
Bohr was wrong about 5f at U; that didn't invalidate his other findings. Same with Mendeleev. He made many wrong predictions. Yet, it was the one's he got right that everyone focussed on. Ditto Bohr.
Differentiating electrons are easy to define and relatively commonly referred to in the literature.
I criticise arguments for Lu that are based on symmetry as a starting point, and conclude that Sc-Y-Lu must therefore be right. I start from the other way around i.e. by looking at what supports Sc-Y-La, given its long-standing popularity. I have questioned the symmetry argument based on examples of asymmetry throughout nature, and the remarkable delays in the advancement of science caused by an obsession with symmetry.
Th under Ce is a convention rather than a symmetry-based argument. In fact Ce-Th is the cause of the assymetrical split-d block. Not that effectively anyone was ever concerned about this.

--- Sandbh (talk) 05:59, 4 May 2020 (UTC)

@Sandbh: Well, the funny thing is that gas-phase configurations don't actually provide a valid explanation. Quick, tell me what oxidation state the lanthanides like to show. +3, of course. Now tell me what naïve use of gas-phase configurations (in which they're usually [Xe]4fⁿ6s²) predicts. +2, not +3. ;) And no, condensed phase configurations are not going to work either, just look at the p occupancy in most of the metals. ;) Simple, yes. Valid, not quite. So we have to go deeper. Everything should be as simple as possible, but not simpler.

The fact that Bohr was wrong about 5f starting after U makes one wonder if he could possibly have been wrong elsewhere. And, indeed, all the evidence I have brought here to support La 4f involvement of the same order as Th 5f involvement proves it. We focus indeed on what Bohr got right, and this is not one of those things. ;)

Differentiating electrons are easy to define, sure. Just try defining them for vanadium vs chromium, there isn't only one. And how often are they in the literature that actually focuses on chemistry? They are probably quite rare there for the simple reason that "add a proton and an electron, that's the next element" is nuclear physics and not chemistry. ;)

Symmetry as a starting point is not totally wrong-headed. Anyone can see symmetry subtends totally from H to Xe, the obvious thing to guess is that it keeps going. So, it actually makes sense to ask for Sc-Y-La as a symmetry break to provide the stronger evidence to support Sc-Y-Lu. Remember, the whole point of this argument is "is this tradition actually right"? So it's unfair to assume the tradition has something behind it from the start. It's fairer to start by saying "well, if the tradition didn't exist, and we were drawing a table based on what we knew about the elements without tradition, would we recreate the tradition, or something else"? And the answer is: clearly not.

Indeed, if you insist on ground-state configurations (which are irrelevant anyway), there is no way to justify Th under Ce other than "convention". Which is a terribly bad argument for reasons I have stated over and over, namely that we are here to figure out if the convention is right, since most people who actually think about it end up advocating its abandonment. Funnily enough, that is not what Seaborg thought it was, which goes a long way to explain why it didn't bother him. He wrote: "It may be, of course, that there are no 5f electrons in thorium and protactinium and that the entry into a rare-earth like series begins at uranium, with three electrons in the 5f shell. It would still seem logical to refer to this as an actinide series." And that's because he could see that later in the series the most common oxidation state becomes not +4 but +3. Now, this is still making the mistake of Bohr (that trivalency of the lanthanides demanded three outer electrons in the gas-phase configurations), but he at least recognises here that there's more to it than the accidents of configurations.

Already in that article, we can see he understood that configurations can vary and that you have to look holistically like I've been advocating: "Of course in the case of some of the elements in the series it may be something of an academic matter to assign electrons to the 5f or 6d shells, as the energy necessary for the shift from one shell to the other may be within the range of chemical binding energies. The electron configuration may differ from compound to compound of an element or even with the physical state of a given compound." It is a pity that he did not take the last step to realise that this supports Sc-Y-Lu, but we can do that for him. ;) Double sharp (talk) 06:13, 4 May 2020 (UTC)

Wood for the trees

@Double sharp: Well, this is where I feel you're losing the plot. You choose not to see the wood and focus on the trees, or to not see the broad contours for the details.

By the time people have to deal with the Ln etc they know and are comfortable with limitations of gas phase configs. At the same time they don't (aside from you) throw the (Bohr) baby out with the bathwater.

In fact, every time someone notes that the gas-phase configuration (which suggests divalence) has very little to do with the actual trivalence of the Ln, they are throwing them out as irrelevant for real chemistry. So I'll gladly stand with Seaborg on this one, thank you. Double sharp (talk) 10:17, 4 May 2020 (UTC)

The d/e in V is a d electron as is the case with Cr. Focus on the wood young DS, not the trees.

Wrong. In passing from V to Cr, we gain two d electrons and lose one s one (in the ground states). There is no single differentiating electron. Double sharp (talk) 10:15, 4 May 2020 (UTC)

@Double sharp: Who said it had to be a single electron? In any event, what is the net gain? Sandbh (talk) 06:22, 6 May 2020 (UTC)

@Sandbh: The moment you call it the differentiating electron, that implies there is a single one. And there's no sense of talking about a "net gain" here. One electron is added, but once you speak of "net" there is no way to determine whether the d orbital or the s orbital has more of a right to claim it. Double sharp (talk) 06:33, 6 May 2020 (UTC)

The other place where I feel you're losing the plot is on how science works. Science is nor pure logic necessarily; convention plays a role; so does reputation; politics; culture; history, leadership; philosophy; and popular opinion or silent majority.

@Sandbh: Thank you for saying this explicitly, because it sheds a strong light on why we disagree here. And it also sheds a light on why I don't think anything you say is going to convince me, because not a single one of those things actually conforms to the whole point of the scientific method: you must regard what you come up with as fallible and test it. If the correctness of a convention is what is under discussion, you cannot just assume that the convention is right. You have to prove that it is right, from the fictitious standpoint of someone who does not know what the answer is in the first place and is independently analysing the relevant knowledge.

I seriously wonder: what, hypothetically, would it take to convince you that Sc-Y-La is wrong? Because falsifiability is the litmus test of being scientific. Double sharp (talk) 10:14, 4 May 2020 (UTC)

@Sandbh: For your attention (it's the falsifiability question again, on what possible evidence could lead you to doubt Sc-Y-La). Double sharp (talk) 05:07, 6 May 2020 (UTC)

Exhibits: Hard cases and La

Exhibit A:

"Scientists should not lose sleep over the hard cases. As long as a classification system is beneficial to economy of description, to structuring knowledge and to our understanding, and hard cases constitute a small minority, then keep it. If the system becomes less than useful, then scrap it and replace it with a system based on different shared characteristics." Jones 2010, Pluto: Sentinel of the outer solar system, Oxford University Press, p. 171).

B: Has Sc-Y-La become less than useful? No, it hasn't.

@Sandbh: Yes, it has. It was always based on a misunderstanding of the role of the f electrons, and now helps perpetuate the wrong idea that La has no f involvement. Which will of course eternally lead to accusations of it applying a double standard to Ac vs Th. Double sharp (talk) 10:14, 4 May 2020 (UTC)

C: Do you have an earth-shattering argument or set of arguments for Lu? No, IMO; not on the "I felt the world move" scale.

@Sandbh: As usual: La has 4f involvement that is not different from 5f involvement of Th. Double sharp (talk) 10:14, 4 May 2020 (UTC)

@Double sharp::

4f involvement in La does not dominate its chemistry
the lack of La-like 4f involvement in Lu does not dominate its chemistry
by convention, the tail does not wag the dog
what does dominate the chemistry of Lu its 14x 4f electrons i.e. the 4f-contraction which it shares with Ce-Lu; here the Lu3+ radius 0.861 is very close to Yb3+ at 0.868
yes, the 4f contraction impacts Hf heavily, making its chemistry more like that of Zr.

Sandbh (talk) 06:16, 6 May 2020 (UTC)

@Sandbh: LOL. As we can see here, both Lu and Hf are suffering the same kind of 4f involvement. Incomplete shielding effects. Hence Lu chemistry is similar to Y (Lu³⁺ 86.1 pm, Y³⁺ 90 pm). Just like Hf⁴⁺ 71 pm vs Zr⁴⁺ 72 pm. Or Ta⁵⁺ 64 pm vs Nb⁵⁺ 64 pm. The one thing that you will not find in Lu is any kind of valence usage of the 4f orbitals at all: Lu chemistry is dominated by it using only 5d and 6s as valence orbitals, never 4f like La-Yb. Indeed, the presence of 4f valence involvement is one significant thing that unites the chemistries and physical properties of La through Yb, as for example Gschneidner demonstrated for physical properties, and the papers I linked here and before demonstrate for La through Yb where we can see how the interplay between 4fⁿ and 4fⁿ⁺¹ dominates the chemistry of La-Yb. The accidental lack of a 4f electron in ground-state gas-phase La means nothing, it can still be occupied in chemical environments. (Just like how 5s is still a valence orbital for Pd or 6d is still a valence orbital for Lr.) So this is still the same old double standard, in which 4f is held up as a reason to put Lu in the f block, while simultaneously ignoring its exactly equivalent role for Hf through Rn.

Meanwhile, let's see what happens if we apply your logic to Th. So far, no one seems to have found an actual compound where the ground state of the Th atom has an f electron; 5f occupancy in Th compounds is only from ligand-metal charge transfer and some charge fluctuations (so, exactly the same as La). So we can go through the same argument all over again, because the 14 5f electrons in Rf are steadily added to +4 ions along Pa-Rf (those exist for Pa-Es and Rf, that's already a majority), and heavily impact (actinide contraction) the chemistries of Db onwards. So Th must go in the d-block and the 5f row must run Pa-Rf. Brilliant! Double sharp (talk) 06:29, 6 May 2020 (UTC)

That is all well and good. What's more important is the elephant in the room i.e. the convention hierarchy (whether you like it or not). The hierarchy looks something like this:

highly successful orbital approximation model
the first 4f electron occurring in Ce
the progressive occupancy of the 4f sub-shell in the trivalent cations of Ce to Lu
incomplete shielding effects
the Ln contraction running from Ce to Lu
no, we don't want a block starting with both members of its first column have no electrons in common with that block
delayed start of filling of 4f as one goes down the table i.e. at Ce for 4f and Pa for 5f
the An lining up under the Ln (including Th)

...arbitrary interval (x)...

8+x. Cu(IV) is known, Cu having a 4th IE of 5,536 kJ/mol; compare the 4th IE of Lu at 4,370 (< La at 4,819); or how about Au (V) at (5,709) in CsAuF₆

...arbitrarily large interval (y)...

8+x+y. Your LOL observations.

Sandbh (talk) 05:14, 7 May 2020 (UTC)

@Sandbh: That's totally wrong, as usual. Orbital approximation is only highly successful when you add the realisation that configurations can change depending on chemical environments. Otherwise one starts wondering how on Earth the ground-state configurations of the Ln relate to their trivalency. As Seaborg and Jørgensen noted, that relationship is not simple. So, the real hierarchy looks like this:

highly successful orbital approximation model, that successfully predicts what orbitals will be involved in chemistry;
the first element with 4f chemical involvement being La (and, for 5f, Ac);
the total absence of 4f chemical involvement from Lu, which uses 4f only for incomplete shielding effects like Hf-Rn.

Case closed! No need to appeal to "lining up under the Ln" for Th. No need to care about delayed collapses that have zero impact on real chemistry. So simple. And it works so well.

P.S. Ionisation energies are not everything. Compare carbon (4th IE 6222.7) with rubidium (5080). You have to consider lattice energies too. And maybe look at electronegativities and wonder how ionic the predicted compounds are going to be. ;) Double sharp (talk) 05:53, 7 May 2020 (UTC)

@Double sharp:: As usual your bombastic sense of righteousness does you a civility disservice.

Have I ever intimated that configurations cannot change depending on chemical environments? No, I haven't. So why bring that up?

That the first element with 4f chemical involvement is La (and, maybe for 5f, Ac?) does not dominate their chemistry; the dog wags the tail, not the other way round.

The the orbital does a good job predicting what orbitals will be involved in chemistry. AFAIK it is not successful all the time. Sandbh (talk) 07:12, 9 May 2020 (UTC)

@Sandbh: Why bring it up? Because despite you agreeing that it happens, you still focus on ground-state electron configurations. For the f elements, where this change is the most important. Never mind the difficulty this inevitably results in for thorium, which is [Rn]5f⁰6d²7s² in the ground state, is [Rn] as a +4 cation, and usually is [Rn]6d¹ and [Rn]6d² in chemical environments where it is +3 or +2. And you still don't recognise the double standard this inherently creates in the La table, in which Ac is summarily expelled from the f block for its lack of a 5f electron in the ground state, and then for Th it goes "oops, I guess some other measures are important after all", for what it is.

You know, there is no element for which 4f dominates its chemistry. 6s and/or 5d always have more contribution. That does not, however, mean there are no 4f elements. In fact there are precisely fourteen elements in which at ambient pressure 4f can be occupied and contributing its electrons for chemical bonding. And lutetium is not one of them. Of course, using the Madelung rule in its standard form (i.e. the conventional form displayed in every textbook that fits the Lu table) predicts the orbitals significantly involved in chemistry perfectly outside the s-block (which is simple enough to add to the empirical method), at least until the really extremely superheavy elements Lv, Ts, and Og where relativistic effects mess it up. The La table, of course, makes it worse by predicting no 4f involvement for La, and 4f involvement for Lu, both of which are totally false. Double sharp (talk) 09:50, 9 May 2020 (UTC)

@Double sharp: I focus on GSEC since that works well enough most of the time, not to mention that (effectively) the entire world-wide chemistry establishment starts there. I've addressed the double standard issue in more recent posts. It's a storm in a teacup. You guessed right, some measures are (more) important after all. Here's a quote from Stone (1979) along the same lines:

"It will be appreciated that simplicity has been achieved in Fig. 1 at some expense in accuracy. It is not possible, in a single account, to present all its modifications and limitations; several descriptions, from different angles, are necessary fully to appreciate the structure of the Periodic Table in this context."

There you go, setting up a paper tiger and then knocking it down. Do you read what I write? I never said there was an element for which 4f dominates its chemistry. I said 4f chemical involvement does not dominate La chemistry. That's all. In fact, 4f involvement in chemistry does not predominate in the chemistry of any of the 4f elements. Rather, the 4f contraction does dominate the chemistry of the 4f elements, staring at Ce. Please, no more on Hf. My focus is on simple, pragmatic divides. I do like the fact that the MR indicates orbital involvement outside of the s-block. There you go with another paper tiger. The MR does not predict orbital involvement unless you choose to interpret it that way. Your La argument is null and artificial.

I'm over two dozen pings behind. I got the first peer review for my article, and need to make some changes, pending r/c of the second PR; there may be a third. I'm working on another periodic table article with three co-authors. It'll take me a while to catch up. Sandbh (talk) 06:15, 11 May 2020 (UTC)i

The same old double standards I have been refuting 9001 times. The MR predicts 4f should begin at La; and, in terms of chemical relevancies, it does. All you can do is plead the "entire world-wide chemistry establishment", never mind the lies-to-children phenomenon that will be rampant in those beginners' textbooks, and how everybody who actually analyses the situation recognises GSCE are nowhere near enough. I rest my case. Double sharp (talk) 06:22, 11 May 2020 (UTC)

D: Are there many arguments in the literature for La? D1: Not that many. D2: The case was considered closed so long ago, that hardly anybody has bothered.

@Sandbh: So: if there are arguments, that is support for La, and if there are no arguments, that means that people think La is too obvious to need support. So can La ever be wrong?

And I wonder how many arguments there were in the literature for Be-Mg-Zn when it was the most popular form? Or for U under W when that was the most popular form? No, people probably felt it was obviously correct. And indeed, it kind of was under the limited knowledge of the time; we knew better only later. And once we know better, i.e. that the original reasoning that led to the standard conclusion was wrong, we must revisit it.

People mostly are moved to defend only the form that they feel is under threat, you know. Double sharp (talk) 10:14, 4 May 2020 (UTC)

E: Are there in fact such arguments that can be made in support of La? There sure are, IMO.

@Sandbh: Only inconsistent ones, as demonstrated copiously here. Double sharp (talk) 10:14, 4 May 2020 (UTC)

A + B + D2 + E >>>> C

Sandbh (talk) 08:46, 4 May 2020 (UTC)

@Sandbh: Well, I reject your A, B, D2, and E, for reasons I have stated above. So it is unsurprising that I am totally unconvinced. Double sharp (talk) 10:14, 4 May 2020 (UTC)

Recasting

Transcluded from an earlier post:

::::Now, does the Sc-Y-La table have actual pedagogical value? Not really, it creates a perturbation of the Madelung rule that results in hands being raised at the back of the classroom (and some confusion as to the profusion of variants here). Is it a good approximation of the facts at the basic level? Not at all, Lu is much more like a normal transition metal than La is. Does it at least visually suggest the right thing? No, it gives the idea that group 3 is somehow different from the other transition groups, when actually heavy group 4 (Zr, Hf, Rf) pretty much like the tetravalent version of group 3 with weak transition properties. Well, is it even right? No, it makes the statement "La is a d block element and Lu is an f block element". That's a falsifiable statement, so it's within the domain of science. And it is indeed false: La uses f orbitals just like thorium does, Lu doesn't have any significant f orbital usage at all. (And there's the "proof" you speak of in the first paragraph; electronic structure to sort out what is essentially an electronic-structure argument, since that's what blocks are supposed to represent.) So, what is the point of it? Double sharp (talk) 05:36, 2 May 2020 (UTC)

Double sharp, here's a recast of your summary paragraph:

Q1: Now, does the Sc-Y-La table have actual pedagogical value?

A: Yes, it does. It shows a better fit to the Madelung rule.

False. The Madelung rule suggests that 4f should start filling before 5d, not in the middle of 5d. This is shown by a Sc-Y-Lu table, not a Sc-Y-La table. And this Madelung rule is borne out by the facts of chemistry, as shown by lanthanum using its 4f orbital for chemistry. Double sharp (talk) 05:21, 3 May 2020 (UTC)

In fact an La table has one less d/e discrepancy than an Lu table. The MR does not accommodate the delayed start of filling of the 4f sub-shell, as you know. La using its 4f orbital for chemistry is not the same as La having its own (contraction-inducing) 4f electron.

Still referring to long-refuted DEs even though I've given the V vs Cr example all the time. As you know, the important thing for chemistry is using the orbital for chemistry, not having the electron. Or else, thorium goes straight to the d block again. And lawrencium to the p block. ;) Double sharp (talk) 08:06, 4 May 2020 (UTC)

Q2: Is it a good approximation of the facts at the basic level?

A: Certainly, we see that La is much more like an incipient transition metal than Lu is, which is what would be expected for the first metal with a 5d¹ electron (Lu is the third).

False. Lutetium has properties similar to scandium and yttrium, which are clearly incipient transition metals. Ever heard of a transition metal that reacts as readily with water as lanthanum? Not to mention that thorium is the first metal with a 6d² configuration (Rf is the second), so the same logic implies Th in the d-block too. Double sharp (talk) 05:21, 3 May 2020 (UTC)

In fact you agree with me that Lu is more like a 5d metal than is the case for La. Yes I'd expect pure Y to react as vigorously with water i.e Y = -2.38 V; La = -2.379 (NIST). Th is indeed the second metal with a 6d configuration unlike Lu which is the 3rd metal with a 5d configuration. Sandbh (talk) 06:46, 4 May 2020 (UTC)

It doesn't. Lanthanum reacts slowly with cold water, quickly with hot water. Yttrium only reacts when finely divided or heated. Reduction potentials are not everything for reactivity. Here Lu and La act similarly according to WebElements, though here the oxide layer doesn't spall and I would imagine it gets some protection from that. Meanwhile, lanthanum corrodes in air much more readily than scandium, yttrium or lutetium. ;) And you're still missing the point that your argument suggests thorium as part of the d-block if applied consistently. Is that really what you want? ;) Double sharp (talk) 08:03, 4 May 2020 (UTC)

Q3: Does it at least visually suggest the right thing?

A: Yes it does. It is commonly recognised that the chemistry of group 3 is more like that of groups 1-2 than is the case for group 4. There are no tetravalent (aq) monocations of Zr, Hf, and Rf.

False. As demonstrated above, such monocations Zr⁴⁺, Hf⁴⁺, Rf⁴⁺ do exist. They do require rather acidic media to be seen, but the same is true of trivalent cations to a lesser degree. You know that at pH 7 you probably have Sc(OH)₃ and Y(OH)₃ rather than Sc³⁺ and Y³⁺ (Wulfsberg p. 127), yes? And that generalises to all the +3 cations (Al, Ga, In, Cr, Fe) except the very largest ones (lanthanides and Ac³⁺)? (And since you like your charts, notice where Zr and Hf appear in your orbital radius vs EN chart below...) The important thing is just "is that cation so acidic that it protonates water already"? And the answer, for the tetravalent cations of heavy group 4 and of Ce and Th–Pu, is "no, they are not". Whereas for Ti, Si, Ge, and Sn the answer is "yes, they are". The limit for cations is usefully drawn as (last cation that can be considered as such in water, which are usually skirting the edge already): At⁺ for +1, Sn²⁺ for +2, Sb³⁺ for +3, Ce⁴⁺ for +4. For +5 and above the idea is already useless, since there are no real cations in water with such a high charge anymore. So if our criterion is monocations, then I guess we have to draw a table where group 4 is Zr-Ce-Th and Ti gets moved to go two spaces over Hf. ;) Double sharp (talk) 05:21, 3 May 2020 (UTC)

I'll rely on the literature any day, on this one.

Q4: So, is "La a d block element and Lu an f block element"?

A: La is predominately a d block element; its chemistry mostly involves the loss of its ds² electrons, although it is also known as La²⁺ d¹. The f electrons in Ce-Lu are rarely involved in their chemistry which instead mostly involves the loss of their ds² electrons. Hence the expression "inner transition metals", with the inner referring to the progressive occupation of the 4f sub-shell, as seen in the series of Ce³⁺ f¹ to Lu³⁺ f¹⁴. Here, La has no f electron of its own; the number of f-electrons in each cation corresponds to its position in the 4f row; and this progressive occupation of the inner 4f sub-shell (Ce-Lu) contributes to the lanthanoid contraction culminating in Lu. Like La, most of the chemistry of Lu involves the loss of its ds² electrons, although it is also known as Lu²⁺ d¹. By convention, Lu is treated as an f-block metal given the f-block contraction culminates in it.

False. The logic being used here to exclude lanthanum from the f-block clearly excludes every other lanthanide from it as well. In actuality, the idea that the f electrons are not involved for real chemistry is a reflexion of the old, long-since refuted idea that the f-block is a degenerate branch of the d-block. Instead we see a strong charge-fluctuation situation of 4fⁿ vs. 4fⁿ⁺¹ configurations in all of La-Yb. Lu cannot be an f-block metal; this interplay does not exist for it and its f-electrons are corelike. Of course, La is quite clearly an f-block metal. That's a self-consistent criterion, to demand that an f-block element must use its f-orbitals as valence orbitals. (Dare I say that it is even intuitive?) And once one adopts that, there's no longer any need for special pleading for thorium. Double sharp (talk) 05:21, 3 May 2020 (UTC)

I'll rely on the literature any day, on this one, including convention.

Q5: So, is Th an f-block element?

A: Like La, Th has no f valence electron of its own.* By convention, since Th lines up under Ce, Th is treated as an f-block metal.

*Its crystalline structure is however influenced by the presence of > 0.5 of an f-electron

This convention is a double standard as the structure of lanthanum and its bonding in compounds is likewise influenced by the presence of a small f-occupancy on average. Meanwhile, lutetium and lawrencium have no f valence electrons of their own, and their crystalline structure is not influenced by their core f electrons at all, but are somehow allowed in the f block anyway by the Sc-Y-La table. Go figure. Double sharp (talk) 05:21, 3 May 2020 (UTC)

P.S. I also wonder why Ac is fcc like Th. Whereas Lr and Rf are probably both hcp, following Y and Zr (and also Lu and Hf). And I also wonder why La follows the early lanthanides with their strongest f-involvements in being dhcp (the structure of La-Pm), whereas excluding some weirdness with transitional Sm and divalent Eu and Yb, the late lanthanides Gd-Lu with weaker f-involvements are hcp like Y. Seems to point completely towards f-involvement in La and Ac influencing the crystal structures, as we see the exact same results in Ce and Th. ;) Double sharp (talk) 06:09, 3 May 2020 (UTC)

I'll rely on the literature any day, on this one, including convention.

It is really hilarious that I've quoted the literature here copiously (which is in fact part of why my posts end up being so long) to support what I say here. Just look at all the sections above, you'll find the sources. But I still get this statement back from you. Do you actually rely on any literature apart from that which you think supports Sc-Y-La? Even when it doesn't? And what is the point of a discussion to find out if the textbook literature is right, if we are going to take their correctness as an axiom like this? ;) Double sharp (talk) 08:00, 4 May 2020 (UTC)

Every one of your five points doesn't fit the facts. As I've quickly recapitulated above, having demonstrated the reasons for that over and over again on this talk page. Double sharp (talk) 05:21, 3 May 2020 (UTC)

There are lots of facts in chemistry, too many to cram into one periodic table. You have to choose what facts and properties to focus on. I choose to focus on the simplest facts and properties that give the greatest explanatory power, as per the role of convention in science. Sandbh (talk) 06:46, 4 May 2020 (UTC)

Too simple to be simple, more like. Just try applying your facts elsewhere on the table. Your focuses can very easily end up supporting Be-Mg-Zn or B-Al-Sc or Th in the d-block if you don't carefully and artificially restrict where they are supposed to apply, thus making them not very simple and not very explanatory after all. ;) Double sharp (talk) 08:00, 4 May 2020 (UTC)

By convention, as they say. Sandbh (talk) 04:53, 6 May 2020 (UTC)

@Sandbh: Well, if you're not going to analyse the convention, then why are you publishing anything about the group 3 issue at all? If you're going to take a convention as your focus, you've got to examine it. At the very least you must address this appearance of a double standard, either by admitting that it is a double standard, or by carefully explaining why the situations that seem to indicate a double standard are not in fact comparable without reference to the convention. Just being a convention doesn't justify the convention by itself. Such an "explanation" has no explanatory power whatsoever. Double sharp (talk) 05:04, 6 May 2020 (UTC)

Appendix VII: What's true

A valence electron is an outer shell electron of an atom, that can participate in the formation of a chemical bond
Neither Sc, Y, La, nor Lu have a valence f electron in the ground state
La and Ac are a "pair out of place" if they go in the f block: their ground state configurations both lack f electrons.
La has low-lying 4f orbitals that may be occupied in chemical environments, by partial hybridization or via ligand contribution (citations: here and doi:10.1103/PhysRevB.66.045106) which is something it has in common with Ce-Yb and not with Sc, Y, and Lu
This concept is more useful for transition and especially inner transition elements, with many configurations close in energy such that changes in the chemical environment can alter which one is preferred.
As such, Y vs La presents a mismatch in chemically available valence subshells, while Y vs Lu does not. [CONTENTIOUS]
It would also present a totally unique mismatch in the periodic table going down a group, other than He over Ne. [CONTENTIOUS]
And while He over Ne has some excuse since the normal chemistry of helium surely matches neon in its inertness a lot better than beryllium (even if it breaks trends), at face value neither Y-La nor Y-Lu looks terribly wrong if we momentarily forget about electrons and just look at their qualitative chemistry, so there is no similarly strong reason for the mismatch. [CONTENTIOUS]

The 4f electrons in Lu are core electrons.
The uncontroversial nine 5d elements (Hf-Hg) all have core-like 4f electrons, which is something Lu has but La doesn't.
Lu and Lr are likewise a pair out of place if they go in the f block: a pair of f elements with corelike f electrons.

In this context, Th has no valence f electron in the ground state, exactly replicating the situation of La and Ac.
Th³⁺ is 5f¹, but only in the gas phase; in chemical environments it is usually 6d¹. [CONTENTIOUS]
+3 is not a major oxidation state for thorium (although it does exist), which is almost always +4. So 5f occupancy for thorium will almost always be via partial hybridization and ligand contribution as well, just like 5f for actinium or 4f for lanthanum. [CONTENTIOUS]
And even if we do find a Th³⁺ complex that is 5f¹, it will be a rather unrepresentative compound precisely because that oxidation state is not favoured by Th. The same would be true for any La²⁺ complex that happens to show 4f¹ (4f¹ is within 1 eV of the ground state and has chances to appear). [CONTENTIOUS]
Therefore, electron configuration arguments seeking to bar La and Ac from the f block constitute a double standard. If applied consistently to thorium, they would bar it from the f block as well. [CONTENTIOUS]

To get from 0 to +3, fourteen out of the fifteen metals from La to Lu might be losing an f electron in a chemical environment, where they may be 4fⁿ or 4fⁿ⁺¹.
Lu cannot do that, as there is no 4f¹⁵

Orbital hybridization occurs
It is not always necessary to invoke hybridization in order to obtain useful generalisations
For the d and f elements, because there are many configurations that are very close in energy, and ligand field effects can easily alter which one is the ground state, it is however necessary [CONTENTIOUS]
It is not necessary to think of integer subshell occupancies as being valid for every possible case
Therefore, the argument that La and Ac don't have an f electron in the gas-phase ground state is irrelevant. In many possible cases La can have 4f occupied. [CONTENTIOUS]

Chemically speaking, the behaviour of Lr is totally uncharacteristic for a late actinide. The late actinides from Es onwards (look at the densities and how they drop there) form divalent metals, and have +2 as a water-stable oxidation state from Fm onwards. Neither of these generalisations hold true for Lr, which instead continues the trend backwards very well from Bh, Sg, Db, and Rf. [CONTENTIOUS]
Au contraire, Ac is a totally normal early actinide shedding all valence electrons happily, like Th, Pa, and U. [CONTENTIOUS]
Lu and La are both totally normal lanthanides, but La makes more sense at the start of the lanthanide trend than Lu at the end of it (because Lu doesn't match the increased stability of the +2 state at Tm and Yb). [CONTENTIOUS]
Lu and Lr are more like transition metals than La and Ac. The d block thus becomes more homogeneous if you put Lu and Lr in it under Y, not La and Ac. [CONTENTIOUS]

Chemistry is not a heap of distinct conceptions standing apart alone, but rather interconnected system of conceptions based on experimental facts.
An La table creates an irregularity that is absent from a Lu table.

There is no sharp boundary between groups 3 and 4, either in terms of ionicity or in terms of main-group-like chemistry. [CONTENTIOUS]
Ionic vs. covalent is gradual, from covalent to polar covalent to mildly ionic to strongly ionic, depending on the difference of electronegativity between the two elements.
And while group 3 has mostly main-group tendencies, so do Zr, Hf, and Rf in group 4. [CONTENTIOUS]
All these elements involved also have incipient transition properties.
There are no sharp boundaries.

We cannot use the most common stable oxidation state as a baseline to compare stabilising effects of half-filled and fully-filled subshells, because it creates nonsense when applied outside 3d. For example, in 5d it singles out +4, and thus implies Ir⁴⁺ as half-full and stable with Os⁴⁺ and Pt⁴⁺ presumably getting horseshoes-and-kisses benefits for being nearby. Which is silly for determining when the 5d block starts, since clearly it has started already before Ta. [CONTENTIOUS]
The point of comparing stabilising effects is lost unless you restrict to the +2 state, because that is the state that corresponds to ionising s electrons and leaving the characteristic subshell alone. [CONTENTIOUS]
Mn and Zn in 3d have more stability in the +2 state. Which is true for Eu and Yb in 4f, not Gd and Lu.

In science, tradition counts for nothing if we learn that the bases for it were flawed. [CONTENTIOUS]

I have added some points from appendix II, plus some others that have been raised here in discussion. Double sharp (talk) 15:44, 26 April 2020 (UTC)

Locality vs. regularity

La arguments are totally local, while Lu arguments are pretty regular. That exactly matches Ptolemy vs. Copernicus. The history just repeats itself. Nothing more to say. Droog Andrey (talk) 14:50, 26 April 2020 (UTC)

Hear, hear!

I am grateful to the honourable gentleman for his point of order--R8R (talk) 15:58, 26 April 2020 (UTC)

“

The key problems afflicting all the significant La arguments, as far as I can see, is locality. Such arguments focus on one extremely local feature and don't work for the rest of the periodic table (e.g. all arguments stemming from +3 being the common state in the lanthanide contraction). In some sense, focusing on ground-state or condensed-phase electron configurations only leads naturally to this problem, because they exclude part of chemistry from consideration and are therefore not holistic enough to serve as a basis for the periodic table. Or focusing on supposed gaps in chemical behaviour between group 3 and following groups: this is a common trap, because we all like our specialties, but Fajans' rules immediately implicate that these gaps move depending on conditions.

Chemically active valence subshells are precisely chosen not to move and to avoid locality. They also explain precisely why it's not relevant to say "oh, but Sc-Y-La does the group 2 trend, and Sc-Y-Lu does the group 4 trend". It's true, but we know that the s-block is the weirdo which starts early. That 4f, 5f, and 5g show delayed collapse is not to do with the fact that they're f and g orbitals, but because we are in the heavy elements by the time we start filling them. Note that Lu already has a low-lying 6p state, and Lr clearly shows that 6d has undergone a delayed collapse too.

I don't include trivial arguments like "lanthanide means "like lanthanum", and La is exactly lanthanum, so it must not be an Ln". Or arguments like "that's the traditional definition of Ln". Well, yes it is, and it's also a plain silly definition of word-gaming: everyone knows that La acts exactly like a normal early lanthanide. (In fact it's Lu and Lr that are rather weird for late lanthanides and actinides respectively, the latter more so.) So I don't care about such bad arguments (you may find such bad ones on the Lu side too and I don't use them). Instead I only address arguments that raise some serious questions. Tradition means nothing if we learn something that overthrows it, because this is science.

The "standard" arrangement Sc-Y-La is pretty much a fossil of the time when the f-block was unknown and Th, Pa, and U occupied positions under Hf, Ta, and W, and it has maintained its place mostly through inertia. If Sc-Y-Lu became the dominant version, and a generation grew up learning it, I bet no one would start advocating for Sc-Y-La as an obvious symmetry break.

”

— User:Double sharp/Idealised electron configurations

Double sharp (talk) 15:11, 26 April 2020 (UTC)

Well, what a fine bunch of sad-sacks you lot are turning out to be ^_^

There's no use crying over spilt milk. You can drag the ball-and-chain of e.g. what would've happened if Lu had become discovered first, or Ptolemy vs. Copernicus, as if you were stuck in the past, for as long as you like having it on your backs, as a dead weight which can't be undone. Or you can cut the chain and ball, stop looking into the past, turn around and look to the future.

"Would've", "should've", "could've" will get you nowhere aside from having pity parties.

Yes, I look at the past too. Not to wail about what should've have happened but to examine how we got to where we are today.

@Droog Andrey: if you think my arguments are local you have an underwhelming appreciation of my approach. I'd be wasting my time going down that path. My focus is intended to be philosophical or systemic rather than descriptive or theoretical. Along the way some more detailed ancillary arguments will be rolled out where I feel these are required to provide context, are novel, or provide useful insights. In contrast, the history of Lu arguments have largely been popgun-like in nature. No wonder they failed to gain sufficient traction.

Lu arguments are not pretty regular' although they may superficially look that way. They introduce new irregularities that no Lu proponent has mentioned, since many of their arguments are locally focussed.

File:Chemistry without orbitals.png

If I may may make somewhat of a comparison. Let us equate La to the highly successful electron orbital approximation. For Lu, let us equate that to the recent release of a manuscript deposited in the chemRxiv server, pending publication, of title General chemistry without orbitals, by G. Lamoureux et al. Here, the electron orbital approximation is proposed to be replaced with the image you can see. Nice try, not. Sandbh (talk) 04:48, 6 May 2020 (UTC)

@Sandbh: LOL. The Lu table simply says "OK, let's not fret too much about configuration anomalies that don't seem to make any difference for real chemistry, and just go for Madelung-style idealised configurations". That's actually simpler than the La table which must somehow figure out when a configuration anomaly has no effect on periodic table placement (Th, Lr) and when it is the reason for periodic table placement (La, Ac). How do you handle that without locality?

We don't discard orbitals, indeed we cling more than ever to them when referring to chemically active subshells to justify Madelung's rule. And there's no irregularity at all when you use them: Lavelle's "pair out of place" is spurious since La and Ac have the required f involvement anyway. And it's certainly more regular than the La arguments that require double standards or locality squared to save themselves from the thorium anomaly. Or sometimes the spectres of Be-Mg-Zn or B-Al-Sc.

We got to this lamentable state of affairs with an inert literature mostly not being aware of the strong evidence against Sc-Y-La (when group 3 isn't their focus, that is) because when it was first put there, we didn't know better about what electronic structure really meant and how it really related to chemistry, and it didn't look obviously chemically wrong. (Y-La doesn't look obviously wrong just looking at descriptive chemistry; neither does Y-Lu, or indeed Y-Gd or Y-Ho.) Well, we got rid of Be-Mg-Zn, and Th-U as 6d elements, once we knew better. There's no reason we can't do the same for getting rid of Sc-Y-La, indeed many chemists have already done it. Now that the group 3 project of IUPAC has given this issue more of a spotlight I'm sure many more will follow. Double sharp (talk) 04:52, 6 May 2020 (UTC)

Jensen on textbooks

“

First, I would note the increasing number of textbooks that use versions of the periodic table whose underlying premises are either ignored or directly contradicted by the text itself. Thus several years ago I called attention to the example of textbooks that used periodic tables in which the elements of the Zn group were explicitly (but incorrectly) labelled as transition elements, but treated (correctly) within the text as main-block elements (2). More relevant to the issue at hand is the case of the well-known text of Cotton and Wilkinson that uses what Clark and White have called the 14CeTh representation¹ of the f-block in the periodic table on the back flyleaf but the 15LaAc interpretation within the text (3), while the textbook by Housecraft and Sharpe uses the 15LaAc representation in the periodic table on the front flyleaf but the 14CeTh interpretation within the text itself (4).

”

— doi:10.1021/ed085p1491.2

One wonders therefore why the "wisdom of the masses" is so important when those masses don't even pass the bar of being self-consistent. And that's not even going to the problem that DePiep already pointed out: if the asterisks appear in the same cells as La and Ac, it is not a Sc-Y-La table but a Sc-Y-* table. Well, this is more or less what you'd expect when the group 3 dispute is very far outside what is of interest to the average basic chemistry textbook.

“

Despite the cogency of this suggestion [Rundle-Pimentel theory, using MO theory and 3c-4e bonds to explain hypervalent molecules], there are still dissenters (13), and despite the nearly unanimous conclusions of theoretical studies that the octet rule is a valid first approximation for the entire main-block and that it is the traditional Lewis 2c–2e model of covalent bonding that requires modification, octet expansion and the 2c–2e bond still reign supreme in introductory chemistry textbooks, in large part because of the widespread belief that they are a necessary component of the highly successful VSEPR model for the prediction of molecular geometries (14).

”

— http://www.che.uc.edu/jensen/W.%20B.%20Jensen/Reprints/135.%20Hypervalence.pdf

So group 3 is not even the only case where the better answer has been cogently argued in the literature many times by many people and has not been taken up by textbooks.

So, which sources are more reliable for such a matter: textbooks, which use pedagogic simplifications a lot and are often not even self-consistent on issues like group 3 which are peripheral for the beginning chemistry student; or well-researched journal articles that actually focus on the composition of group 3, which taken as a whole skew towards favouring Lu? Double sharp (talk) 12:20, 29 April 2020 (UTC)

@Double sharp: I agree with Jensen to some extent i.e. with regard to the "textbook error" phenomenon. So, the wisdom of the masses is fine, and work well, provided you know you're way round. Group 3 as Sc-Y-La is not in this category. The wisdom of the masses supports Sc-Y-La. There are some dissenters, of course, outnumbered by a 4:1 margin. That's to be expected when neither option can be "proved" so to speak. The journal articles are mostly well-researched within their myopic focii. That's why I call them pop-gun arguments. There is a tiny pop which effectively no one hears. Meanwhile the chemistry establishment rolls on. You know how it is, much as you find it to be "wrong". Sandbh (talk) 03:51, 6 May 2020 (UTC)

@Sandbh: It can be proved as I've done so many times here: an f-block element must have some usage of its f orbitals for chemistry. That's necessary to have blocks mean anything at all chemically, and forces La in the f-block and Lu in the d-block. Anything else creates a double standard, usually with regard to Th or Lr.

And of course, all those arguments for Sc-Y-La are equally pop-gun as the ones for Sc-Y-Lu that you criticise. (And I've criticised the more pop-gunnish ones here too. That's why mine go straight from the point of blocks and electron configurations and achieve a holistic view that way.) Realistically, what more likely happens is that the average chemist writing a textbook doesn't even mention the controversy at all. And maybe even because they've never heard of it in the first place:

“

In fact, so overwhelming is the evidence for this assignment that Mazurs adopted it in the 1974 edition of his classic monograph on the periodic table (14). However, a quick examination of over fifteen freshman chemistry texts and four popular inorganic texts published since 1975 revealed that none of them had revised their periodic tables (15). Indeed, in talking with his fellow chemists, the author discovered that none of them was aware of the evidence favoring the reassignment of lutetium and lawrencium or indeed that there ever was any question about their placements (a category in which the author must include himself until very recently).

”

— http://www.che.uc.edu/Jensen/W.%20B.%20Jensen/Reprints/018.%20La%20vs%20Lu.pdf (my italics)

So much for a supposed rolling on of the chemistry establishment. Since when are people who have never heard of the controversy a good source for deciding on it? When the majority of those who actually focus on the controversy support the Sc-Y-Lu option? And when it is far easier to find Sc-Y-Lu tables today than when Jensen wrote that? Double sharp (talk) 04:01, 6 May 2020 (UTC)

@Double sharp: Nothing can be "proved" about Group 3, as you know. There you go, making up definitions that don't exist, and ignoring every description I gave about the attributes of the chemistry establishment, and how it (illogically) works. Singly, my arguments are one shots. Gathered together, they are systematic i.e. mutually reinforcing, consistent with the nature of periodic table as an integrated, complex structure whereas Lu in group 3 unravels this rich tapestry of chemical relationships. That's my aim anyway, as I keep on trying to fly through the well-intentioned flak!

@Sandbh: LOL. Gathered together, your arguments are not only one-shots, but they all are based on false premises. Let's look at my logic.

Lutetium has no f involvement, its chemistry is dominated by 5d and 6s alone.
Lanthanum has f involvement that is basically identical to that of thorium (which everyone thinks is an f element, nota bene), and identical to all the other lanthanides' (4fⁿ vs. 4fⁿ⁺¹)
For a block to be more than just formality, its constituent elements ought to have the involvement of that subshell.
The midway and final elements of a block should reflect the stabilisation (especially for the first row where double periodicity is stronger), which is true for Eu and Yb, but not for Gd and Lu.
We can see that lutetium under yttrium leads to better trends as would be expected from the periodic law; the 4f row becomes consistent with the 3d row, and the 5d row becomes more homogeneous.
And we can see that it leads to easier pedagogy, as now the Madelung pattern holds perfectly without any exceptions.
And it leads to a solid understanding of the facts that you cannot just naïvely predict valency from ground-state gas-phase configuration and that the f electrons are not core electrons in La-Yb.

Seems to be self-reinforcing: each step justifies the next one.

And your arguments base themselves on:

Things that no one has ever thought were valid ways to decide what element goes under another, like looking for which elements form aqueous cations.
Double standards. Putting similar elements together is kosher when it's about separating groups 1 to 3 from group 4 (neglecting Zr, Hf, and Rf all the time, of course), but not kosher whenever it's pointed out that Lu is more similar to Y than La is, and that Lu-Hg makes a more homogeneous d block than La-Hg. Double standard, ahoy!
Things that are ill-defined, like differentiating electrons.
Things that are irrelevant, like ground-state gas-phase configuration anomalies (that is the basis of Lavelle's "pair out of place" argument).
Things that cannot be generalised to the whole table, like 234 maximum oxidation state triads.
Things that are incomplete, like Restrepo's analysis.

And far from mutually reinforcing, they have to be artificially limited to avoid tearing at each other's throats. Well, for example, if you insist on isodiagonality, then Al must go over Sc in order to not artificially break apart the Be-Al-Ti diagonal relationship. Ah, except gas-phase configurations say that cannot happen, because Al has a p DE and Sc has a d DE. Oh, wait, but Sc has partial p occupancy in the condensed phase. Ah, and aluminium acts chemically like a pre-transition metal, which is like Sc-Y-La but not Ga-In-Tl because of the noble gas configurations of M³⁺. Oh, and comparing the pairs Be-B and Mg-Al will suggest Ca-Sc as the next pair instead of Ca-Ga. So now we have to go find some reasons why the arguments you use and listed in Archive 42 cannot be applied here and must be limited to only explaining La. Which makes them lose almost all explanatory power and simplicity for the periodic law by forcing you to say "there is one reason here and another reason there". And you call this "systematic" and "mutually reinforcing". Brilliant!

Somehow, no matter how many times the flaws in any of these six things are exposed, they are never acknowledged and the same reasons keep getting put forward. I rest my case. ;)

Do you think anything could be proved about the actinides? Because if we travel back in time a few decades, Th, Pa, and U as eka-Hf, eka-Ta, and eka-W was the chemistry battleship. Double sharp (talk) 09:23, 6 May 2020 (UTC)

Never trust anything Mazurs writes without checking the original sources. He redrew most of them, adding elements not known to the original author and distorting them in all sorts of ways. He is only reliable as a source for his own representations, which are original and often very interesting. His bibliography, on the other hand is highly accurate and very valuable, though difficult to use because it is arranged in the order of his confusing classification of images, but his very complete index helps to track down the references.

@Sandbh: LOL. I'm not quoting Mazurs, I'm quoting what Jensen said about him. And since this is about what he adopted, it's completely reliable as a source that he found it totally convincing. Double sharp (talk) 09:23, 6 May 2020 (UTC)

@Double sharp:

Really. So, 1. Jensen makes some arguments in favour of Lu. 2. These fail to gain sufficient traction and are subsequently referred to being as selective. 3. Jensen retrojects his interpretation of why Mazurs adopted Lu, when Mazurs did not do so; Jensen is therefore a "completely reliable source" in this regard. Err, no. Sandbh (talk) 05:42, 7 May 2020 (UTC)

As you know, bar something threatening appearing on the radar of the chemistry establishment, it plows on. Jensen's comments show that Lu didn't make any such appearance.

@Sandbh: Nope. In fact, even if something threatening appears on the radar of the chemistry textbook establishment, it plows on. Only the chemists complaining about textbook errors take notice. Just open lots of chemistry textbooks and see how they explain hypervalent molecules like SF₆. Double sharp (talk) 09:23, 6 May 2020 (UTC)

@Double sharp: I concur.

@Sandbh: So, have you considered the possibility that Sc-Y-La might be an analogous textbook error, instead of appealing to its status as a convention? Just look at my 23 and counting points below. ;) Double sharp (talk) 06:25, 7 May 2020 (UTC)

Since when are people who have never heard of the controversy a good source for deciding on it? Since they never heard of the isolated popgun Lu arguments, or Jensen's too-selective effort, that's when. Why would such isolated one-shot arguments get on their radar?

@Sandbh: Because they're not isolated one-shot arguments. They're mutually reinforcing. Electronic considerations mean that Lu must go under Y, and we can see that it creates better trends. Double sharp (talk) 09:23, 6 May 2020 (UTC)

The majority of those who actually focus on the controversy "stupidly" support the Sc-Y-Lu option on the basis of isolated pop-gun arguments (like I used to do, until Scerri opened my eyes). Same reason why its easier to find Lu tables. Publish or perish; don't do OR; parrot what others write etc, textbook errors etc; there'a a long history of this kind of thing.

Sandbh (talk) 08:27, 6 May 2020 (UTC)

@Sandbh: LOL. So if the Lu tables are in a minority, it's because no one took notice of the arguments for them. And if the Lu tables become more popular, it's because people are being stupid. Way to go putting Sc-Y-Lu into a no-win situation, compounded by shutting down cogent analyses of its flaws with "look at the chemistry establishment". That seems to be the definition of textbook errors, parroting what others write, and not doing OR. Funnily enough, the ones who focus on the controversy and support the minority option are by definition doing OR and not parroting what the chemistry establishment writes. Because if they were parroting what the chemistry establishment wrote, they would not be in the minority. ;) Double sharp (talk) 09:23, 6 May 2020 (UTC)

@Double sharp: Yes, that right. It suck's doesn't it? There are so many vectors out there in favour of La, and so few in favour of Lu. The ones who support the minority option do myopic OR. They think one-shot arguments will do, more fool them. Sandbh (talk) 05:58, 7 May 2020 (UTC)

@Sandbh: LOL. Make up your mind on how to criticise authors who come to the conclusion you don't like. Are the Lu authors doing OR, or not? Double sharp (talk) 06:07, 7 May 2020 (UTC)

@Double sharp: If you carefully read what I said, I said, "The ones who support the minority option do myopic OR. They think one-shot arguments will do, more fool them." Sandbh (talk) 07:00, 9 May 2020 (UTC)

@Sandbh: And yet above that you wrote "Same reason why its easier to find Lu tables. Publish or perish; don't do OR; parrot what others write etc". So do you actually read what you write? Double sharp (talk) 09:52, 9 May 2020 (UTC)

@Double sharp: Pot calling the kettle black! Do you actually read what I write? They think quick-fire one-shot arguments will do, without surveying the literature, and looking at both sides of the argument. They are more interested in getting their idea published, then putting in additional effort. Sandbh (talk) 05:40, 11 May 2020 (UTC)

@Sandbh: You consistently do not grapple with what I quote from you (bolding mine, everything else yours):

“

The ones who support the minority option do myopic OR. They think one-shot arguments will do, more fool them. Sandbh (talk) 05:58, 7 May 2020 (UTC)

Same reason why its easier to find Lu tables. Publish or perish; don't do OR; parrot what others write etc, textbook errors etc; there'a a long history of this kind of thing. Sandbh (talk) 08:27, 6 May 2020 (UTC)

”

Can you explain this self-contradiction? Double sharp (talk) 06:43, 11 May 2020 (UTC)

@Sandbh: P.S. Scerri? You mean Scerri who even last year wrote an article in Foundations of Chemistry about how Sc-Y-La "must die" (doi:10.1007/s10698-018-09327-y)? And when he says what I have been repeatedly saying here?

“

If lutetium occupies this position, following its removal from the f-block as discussed above, lanthanum becomes the first member of the f-block elements. Some authors object to this placement because lanthanum lacks f-orbital electrons. But, this is not an anomaly since more serious cases are tolerated. For example, thorium’s atom possesses no f-orbital electrons, yet there is no dispute that it belongs in the f-block.

Electronic configurations are ultimately approximations to what is more fundamentally described as a superposition of several closely lying configurations. Atoms do not require a particular kind of differentiating electron in order to belong to the corresponding block of the periodic table.

”

— Scerri, E. R. (2019). Five ideas in chemical education that must die. Foundations of Chemistry. doi:10.1007/s10698-018-09327-y

Precisely. You just need the right orbitals to be used for chemistry, as can be seen for La, Ac, and Th. And once you realise that that is the important thing, which is in fact even simpler than the ground-state electron configurations because you don't need to care about Madelung-rule anomalies anymore, La and Ac stop being exceptions at all. ^_^ Double sharp (talk) 06:20, 7 May 2020 (UTC)

@Double sharp: That article you refer to is a recycled version of what appeared online some years ago. It’s good to have it in hard copy somewhere, that’s all. I agree with what he said but for not addressing the Lavelle premise. Ironically, Scerri’s quote supports Lu in the f block just as well. I see you disparage the d/e concept but you have no objection if it appears in a Scerri quote. Sandbh (talk) 11:46, 8 May 2020 (UTC)

@Sandbh: I have no objection to it because Scerri is disparaging their relevance too. "Atoms do not require a particular kind of differentiating electron in order to belong to the corresponding block of the periodic table" is what he says and I wholeheartedly agree with that. They are totally irrelevant to block assignment. I just go a little further by noting that differentiating electrons are not even well-defined sometimes, in addition to being irrelevant.

Meanwhile, Lavelle's premise is based on a misunderstanding of chemistry that I have already debunked many times over (as has Droog Andrey) with reference to Seaborg, Jørgensen, etc. Broken record time: ground-state configuration anomalies mean nothing for the chemistry involved, which merrily goes along and uses the same subshells as if there was no such thing. Lanthanum has 4f involvement and occupancy in its compounds (e.g. LaF₃ has 0.34 of a 4f electron on La on average and the highest 4f-2p bond order of all LnF₃, see doi:10.1039/c3cp50717c), that's completely analogous to thorium 5f involvement and occupancy in its compounds, and what is known of actinium. Therefore "a pair out of place" is based on something that has zero relevance to normal chemistry.

Of course, if Lu were in the f block, it and Lr become a singular, unprecedented anomaly of elements in a block with absolutely no chemical involvement of that orbital. Not even in antibonding orbitals that tell prospective bonding atoms to keep out like He 1s or Ne 2p. That's obviously much worse than the situation Lavelle points out, because that one is not actually an issue when you look at the real chemistry instead of formal ground-state electron configurations, which are always mixed in a real chemical environment anyway for a d or f element with many states close to the ground state in energy. But this is a real chemical issue. The amount of valence f involvement of Lu in any real compounds is basically zero. Double sharp (talk) 12:20, 8 May 2020 (UTC)

@Double sharp: I feel the issue you to face is convention. In the case of block assignment this is not necessarily based on, as Scerri and you have observed, ground state configurations. Rather, it is based on several other considerations, including the overall chemistry involved, patterns seen in the periodic table, pragmatism, practicality, the idealised filling sequence v the actual filling sequence, and bang for buck. The latter would include, among other things, the old history about re confusion on where the 4f¹⁴ sub-shell was completed, and the realisation that nothing changed wrt to the chemistry of Lu. Elsewhere I think you asked me about analysing the convention, or not, and I'll get to that in due course.

The concerns you raise about 4f involvement in La, (maybe) Ac, and Th, are valid, in a footnote or 20/80 kind of way. I'd not describe them as headline material. I feel there isn't enough to it, to invalidate the 80/20 approach that convention appears to be based on. We've discussed this before in (kind of) the context of this table:

Order	Type
0th	Main group elements (typically colourless salts)		Transition elements (typically coloured salts)
1st	s block	p block	d block	f block
2nd	s(d) bloc	p(s) bloc	d(s) bloc	f(dp) bloc
3rd	H, Be	Al	Group 11	-- solid state configurations of Ln and An -- f-orbital involvement seen in early An

etc.

I start at the top of the table and work down only as far as the 80/20 level. I feel you can't accommodate the neglect of the 20, and have to work further down, never mind what existing useful patterns or relationships you disrupt along the way.

In the contest of ideas we can't accomodate every property in the PT. We have to focus on our priorities. I choose to focus on, among other things, where each block starts, based of ground state configurations and. e.g. that the 4f contraction starts at Ce and finishes at Lu (with a knock-on impact to Hf+). You choose to focus on 4f involvement in La, which hardly dominates the chemistry of La.

@R8R: Could you chime-in with your perspective on having to choose which properties to focus on? Sandbh (talk) 06:55, 9 May 2020 (UTC)

@Sandbh: I'll give it some good thought before replying, so sorry if that won't happen right away. I have noted the question and I'll try to get back with a well-thought-out response in a reasonable period of time.--R8R (talk) 10:49, 9 May 2020 (UTC)

@Sandbh: 4f doesn't dominate the chemistry of any lanthanide. The directly valent orbitals are usually 5d and 6s, the 4f contribution is always pretty slight. So, by your logic, there are no 4f elements at all. (Of course, even this little fact is inconvenient for the La table, because the lanthanides with the biggest 4f contribution are, you guessed it, cerium and lanthanum.) Of course, you don't note that there's such a thing as indirect involvement of a subshell, in which it can contribute because its electrons get to go to more direct valence subshells due to charge fluctuations. Meanwhile you ignore the elephant in the room that Lu can do no such thing and has only corelike 4f subshells. Even at 202 gigapascals when even Tm is happily using 4f as directly valent. XD

Guess what, in the 1940s there was a lot of confusion about where 5f started, too. Well, people traditionally since Mendeleev put uranium in group VI under tungsten. The chemistry is not an exact match, but it is not worse than bismuth below antimony. And after Seaborg probed the chemistry of the transuranium elements nothing changed in the chemistry of uranium. So, bang for buck would imply that in the 1940s, the old periodic table with U under W should have been retained, and that everyone made a big mistake listening to the upstart Seaborg. XD

My 80-20 is so much simpler. Just understand what chemical activity means, and then don't bother going below the first level. La-Yb have 4f valence involvement, Lu doesn't have any, so Sc-Y-Lu is immediately recommended. So much simpler, no need to focus on uselessly irrelevant ground-state configurations. And physical properties unanimously confirm it. And especially no need to shoot your own arguments in the foot for thorium, in which you above say that 5f in thorium is valid "in a footnote or 20/80 kind of way", and then support a table which decides to elevate that to the 80/20 level and put in in the f block anyway. Do you have any argument for why Ac and Th are treated so differently, despite their similar band structures and 5f involvement types, that isn't just "convention"? Double sharp (talk) 09:17, 9 May 2020 (UTC)

@Double sharp: Yes, agree 4f involvement in chemistry does not dominate 4f metals. So would (effectively) the entire chemistry establishment. In the 1940s they had the argument and the current form was adopted. Time to move on. Your 80-20 is based on a 20-80 premise of marginal, non-predominant, bonding involvement. "And physical properties unanimously confirm it." ROTFLOL! I've addressed Th elsewhere. Sandbh (talk) 10:19, 11 May 2020 (UTC)

@Sandbh: LOL. What argument? Care to show me articles from 1940s in which we can see the heroic partisans of both the Sc-Y-La and the Sc-Y-Lu sides of that era? All I see is a lot of authors arguing for Sc-Y-Lu, and the silent majority of Sc-Y-La (which is only a majority if you consider sources that don't focus on the issue) never bothering to examine itself. Lavelle had a go and Jensen utterly demolished it. Now, if you think 4f involvement in chemistry of Ce-Yb doesn't dominate for them, and that it's the same for La, don't you notice a double standard between the two cases? And where does that leave Lu with not even a tiny scrap of non-dominating 4f involvement in chemistry to speak of?

Meanwhile, just look at every physical property and see double periodicity supporting La-Eu and Gd-Yb tranches, how the f electrons in La cause it to have a depressed melting point compared to Lu, a different structure compared to Lu, superconductivity similar to Ce, and phase changes similar to Pr and Nd. At least when I answer with "LOL" or "ROFL" I actually back up what I'm saying. XD Double sharp (talk) 12:20, 11 May 2020 (UTC)

@Double sharp: I was referring to the adoption of the actinide hypothesis, which you referred to i.e., "in the 1940s there was a lot of confusion about where 5f started." Lavelle had a go and his convention-based argument about La-Ac not starting the f-block still stands. I reject out of hand your wild assertion that "every" physical property shows double periodicity supporting La-Eu and Gd-Yb tranches. Some 4f hybridization in La causing its lower melting point is plausible. I don't count such hybridisation as being in the same league as what occurs in Ce and Th. The different structure of La, as you know has been attributed to extra 3d occupancy. Ce-Lu spans the 4f contraction; La does not. La is a superconductor at ambient P; Ce-Lu are not. Phase changes OK. The picture is not as clear as you seek to portray it. Sandbh (talk) 03:14, 12 May 2020 (UTC)

@Sandbh: Well, guess what: they are still having the group 3 argument. It is not finished, IUPAC still hasn't made its decision. But the vast majority of chemists who actually look at the issue support Sc-Y-Lu. I put it to you that an argument that changes what it is supporting with time is simply not scientific. Your argument, if applied to the actinide hypothesis in the 1940s, would come out against it, despite the prominent adherents forming the majority among those who examined the issue, with their impeccable logic for the time! The rest is the same old double standard in order to get rid of La 4f (of the same order as Th 5f), and not actually looking at the physical properties (come on, try it; in every single case Eu and Yb are the anomalies for an obvious reason) that I won't respond to. Double sharp (talk) 03:23, 12 May 2020 (UTC)

@Double sharp: Let's put things into perspective. Maybe two dozen chemists have expressed support over the past 60+ years in support of Lu, largely by way of one-issue arguments. We may compare this to whoever many millions of chemistry and physics papers have been published over the same time.

We may contrast the two-dozen with Hamilton (1965), who showed a split d block (the gap is between groups 3 and 4) and says that—without any fuss—this is "the periodic table as it is usually presented". Indeed.

And Reger, Scott and Ball (2010, p. 295), who write that "perhaps" the correct shape of the 32-column periodic table should feature a split d block given the electron configurations of La and Ac, but that "we avoid these structures by splitting the f block from the rest of the periodic table. This also has the advantage of being able to print a legible periodic table on a single piece of paper." (They show La below Y in the rest of their book.) Indeed.

There has never been a groundswell of opinion in favour of Lu. In contrast, for example, arguments about the actinide hypothesis were largely settled by the end of the 1940's. There has been no groundswell of opinion within the chemistry community for Lu. No groundswell, no change. Sandbh (talk) 04:22, 12 May 2020 (UTC)

@Sandbh: So: on one side of your scale, you put two dozen papers for Lu, ranging in date from 1921 (Bury) to 2020 (Scerri), and disparage them all as "one-issue arguments", even if the much fewer La-argument papers can also be characterised the same way. On the other side, you put millions of chemistry and physics papers, the vast majority of which say absolutely nothing about group 3.

@Дрейгорич, Droog Andrey, and R8R: Presented without further comment for everyone else to do so instead. Double sharp (talk) 04:37, 12 May 2020 (UTC)

@Double sharp: Yes, Lu is noise. Effectively, no one is listening. As usual, you exaggerate. I never referred to them "all" as one-issue arguments; I said most of them were.

Bury (1921) is a poor choice.

For one, it spreads the two dozen Lu supporters over 100 years, rather than 60+.

Second, as we said in our IUPAC paper:

"Bury shows Sc-Y-Lu on the basis of chemical properties, but does not elaborate which properties he had in mind. He draws an analogy to Be and Mg resembling Zn better than Ca. The fact that modern periodic tables generally show Be-Mg-Ca rather than Be-Mg-Zn, despite these resemblances, calls into question the validity of Bury's analogy. At the very least, it suggests that there are other factors at work that can overrule these resemblances, and that these may also apply to the question of group 3."

OTOH, there is Landau and Lifshitz (1958, pp. 256–257) who argued for group 3 membership of Lu on the basis of its complete 4f shell. Scerri, who is the chair of the IUPAC project, referred to this as "one of the oldest categorical statements in favor of Sc Y Lu Lr". Sandbh (talk) 05:47, 12 May 2020 (UTC)

@Дрейгорич, Droog Andrey, and R8R: Presented without comment for everyone to remark on whether it is fair to weigh the papers supporting Lu against all chemistry and physics papers published over sixty years even if they say absolutely nothing about group 3. Never mind that the papers supporting La are even more of a blip compared to the ones supporting Lu. Double sharp (talk) 05:49, 12 May 2020 (UTC)

And at the very least, it is hilarious to quote Hamilton (1965) for the statement that Sc-Y-La was how the periodic table was usually presented (no doubt, in 1965; now you will find much more variation), without also pointing out that he supported Sc-Y-Lu. His paper is doi:10.1119/1.1972042. Double sharp (talk) 06:08, 12 May 2020 (UTC)

So, if I understand correctly, Sandbh is citing a pro-Lu paper in support of La? What, how?! ― Дрейгорич / Dreigorich Talk 13:02, 12 May 2020 (UTC)

@Дрейгорич: Well, I guess Sandbh's point was that Hamilton did say that the La table was the popular form. Which is true; he did say it. Whether it was literally true in 1965 is, now that I think about it, also questionable. Many of the strong Lu arguments had not yet been written (Chistyakov wrote his in 1968, Jensen from 1982 onwards); but Sc-Y-* was definitely competing with Sc-Y-La. But of course, claiming that he said it "without any fuss" (to quote Sandbh) is somewhat strange given that he made enough fuss to write the whole rest of his article in support of the Lu form instead.

Meanwhile, of course, while Hamilton is a great source on what the most popular form was in 1965, I do not think he can be used as a great source for what the most popular form is in 2020. Which I think you'll find has a significantly larger proportion using Lu than it did in 1965. Not to mention that it is unclear where, if anywhere, to count books showing periodic tables which put La under Y, but also put the * meaning "all other lanthanides" in the same box as La, and then present the unadorned Madelung rule that literally supports Lu under Y. In case you think I made that up, no, I didn't. That is in fact exactly what The Cartoon Guide to Chemistry by Gonick and Criddle does. While it does have a beautiful flowery table with d elements in loops and f elements in an extra loop, we have a periodic table on p. 38 doing exactly what I said (under Y comes "La*"), a standard Madelung rule on p. 33, complete with equivocation about exactly where the f elements start and end:

“

The sixth row has a loop within a loop, as 4f orbitals fill before 5d. (See p. 33!) As there are seven 4f orbitals, this loop has 14 elements. It is called the lanthanide series, after its first element, lanthanum.

”

— The Cartoon Guide to Chemistry, p. 37

“

The 14-element f-loop, after 57, lanthanum, is cut out and put below the main table.

”

— The Cartoon Guide to Chemistry, p. 38

So is the f-loop La-Yb or Ce-Lu? On two consecutive pages we learn two consecutive different things. And that, while somewhat annoying for the reader with an eye for detail, is basically inconsequential, since this is absolutely a beginner's text and the chemistry of the f elements concerns us basically not at all. (But funnily enough, they cover polarity and the continuum from covalent to ionic on pp. 62–63 with electronegativity, which Sandbh was busy trying to turn into "predominantly covalent" vs "predominantly ionic" for single elements in Archive 42. I also recall that while I kept explaining that there is no such thing, using the example of Na bonded to everybody else, which is obviously ionic if "somebody else" is F, obviously metallic when "somebody else" is Na, and somewhere in the middle if "somebody else" is As, he didn't change his stand until he saw his own source saying the same thing I said. XD)

This is of course an extreme example. But given that the standard Madelung rule is, well, absolutely standard (feel free to show me a Madelung rule graphic which notes a 4f anomaly to fit with the La table), I have no doubt that you will find many like it. And while I think The Cartoon Guide to Chemistry is just lovely as a first chemistry book to give a bright kid (hopefully along with an actual chemistry set), it strikes me that it should probably not be weighted equally with Hamilton's or Jensen's papers as a reliable source weighing in on the group 3 question. But that is what just counting the sources baldly would do. And that's a counting of sources which actually show a periodic table at all, not Sandbh pointing on the other side to millions of chemistry and physics papers, the vast majority of which are not related to group 3 at all. XD Double sharp (talk) 14:08, 12 May 2020 (UTC)

P.S. Now that you mention convention, I wonder what your current view of He over Be is. I seem to recall that you have expressed support for it before on the grounds that it causes one less DE anomaly. Of course, it has about zero status as a convention at the moment. Even if I do think you were right on that periodic table issue, albeit for the wrong reasons. ;) Double sharp (talk) 06:51, 6 May 2020 (UTC)

Pending. Sandbh (talk) 08:05, 11 May 2020 (UTC)

Falsifiability redux, and the alphabet of Sc-Y-Lu arguments

@Sandbh: One more time: is there any possible finding that could lead you to doubt Sc-Y-La? (Just in principle, since evidently nothing I have said yet will do it.) Double sharp (talk) 09:36, 6 May 2020 (UTC)

@Double sharp: I don't know. Not ruling it out but. Now that you ask, I remember every time I find some aspect of group 3 etc that I hadn't thought about before I always wonder if, upon reading further it'll be a counter-example i.e. a clear cut case of Lu trumping La. Hasn't happened so far. That's likely to be your experience, the other way round, I'd expect. Sandbh (talk) 02:03, 7 May 2020 (UTC)

@Sandbh: That's precisely how it should not be. In science, you've got to hold to a standard of falsifiability. Well, suppose you have a theory: there must be some things that it predicts should not happen. If they happen anyway, your theory is in trouble. Well: for me, I have simple and clear falsifiability criteria for my Sc-Y-Lu stance. Because that stance is based on the notion of what subshells are being used for chemistry. Therefore, Sc-Y-Lu would be falsified if:

Lu displayed significant 4f valence involvement (same for Lr 5f; I just put that in parentheses because the inherent difficulty of working with it makes it less likely that the refutation might come from Lr rather than Lu);
if it was demonstrated that lanthanum and actinium lacked significant valence f involvement, and that a consistent choice of what counted as "significant" would lead to confirming that thorium had significant f involvement instead (so you wouldn't get a double standard).

So far, the evidence has led to rejecting both of these: Lu seems to have no significant 4f valence involvement whatsoever, Lr seems to have no significant 5f valence involvement, and the way in which La uses its 4f orbitals seems to be exactly analogous to the way Th uses its 5f orbitals. If in principle these were overturned by some new findings, I would definitely change my mind back to Sc-Y-La. In fact, my previous support for Sc-Y-La was because I thought the above two points were true. Then I found out that they were not, so I changed to Sc-Y-Lu. Is there any possible thing that could make you do the same? Bearing in mind that:

A. Lu clearly trumps La in terms of simplest sufficient complexity, because in order to teach it, you just have to teach the Madelung rule and say that all those anomalous configuration don't matter; whereas teaching the La table requires focusing on those anomalous configurations, harping on the "pair out of place" pseudo-status of La and Ac that simply goes against real chemistry (see point E), and then having to figure out a way to not lead to awkward questions about Th [Rn]5f⁰6d²7s²;

Teaching the La table does not necessarily require focusing on those anomalous configurations, harping on the "pair out of place" pseudo-status of La and Ac, and then having to figure out a way to not lead to awkward questions about Th. The only to thing to note is where each block starts and perhaps the delayed start of the f block. Sandbh (talk) 08:25, 9 May 2020 (UTC)

Which will immediately lead to the awkward questions about thorium, since its 5f involvement is the same as that of actinium, yet the La table treats it so, so differently. No, this won't cut it. Double sharp (talk) 10:04, 9 May 2020 (UTC)

B. Lu clearly trumps La in terms of creating consistent vertical trends in the d-block, because Y-Lu is analogous to Zr-Hf and Nb-Ta;

Just like Sc-Y-La is analogous to group 1 and 2 trends. Sandbh (talk) 08:25, 9 May 2020 (UTC)

And why would that be relevant, given that group 3 is a d-block group? Double sharp (talk) 10:04, 9 May 2020 (UTC)

C. Lu clearly trumps La in terms of creating consistent horizontal trends in the d-block, as it is far more like the other 5d metals than La is;

Circular argument. Sandbh (talk) 08:25, 9 May 2020 (UTC)

In what way? Double sharp (talk) 10:04, 9 May 2020 (UTC)

D. Lu clearly trumps La in terms of creating consistent electronic configuration trends throughout the table, by making sure that every time we reach an even-numbered period in a non-s block, a new core orbital is added to every element: compare Al [Ne]3s²3p¹ to Ga [Ar]3d¹⁰4s²4p¹; In [Kr]4d¹⁰5s²5p¹ to Tl [Xe]4f¹⁴5d¹⁰6s²6p¹; and we see that similarly, what goes below Y [Kr]4d¹5s² should consistently be Lu [Xe]4f¹⁴5d¹6s² and not La [Xe]4f⁰5d¹6s²;

@Double sharp: I left this one for last, since it is so convoluted, I couldn't understand it. That by itself is enough to treat it as a non-starter. "Every time we reach an even-numbered period in a non-s-block, a new core orbital is added. Really. This argument is based on an idealized (false, as you say) electron configuration filling sequence, rather than the real life sequence. Sandbh (talk) 04:53, 10 May 2020 (UTC)

LOL. It's exactly what Jensen says. We see this pattern only with a Lu table. And in real life, 4f is already occupied at La in chemical environments. Your Sc-Y-La sequence with one 5d electron hanging up is false. And yet adhered to despite a crushing ton of evidence supporting 4f activity at La already, and in the face of the crushing contradiction between how the La table treats Ac vs Th. Double sharp (talk) 05:47, 10 May 2020 (UTC)

E. Lu clearly trumps La in terms of its understanding of electronic structure, which (as Seaborg, Jørgensen, and many others remarked) is not solely dependent on ground-state gas-phase configurations, because many other configurations can become favoured in compounds: note for example that the gross mismatch of ground-state configurations in group 10 (Ni [Ar]3d⁸4s², Pd [Kr]4d¹⁰5s⁰, Pt [Xe]4f¹⁴5d⁹6s¹) makes no difference to their still similar chemistry, and part of the reason for this is that the "right" configurations are close in energy anyway (for Pt it's hilariously close);

Yes, electronic structure, (as Seaborg, Jørgensen, and many others remarked) is not solely dependent on ground-state gas-phase configurations. That said the connection has been highly successful.

@Sandbh: So, tell me what the preferred valency of the 4f elements is. Despite the typical [Xe]4fⁿ6s² configurations, it is not +2. And, please, don't give me the wrong simplification of condensed-phase configurations into [Xe]4f^n-15d¹6s² either, because it's not true. Or, actually, even if you do, then please tell me what the preferred valency of the early 5f elements Th-Pu is and whether this is something that could have been guessed from that. Compare and contrast samarium and plutonium with matching ground-state gas-phase configurations and horribly mismatching chemistry. Then compare and contrast nickel and palladium with horribly mismatching ground-state gas-phase configurations and matching chemistry. Then tell me in what sense the connexion is "highly successful". XD Double sharp (talk) 10:04, 9 May 2020 (UTC)

@Sandbh: Ah, yes, some "set-up to fail questions. Is that the best you can do? As you know, the connection has been highly successful. Has it been perfect? No. But it's been good enough. When it doesn't work we make further inquiries. That's all.

Yes, the simplification for the Ln is good enough, in the first instance. The preferred valence for Th-Pu is +4, +5, +6, +5, +4. For Th, Pa, and U this accords with their configurations. It doesn't for Np, Pu so we know there must be something else going on. That said, we know Np can get to +7, and there has been speculation about +8 for Pu.

Sm-Pu is stupid question given we know there are additional factors at play for Pu, and Pu is more like a transition metal, like Os, which is quite relaxed with +8.

Ni-Pd is another stupid question because we know that s occupancy in the d-metals is rather weak, and that for many (but not all) purposes it's useful to consider them as (ds) metals. So we have Ni ds⁸ and Pd ds⁸.

Effectively the entire chemistry establishment recognises the utility of the connection. They must be wrong, of course. I look forward to the headlines: [1] "DS reckons anybody who thinks the connection is successful has rocks in their head!"; [2] "IUPAC announces the entire chemical community has rocks in its head!" Sandbh (talk) 06:54, 11 May 2020 (UTC)

@Sandbh: What you call "set-up to fail questions" are generally called: refutations. No, I don't know that the connexion has been highly successful, as it's not: I've multiplied quotes here from luminaries going up to Seaborg saying that there is no simple connexion. And it is amazingly funny to see Ni and Pd explained away as not an anomaly by saying that actually in this case the ground-state gas-phase configurations are not the thing that matters, and supporting (ds)⁸ [sic] configurations almost like what I propose which is (dsp)¹⁰. But, of course, it is somehow totally different when I say it and when you say it. XD And of course, your hilarious hyperbole can also be applied to Jørgensen, as I quoted him in Archive 42: "There is not the slightest doubt that no simple relation exists between the electron configuration of the ground state of the neutral atom and the chemistry of the element under consideration. Thus iron and ruthenium differ much more from each other chemically than do nickel, palladium, and platinum, though the configurations are analogous in the former case but differ in the latter." (We'll give him a pass that he didn't seem to know what the ground state of Ru is, because it matters not at all for chemistry, and because one can easily come up with the even funnier yet accurate example of helium and beryllium.)

Effectively the entire chemistry establishment agrees that the relationship between ground-state gas phase configurations and chemistry is not simple. No, I didn't make that up, Jørgensen made that claim about chemists in general. As I quoted further up this page:

“

The two major reasons why this series intended for gaseous atoms strongly bewilders chemists is that undue emphasis is made on irrelevant irregularities (such as the chromium, rhodium, palladium .... , atoms) and that the lowest level of two different configurations, such as [Xe]4f⁹6s² and [Xe]4f⁸5d¹6s² are only separated by 285 cm⁻¹ in the terbium atom, much less than 1% of the spreading of J-levels of each of the two configurations, and quite negligible for chemical purposes.

”

Ground-state configurations work for the s and p blocks well, where they follow Madelung perfectly, but elsewhere they show anomalies that are basically meaningless. I suppose Greenwood and Earnshaw have rocks in their head, too, for calling TM complexes just dⁿs⁰ for the most part in their tables.

And what about this gem from the old group 3 submission where I was totally wrong:

“

We agree with Scerri (2015) that solid state electron configurations are more relevant to the chemistry of the elements.

”

And then used it to support the La table based on false integer-occupancy configurations? Hmm? Double sharp (talk) 07:31, 11 May 2020 (UTC)

F. Lu clearly trumps La in terms of the logic of electronic structure in the periodic table, because La has some 4f valence involvement that is not dissimilar to the 5f valence involvement of Th (an uncontroversial 5f element), but Lu doesn't have any and has corelike 4f involvement that exactly matches that of Hf through Rn; notably, La actually has one of the highest 4f involvements of the Ln, with only Ce as competition (see Gschneider and doi:10.1039/C3CP50717C; LaF₃ has about 0.34 of a 4f electron on La, for example);

Minutiae. Sandbh (talk) 08:25, 9 May 2020 (UTC)

Ah, I get it now. f occupancy in La compounds and La metal = minutiae, f occupancy in Th compounds and Th metal = justification that it should go in the f-block. Just to quote you:

“

Anyway La and Th aren't directly comparable since Th³⁺ shows 4f [sic] chemistry with its own 4f electron, reliant on neither partial hybridization nor ligand donation

”

— Sandbh

Stupéfiant! Étonnant! Et complètement faux! Because trivalent thorium compounds have 6d¹ even though the ion is 5f¹! So, back to the double standards pile this argument goes! Double sharp (talk) 10:04, 9 May 2020 (UTC)

G. Lu clearly trumps La in terms of the logic of blocks, which by all rights ought to match the electronic structure if their names are supposed to mean anything;

Lu does not clearly trump La in terms of the logic of blocks. There is no such logic, other than convention. Please pardon my mirth at this silly argument. Sandbh (talk) 08:25, 9 May 2020 (UTC)

Well, logically the f block should contain elements using their f subshells somehow. That's kind of obvious. Without such a connexion, the labels become just convention. In which case your argument about the 4f contraction supposedly running Ce³⁺ to Lu³⁺ is also irrelevant to the f block composition. So I don't even need to note that it was invalid in the first place, by looking at how nobody in the 6th period seems to have a 6s electron in their most common oxidation state until Tl⁺, and so the 6s block has to start there. ^_^ Double sharp (talk) 10:04, 9 May 2020 (UTC)

H. Lu clearly trumps La in terms of the logic of contractions, for which the important generalisable thing throughout the table is the incomplete shielding effects that follow them; here Lu has 4f involved only via incomplete shielding effects, and therefore should be considered in the same class as the analogous Hf through Rn (just like Ga belongs with Ge through Kr after the 3d contraction finishes); the constant +3 oxidation state of the lanthanides cannot be generalised anywhere else, because already +2 for the 3d elements is not the most stable state for all of them; +3 and +4 both vie for having a majority for the actinides; and for the 4d, 5d, and probably 6d elements, you can forget about having any common oxidation state at all;

@Double sharp: Yes, I agree, the unique nature of the Ln, their constant +3 most stable oxidation state, combined with the progressive filling of the 4f sub-shell from Ce³⁺ 4f¹ to Lu³⁺ 4f¹⁴, marks them out. Sandbh (talk) 04:30, 10 May 2020 (UTC)

So much for periodicity, then, which is basically the opposite almost by definition of one-off occurrences. Double sharp (talk) 07:54, 11 May 2020 (UTC)

I. Lu clearly trumps La in terms of keeping similar elements together, because not only is Lu more similar to Y, but group 3 isn't cut off anymore in a Lu table from the chemically and physically similar heavy group 4 elements Zr, Hf, and Rf (and, to some extent, the heavy group 5 elements Nb, Ta, and Db); and also, it gives the right idea that the lanthanides share properties of s and d elements, instead of just being a degenerate sort of d element, by putting them between the s and d blocks rather than stuffing them inside the d block;

The greater chemical similarity of group 3 to groups 1-2 is widely recognised in the literature. The rare earths Sc, Y, La, and Ce to Lu are certainly more like s metals than d metals. Sandbh (talk) 08:25, 9 May 2020 (UTC)

@Sandbh: LOL. And how much literature treats group 3 as a main group, instead of putting it as a transition group and covering it with groups 4 through 11 at least?

Indeed, the biggest rare earth atoms La-Eu have significant s-like character, just look at their increased reactivity. But the heavier ones Gd-Yb increasingly act like d metals. (The divalent ones Sm, Eu, Yb are more s-like as an exception). And that's exactly why, in order to put them with similar elements, it's better to put them between the s and the d block, rather than inside the d block, like I said. So that supports the Lu table, actually. XD Double sharp (talk) 10:04, 9 May 2020 (UTC)

@Double sharp: As you know, even the literature that treats group 3 as TM will often comment on the absence of TM chemistry.

Here are the standard reduction potentials; group 3 looks closer to group 2, than it does to group 4:

 1         2           Δ     3         Δ       4
 K  -2.93  Ca -2.87  -0.84   Sc -2.03  -0.82   Ti  -1.21
 Rb -2.92  Sr -2.89  -0.52   Y  -2.37  -0.83   Zr  -1.54
 Cs -3.08  Ba -2.91  -0.55   La -2.36  -0.66   Hf  -1.7
 -------------------------------------------------------
Avg -2.98     -2.89  -0.64      -2.25  -0.77       -1.48

Who says Gd-Yb increasingly act like d metals? Sandbh (talk) 07:56, 11 May 2020 (UTC)

@Sandbh: LOL. I can make funny-looking but irrelevant tables too. Let's plot M²⁺/M for group 12, M³⁺/M for group 13, M⁴⁺/M for group 14:

12         13         14         Δ(13-12)  Δ(14-13)
Zn -0.76   Ga -0.53   Ge +0.12   +0.23     +0.65
Cd -0.40   In -0.34   Sn +0.01   +0.06     +0.35
Hg +0.85   Tl +0.72   Pb +0.78   -0.07     +0.06
                            Avg: +0.07     +0.35

(For Sn⁴⁺/Sn and Pb⁴⁺/Pb I calculated the values. Since Sn²⁺/Sn is -0.13, Sn⁴⁺/Sn²⁺ is +0.15, we add them, but then halve the result because then we are removing four electrons in the final reaction Sn⁴⁺/Sn rather than two. That's just an algebraic hack, the explanation for what is really going on is here.)

Wow, apparently group 13 is closer to group 12 than group 14! And we can also see that because group 13 forms real +3 cations in water and group 14 doesn't form real +4 cations! So, let's draw our periodic tables with groups 4 to 13 as the d block instead! How do you avoid this double standard, particularly since the average difference here is so much bigger? ^_^

The literature will also surely point out that group 3 has totally d-block-like physical properties. And, even if it doesn't explicitly say so, you may just compare what they say about Zr and Hf, and do a mental checklist against the properties that make them apologise for group 3 having weak transition properties. XD

It's obvious that Gd-Yb are more d-like than La-Eu, they have more localised f shells, are smaller, and are less reactive. Not to mention what is at User:Sandbh/Group 3#Conduction band structures:

“

At any rate, x-ray isochromats of Gd to Lu do not support Merz and Ulmer's conclusion that Lu is more favourably placed in group 3. Bergwall (1966) recorded these and found that they were rather constant, "which on account of the atomic configuration in these elements is expected." (p. 13) In other words, over half the lanthanides–not just lutetium—have conduction band structures that are more characteristic of transition metals such as hafnium.

”

Surely this is still valid even if I am using this observation to argue for Lu under Y instead of La under Y. And, BTW, if you think the rare earths are much more like s elements than d elements, then why shove them inside the d block as the La table does, rather than put them in between the s and d blocks like the Lu table does? Double sharp (talk) 09:16, 11 May 2020 (UTC)

J. Lu clearly trumps La in terms of understanding the lanthanides chemically, because the trivalency is based on the general charge-transfer motif 4fⁿ vs. 4fⁿ⁺¹ and not a d-electron hanging up; and that fails precisely for Lu and for no other Ln;

The chemistry involved can be quite easily accounted for by the consistent f^{n=1 to 14}d¹s2 configurations, and f¹ to f¹⁴ configurations of the trivalent cations, including Lu (noting Eu and Yb start with no d electrons, so there is a 4fⁿ to 4f^n–+1 transition. Sandbh (talk) 08:25, 9 May 2020 (UTC)

@Sandbh: And you manage that by accounting for the chemistry based on false configurations, since in the gas phase the Ln are for the most part not that, and in the condensed phase they are all not that because of hybridisation plus minor 4f involvement. I, of course, need do no such thing. XD Double sharp (talk) 10:16, 9 May 2020 (UTC)

K. Lu clearly trumps La in terms of understanding the lanthanides physically, as 4f electrons have been implicated (Gschneidner, Wittig) as a contributor to the metallic bonding of every lanthanide except lutetium;

This is from Johansson and Skriver 1997, in DF McMorrow et al. (eds), Magnetism in metals: A symposium in memory of Allan Mackintosh, Copenhagen, 26-29 August 1996 : Invited review papers, Kgl. Danske Videnskabernes Selskab, Copenhagen:

"This firmly establishes that there is a profound change in the behaviour of the 5f electrons when proceeding from Pu to the next element Am."

"Another point to notice is that the atomic volume for cerium in the α-phase deviates considerably from the general behaviour of the lanthanide elements. Later we will show that this is due to itinerant 4f electrons, a property which is in contrast to all the other lanthanides where the 4f electrons are localized with an integral occupation of the atomic-like f level, 4f n."

"Once more we emphasize that at zero pressure there is a profound difference between the early and late An metals, in the sense that the 5f electrons are itinerant (metallic) for the elements up to and including Pu, while they are localized and non-bonding (atomic-like) for the elements beyond Pu (Johansson, 1975). Thus in this respect the later (heavier) An and their 5f electrons behave like most of the Ln with their localized 4f n atomic-like configurations. On the other hand, among the Ln the first element with a substantial occupation of the 4f shell, i.e. cerium, shows already at rather low pressures or at low temperatures a behaviour very reminiscent of the early An (Johansson, 1974)…

"We illustrate this by arranging the An relative to the Ln introducing a displacement in atomic number (Johansson and Rosengren, 1975a):

           Ce Pr Nd Pm Sm Eu Gd
Th Pa U Np Pu Am Cm Bk Cf Es Fm

(The physical reason for this displacement is the larger spatial extent of the 5f orbital as compared to the 4f orbital for the corresponding element.) This suggests a most interesting connection between the 4f and 5f series, but this has not yet been fully explored."

See also Johansson and Li (2009) doi:10.1080/14786430902917632:

"For the rare earth metals (the lanthanides), it has been long known that the 4f n atomic configuration remains essentially intact when introduced into a solid (metal) phase."

"Thus, thorium is a genuine 5f metal, since, without the presence of 5f electrons, it would otherwise be a normal tetravalent hcp metal."

I see good support here for the Ce to Gd tranche, and Th as an f-metal, as well as bringing Gschneidner, and Wittig, into question. Not to mention the irrelevance, in this context, of La, Ac, and Lu.

--- Sandbh (talk) 04:21, 10 May 2020 (UTC)

LOL. Without the presence of f electrons, La and Ac would similarly be totally normal hcp metals. Yet they are not. Funnily enough, what you quote directly supports my tranches, because as usual the crash into more localised f electrons happens at Am. The congener of Eu. Double sharp (talk) 05:46, 10 May 2020 (UTC)

L. Lu clearly trumps La in terms of understanding the melting point trends, because the melting point depression at the start of the f rows is because of f hybridisation with the sd band (Wittig, citing Matthias et al.; note that Gschneidner points out that La without f involvement should have a higher m.p. than it actually does; and compare the melting points of La vs Lu, Ce vs Hf, Ac vs Lr, Th vs Rf, of course using predictions for Lr and Rf);

@Double sharp: I think the melting point trends are not particularly clear.

LOL. You're missing the point. Just compare the melting points of La vs Lu, Ce vs Hf, Ac vs Lr, Th vs Rf. In every case f involvement causes melting point depression. Double sharp (talk) 05:46, 10 May 2020 (UTC)

Here, let me tabulate them for you (all in K), because apparently just listing the pairs involved will still lead you to consider what I'm not talking about:

La	Lu	Ce	Hf	Ac	Lr	Th	Rf
1193	1925	1068	2506	1323	(1900)	2115	(2400)

In every case where I claim f electrons are relevant (La, Ce, Ac, Th), regardless of whether they happen to be present in the ground-state gas-phase configuration, the result is melting point depression vs the corresponding element with no relevant f involvement (respectively Lu, Hf, Lr, Rf). Double sharp (talk) 04:27, 11 May 2020 (UTC)

M. Lu clearly trumps La in terms of understanding the superconductive properties of the f elements, because lanthanum is a normal f band superconductor (Wittig);

@Double sharp: What’s a “normal” f band superconductor? Sandbh (talk) 13:45, 9 May 2020 (UTC)

@Sandbh: Like cerium, which I suppose you agree is an f metal. What I mean is that there's nothing significantly different between La's 4f usage and Ce's here. Just look at the structures, as well; La has a very similar pressure-temperature diagram to Pr and Nd. Double sharp (talk) 14:11, 9 May 2020 (UTC)

@Double sharp: Ce to Lu don't superconduct at normal pressure. So, I ask once more, "What’s a “normal” f band superconductor?" Sandbh (talk) 10:35, 11 May 2020 (UTC)

@Sandbh: Why are you so focused on normal pressure alone? The point is that the mechanism by which La superconducts is the same as the mechanism by which Ce superconducts at higher pressure. You can get a far more complete picture of trends (rather than just seeing a "Main screen turn on!") by just plotting critical temperature against pressure. Double sharp (talk) 12:25, 11 May 2020 (UTC)

“

We do not expect that pressure will change the term 4f^ε fundamentally, since we think it represents the screening charge of a 4f scattering resonance safeguarded deep in the interior of the lanthanum ion core (in agreement with our picture for Ce).

”

— Wittig

Double sharp (talk) 14:31, 9 May 2020 (UTC)

@Double sharp: I was comparing like with like. Sandbh (talk) 03:19, 12 May 2020 (UTC)

@Double sharp: I was looking at how to respond to item L, when I re-read Wittig (1973, p. 383) doi:10.1007/BFb0108579, "Electron tunneling data have recently revealed strong phonon-induced structure in the second derivative of the tunneling current, which demonstrates that La is a superconductor with strong electron phonon coupling [30, 31]. This result ends the speculation about a special "f electron mechanism" [32]." That also reminded me of Ratto, Coqblin and d'Agliano (1969, pp. 498, 509), who suggested that Lu's lack of superconductivity might be attributable to a small 4f character. Sandbh (talk) 04:21, 10 May 2020 (UTC)

I was also reminded that at 20 GPa, La's Tc rises to 12.8 K and that, while Lu is (apparently) not a superconductor, it does become a superconductor at 18GPa, with a Tc of 1.2 K. See here.

LOL. And what you don't quote is the very next line in Wittig: "The experiment does not exclude, however, that La may be a 4f-band metal of a similar type as α-Ce." I rest my case. Particularly since Wittig then marshals evidence to support La as an f band superconductor anyway. Double sharp (talk) 05:46, 10 May 2020 (UTC)

@Double sharp: I'd place more weight on "ends the speculation" than a wishful "may". What seems more s/f is that none of Ce-Lu are superconductors at normal pressure. Whereas La is. We already know that La has the greatest d occupancy. And we know that Tc tends to peak when the number of d electrons are the highest, and there is no interference from a half-full sub-shell, and 3d row magnetic effects. And then there is the old speculation about Lu not being superconducting due to the presence of some small f character or influence. That seems like a coherent pattern to me. Sandbh (talk) 05:31, 11 May 2020 (UTC)

@Sandbh: LOL. You refuse to consider "may", considering it wishful despite all the evidence Wittig then marshals for it, and then refer to "old speculation" about Lu 4f determining lack of superconductivity. My sincerest congratulations for this amazing double standard. And way to go for not mentioning that whether Lu is or is not superconducting at one bar pressure is itself disputed. Double sharp (talk) 12:35, 11 May 2020 (UTC)

@Double sharp: I looked up one of Wittig's "strong electron phonon coupling" references doi:10.1103/PhysRevLett.29.858:

"Nevertheless, tunneling studies continue to indicate an absence of strong structure directly attributable to f band effects [in La], revealing instead only modest deviations from the BCS tunneling density of states (TDS) reminiscent of phonon structure."

"The anomalously low value of u* = 0.018 remains an open issue in that it could either represent a genuine-band effect or be accounted for by substantial amounts of residual attenuation."

That did not fill me with confidence as to the rest of Wittig's paper. He also wrote:

"The data seem to imply that there is at present no point in specifically explaining the increase of T¢ with pressure for La by a model which involves 4f states. The increase of the with pressure is apparently a more general property of the transition metals of the third (and fourth) column of the periodic table. One is perhaps even tempted to go one step further by asking: can we forget about the whole 4f story? This was an apparent trend of opinion at a recent conference on the superconductivity in d- and f-band metals. Is La, after all, a pure sd-band superconductor like Y and Lu?"

After beating himself up three times, Wittig then goes on anyway to suggest La does have some 4f character. Notably his paper was cited only seven times by other authors (twice including himself) in the ensuing nine years (up to 1981), and once in 1987. That does not fill me with confidence.

We covered Lu superconductivity in our IUPAC submission. More recent authorities appear to discount Lu as a superconductor, which I agree is convenient for me. Sandbh (talk) 04:04, 12 May 2020 (UTC)

@Sandbh: And so how exactly do you plan to explain La's high T_c at all pressures without Wittig's proposed 4f mechanism, which is not the same as the one he agreed didn't exist? Especially since it is the only anomaly among the d elements if you think La is one, but represents no anomaly at all if La is considered an f element and Lu a d element? Double sharp (talk) 04:08, 12 May 2020 (UTC)

@Double sharp: The Tc of La, at 6 K is comparable to V 5.4; Nb 9.25; Tc; 8.2; Hg 4.15; Be 9.95; Pb 7.2. If La is placed in the d-block where is the anomaly? There are plenty of other anomalies in the d-block. And there are no anomalies among the 4d metals. I'm not discounting Wittig. I'm saying that plenty of other folk considered La to be another sd superconductor. Sandbh (talk) 05:30, 12 May 2020 (UTC)

@Sandbh: And, as Wittig pointed out, La's high critical temperature cannot be explained by the model that it is only an sd superconductor. Just compare its T_c at any pressure with the early 5d metals. It doesn't fit the trend. At 1 bar it is anomalous as while the pairs Zr-Hf, Nb-Ta, Mo-W, Tc-Re are both superconducting, Y-La has one superconducting (La) and one non-superconducting (Y) element. This is fixed with Lu, based on recent authorities which discount it as a superconductor at 1 bar. And at high pressure the T_c of La soars beyond any of the 4d or 5d metals. Double sharp (talk) 05:46, 12 May 2020 (UTC)

Let's see how Hamilton (1965) already explained it (doi:10.1119/1.1972042):

“

La becomes superconducting at 4.9°K, but no superconductivity has been observed in Sc, Y, or Lu yet, even through [sic] measurements have been made to temperatures below 0.3°K. This is another experimental fact that supports the thesis of this article [Sc-Y-Lu], but to discuss it properly we must give a little background. During studies of superconductivity in the transition metals, it was found that the superconducting transition temperature is determined mostly by n, the average number of valence electrons per atom. Thus, for the alloy NbW, the value of n would be (5+6)/2. If the transition temperature is plotted as a function of n as in Fig. 3, the curve is more or less symmetrical about the middle of the series at n = 6, having a maximum near n = 5 (Nb) and another near n = 7 (Tc). If La is considered to be a transition element, one might object that n = 3 is also a value of n that is favorable for a high superconducting transition temperature. Indeed, it was in part just this objection that led Mathias to propose a third maximum at n = 3. [Never mind its failure for Sc and Y.] If La is classed as a rare earth, the simple, symmetrical behavior of the transition temperature as a function of n is retained. It is the author's view that this is a clear-cut example of how continued use of the "old" periodic table, in which La is placed in the same column with Sc and Y, can obscure the situation.

”

(Such pellucid prose. If only it was as easy to write so well as the result makes it look!) Double sharp (talk) 06:17, 12 May 2020 (UTC)

N. Lu clearly trumps La in terms of understanding the superconductive properties of the d elements; the critical temperature of the corresponding 5d metal is always lower than for the 4f metal in groups 4-7 and 9, and group 3 only follows that with Lu in it (Wittig; Ru/Os in group 8 is an exception due to incipient magnetism);

@Double sharp: The 4d 5d relationship works only for groups 4 to 7. So what? Sandbh (talk) 13:45, 9 May 2020 (UTC)

@Sandbh: Because there's a very simple reason why it should fail to work for group 8: incipient magnetism. Once that goes away, for group 9 it works again. So, tell me: what is the reason it should fail for group 3? Sc-Y-La looks absolutely analogous to Ti-Zr-Ce on the graph. Double sharp (talk) 14:11, 9 May 2020 (UTC)

@Double sharp: The relationship fails at group 9. Rg is 35 μK; Ir is 0.1 K. It doesn't "fail" in group 3. There's nothing to compare the 5d metal with, since neither Sc not Y superconduct at normal pressure. Sandbh (talk) 05:31, 11 May 2020 (UTC)

@Sandbh: It's at high pressure, as the graph points out. That doesn't give much of a problem because everyone can see there is a trend when you plot critical temperature against pressure. Otherwise it would be far too spotty to get any trends out of. Meanwhile, Wittig, Probst, and Wiedemann wrote in "Superconductivity of Lutetium at Very High Pressure: Implications with Respect to the Superconductivity of Lanthanum": "In conclusion, we believe that the very high T_c of La at all pressures (leading to the highest T_c ~ 12°K at ~ 140 kbar among pure elements) is at present the important real anomaly-and, with respect to the situation in the past, the only remaining anomaly-about its superconductivity. Efforts should now be made to explain the unusually high T_c at all pressures.", and reiterated the 4f-enhancement model for La. Double sharp (talk) 12:40, 11 May 2020 (UTC)

@Double sharp: Which graph are you referring to? Sandbh (talk) 03:26, 12 May 2020 (UTC)

@Sandbh: Obviously, Figure 3. Actually, here is the data itself, from the 1972 article I mentioned. Here they seem to omit rhodium, maybe that was found between 1972 and 1973:

Superconducting transition temperatures of 4d and 5d metals at ~150 kbar (so: *comparing like with like*)
3	4	5	6	7	8	9
Y	Zr	Nb	Mo	Tc	Ru	Rh
2.7	0.6	9.3	0.9	7.7	0.51	—
Lu	Hf	Ta	W	Re	Os	Ir
0.5	0.1	4.5	0.01	1.7	0.66	0.1

Whereas: La 12.0. Gatecrasher La destroys yet another pattern that spans the entire first half of the d series. Double sharp (talk) 03:45, 12 May 2020 (UTC)

@Double sharp: Which 1972 paper are you referring to? Sandbh (talk) 04:44, 12 May 2020 (UTC)

@Sandbh: doi:10.1007/978-1-4684-2688-5_99 (yes, I know it says 1974, but it's proceedings from a 1972 conference). Double sharp (talk) 05:52, 12 May 2020 (UTC)

@Double sharp: Why 150kbar? Why not 1 bar?"

Superconducting transition temperatures of 4d and 5d metals at 1 atm (so: *comparing like with like*)
3	4	5	6	7	8	9	10	11	12
Y	Zr	Nb	Mo	Tc	Ru	Rh	Pd	Ag	Cd
–	0.6	9.25	0.92	8.2	0.5	0.000035	–	–	0.52
Lu	Hf	Ta	W	Re	Os	Ir	Pt	Au	Hg
–	0.38	4.4	0.01	1.7	0.7	0.1	–	–	4.15
–	↑	↑	↑	↑	↓	↓	–	–	↓

No pattern that I can see. Sandbh (talk) 05:14, 12 May 2020 (UTC)

@Sandbh: Because Wittig, being an expert in the field, thinks 150 kbar "introduces only little arbitrariness".

Meanwhile, the pattern even at 1 bar is completely obvious:

Either both the 4d and the 5d element are superconductive, or neither are.
In the first half of the d-series, critical temperature goes up passing from 4d to 5d; in the second half it goes down.

Since Y and Lu fail to exhibit superconductivity at 1 bar, but La does, it stands to reason that Lu should be the element below Y in the periodic table and not La.

So at 1 bar the data supports Jensen's argument, and at 150 kbar it supports Wittig's argument. In both cases Sc-Y-Lu is far more regular. Nice going. Double sharp (talk) 05:38, 12 May 2020 (UTC)

And again, completely supporting my statements that La is most analogous to Ce with its high 4f involvement, we have doi:10.1016/0378-4363(80)90188-6:

“

Ab initio electronic structure calculations on fcc La and Ce at normal and reduced lattice constants have provided a great deal of insight into the origins of their unusual phase transitions and superconducting transition temperatures. The 4f electronic states which occur in these early lanthanides are found to possess a novel bonding character which depends sensitively on the environment, and in particular on atomic volume. The behavior of these 4f states is similar in many respects to that of 5f states in the actinides and supports previous suggestions that studying both systems in parallel will be useful in increasing the understanding of both 4f and 5f band materials.

”

They must be wrong, of course. Surprise me. Oh wait, I know how this will go: you will claim La has no 4f electrons, I will cite 9001 papers proving otherwise in chemical environments and in the metal, you will say those are minutiae, I will note that by that standard the f character of Th is equally minutiae, you will agree(!), I will then ask why you don't ask for the 5f block to consistently start at Pa, and then you will plead tradition, and I will note that (1) your tradition is based on authors who don't analyse what they're showing most of all, and that (2) the important tradition for WP is composed of authors who do analyse what they're doing, who support Sc-Y-Lu for the most part. And I will now also point out that you have claimed above that if Lu had become standard based on these very same arguments, you wouldn't be opposing it, which is a strong sign that your stand is hardly being scientific. Maybe we can also go on a side note where you claim my approach lacks simplest sufficient complexity, and I point out that by neglecting anomalous configurations and not having to have some arguments unplugged to avoid short-circuits about Al over Sc mine is obviously simpler. Somehow, after every single cycle of this, you change nothing, start the cycle from the beginning with the supposed lack of 4f electrons on La and La³⁺ (only true for gas-phase atoms which is about as far from chemical environments as you can get), and either don't answer the question about how your theory could possibly be falsified or suggest something, that I note I have already falsified, and then simply go on. Yes, I can find quotes for every single one of these if you want. Double sharp (talk) 04:03, 11 May 2020 (UTC)

In fact, here are those quotes, because this endless cycle is immensely annoying. On your side, because I obviously don't need to quote myself to justify what I go on record above as saying about what I say:

“

@Double sharp: Remind me again why the 0 4f electrons in La explain why it prefers the +3 os? And, obviously, we do have 4f metals as can be discerned by e.g. the configurations of the trivalent cations. As your luminary Wulfsberg says, focus on the configurations of the ions. Sandbh (talk) 11:34, 10 May 2020 (UTC) [so I guess Na is not an s metal either, as Na⁺ is the major oxidation state and it has no 3s electron anymore]

The concerns you raise about 4f involvement in La, (maybe) Ac, and Th, are valid, in a footnote or 20/80 kind of way. I'd not describe them as headline material. ... Sandbh (talk) 06:55, 9 May 2020 (UTC)

On Th, this is only a question of degree, and bang-for-buck. Ce and Th are the first metals where we see a significant impact of f involvement. We don't see anything on that scale in La and Ac. Sandbh (talk) 06:08, 10 May 2020 (UTC) [self-contradiction about thorium, ahoy!]

I start at the top of the table and work down only as far as the 80/20 level. I feel you can't accommodate the neglect of the 20, and have to work further down, never mind what existing useful patterns or relationships you disrupt along the way. ... Sandbh (talk) 06:55, 9 May 2020 (UTC) [never mind that, by definition, stopping at the Madelung rule and ignoring anomalous configurations as I do is working less far down in terms of what you teach the students; only to justify it you need to go a bit further to show lanthanum 4f involvement beyond doubt]

Off the top of my head what could falsify my stance is a case of an element which has a mismatch between its block and its most chemically important orbital. Sandbh (talk) 04:42, 25 March 2020 (UTC) [and as I immediately pointed out, Lu and Lr hardly have f as their most chemically important orbital, as it's a core orbital]

If Sc-Y-Lu had become standard then no, I doubt I would've been criticizing this convention. Unless anti-Jensen had published an argument in favour of La. I supported Jensen, until Scerri (who supports Lu) opened my eyes to the limitations of Jensen's approach. Sandbh (talk) 06:08, 10 May 2020 (UTC) [and of course, in that same post above, my question about what could falsify your Sc-Y-La stance is still not answered]

I don't know. Not ruling it out but. Sandbh (talk) 02:03, 7 May 2020 (UTC) [in response to my question about what could falsify your Sc-Y-La stance]

”

Such iconic rhetoric, as DA said. Well: we are never going to agree on this until you recognise that lanthanum 4f involvement is exactly of the same type and order as thorium 5f involvement, and that in the absence of some really good reason that is not the convention we are explicitly discussing, it constitutes an egregious double standard to allow one into the f block and not the other. I have already supported lanthanum 4f involvement with tons and tons of papers, it is by now just plain unarguable, by the measures of both truth and verifiability. Double sharp (talk) 04:13, 11 May 2020 (UTC)

O. Lu clearly trumps La in terms of understanding the high-pressure properties of the f elements, because while the late lanthanides Gd-Tm show a very high-pressure (megabars) monoclinic C2/m phase due to the delocalisation of the 4f subshells, this is not known at all for lutetium. Which is especially amusing because, astonishingly, this is also known for yttrium (doi:10.1088/0953-8984/24/36/362201), in which it has been suspected that the empty 4f orbitals become occupied at these really extreme pressures because of electron transfer from 5s and 4d. But lutetium has no 4f vacancies and 4f for it is stuck in the core; and note that high pressure favours delocalisation of the f electrons, so the complete absence of this state for Lu even at 202 GPa is telling;

@Double sharp: This does not tell me anything I can’t already tell from the electron configurations of the metals involved. Sandbh (talk) 13:05, 9 May 2020 (UTC)

@Sandbh: It tells you: Lu has zero f involvement. So it does not belong in the f block. Guess what, lanthanum can probably do this very same thing, albeit at 1100 GPa; there are no such predictions for lutetium (doi:10.1016/B978-0-444-59536-2.00004-0). Of course, the crystal structure of La at ambient pressure is already a smoking gun for 4f involvement, see point Q. Double sharp (talk) 13:21, 9 May 2020 (UTC)

P. Lu clearly trumps La in terms of understanding the actinides physically, because actinium and thorium both have fcc structures and similar band structures, with itinerant 5f bands hybridising with 6d and 7s;

Physically this has little to do with the An, where the early An are characterised by low symmetry structures, where the f electrons are delocalised; and the balance between the delocalised and localised electrons occurs at the metal from hell, Pu, before being localised in the later An. Sandbh (talk) 12:38, 9 May 2020 (UTC)

F electron delocalisation leads to more complex structures for Pa-Pu, but that is not the only thing they can do. Just look at Th, whose being fcc can squarely be blamed on f electrons. Otherwise it would follow Ti, Zr, Hf, and Rf in being hcp. Just read the paper doi:10.1103/PhysRevLett.75.280 that explains how f involvement is to blame for the crystal structure of Th.

And as I note in point Q, the exact same situation is at work for La and Ac. If no f bands are involved, the structure of the transition metals can be predicted absolutely perfectly from theory based on their number of valence electrons. The fact that this fails horribly for La (dhcp) and Ac (fcc), in contrast to Lu and Lr which are hcp like Sc and Y, is a strong warning sign that f bands must be involved here. Double sharp (talk) 12:46, 9 May 2020 (UTC)

Q. Lu clearly trumps La in terms of understanding the crystal structures of the transition metals. The fcc structure of actinium seems to be already a significant warning sign. Logically speaking, Ac with no 5f involvement should resemble very closely Lr, as both elements would have the same (6d 7s)³ conduction band configuration; that is the same argument Wittig uses about Ce vs Hf, and the paper linked below about Th uses about Th vs Hf. But Lr is expected to be hcp. We have a similar situation for La dhcp vs Lu hcp; and Sc and Y follow Lu and Lr in the hcp crystal structure. Since the argument has been used by Wittig for Ce vs Hf across the lanthanide contraction, it should be valid here too: Wittig additionally notes "[cerium] destroys a beautiful piece of the harmony of the physics of transition metals whose structure varies regularly with valence, unless they are magnetic" as evidence that Ce is not a real sd transition metal. This immediately casts some serious aspersions on La and Ac as transition metals because they constitute crystal structure anomalies which are unprecedented in the transition from the 4d to the 5d row in groups 4 through 11, and in the transition from the 5d to the 6d row in groups 4 to 9.

@Double sharp: From our IUPAC paper: “The example given is true, but its relevance is questionable. For example, the structures of the group two metals Be, Mg, Ca, Sr, Ba, and Ra are HCP; HCP; face centred cubic; face centred cubic; body centred cubic; and body centred cubic. Groups 7, 8, 9, and 10 also show inconsistencies in crystalline structures.” Same principle applies here. Sandbh (talk) 13:02, 9 May 2020 (UTC)

@Sandbh: You just point at inconsistencies, and you don't analyse them to see the theory. Which for transition metals predicts crystal structure perfectly from valence, except for those first-row anomalies with the magnetic elements in the 3d row. Therefore there is absolutely much more significance attached to the anomaly of crystal structure for group 3 than there is for groups 7 through 10, as it is a smoking gun for f involvement for La and Ac. Double sharp (talk) 13:21, 9 May 2020 (UTC)

“

As noticed by many authors[17, 38, 39], the difference in the crystal structures of La is, however, an important fact which must have a reason. We think the structural differences are subtle indications that the electronic structure of La is not simply (6s 5d)³ in the solid, but much closer to those of the light rare earth metals. Praseodymium and neodymium, for instance, seem to have pressure-temperature phase diagrams isomorphous with La [40]. If they would simply have the (6s 5d)³ conduction band configuration, we could almost certainly expect that the hcp structure is the stable structure (at normal temperature) similar as for the "regular" trivalent metals Sc, Y, and Lu.

”

— Wittig

As you can see, it's not my OR, Wittig said it too. Double sharp (talk) 14:14, 9 May 2020 (UTC)

@Double sharp: Pettifor doi:10.1016/0364-5916(77)90009-8 attributes the dhcp structure of La, as follows:

"Self-consistent band calculations show that La has approximately 0.6 electrons more than Lu, because of its larger core size (see Figure 1 of (27)). As can be seen from Figure 10 this is just sufficient to take the lattice from hcp (Lu)to dhcp (La)."

La is more of a d metal, in this context, than Lu is. I recall saying this before but I didn't know then that this explained its dhcp structure. Sandbh (talk) 02:15, 11 May 2020 (UTC)

@Sandbh: And let's see what Pettifor says later, with his underlines:

“

However, Figure 10 raises the question as to why such a crystal structure sequence is not found amongst the early transition metals, for example in going from Y to Zr, where the number of d-electrons also changes from about 1½ to 2½. The answer most likely lies in the neglect of hybridization which can modify the structural energy differences. Figure 11 shows (22) that the inclusion of hybridization does not affect the basic shape of the bcc-fcc and hcp-fcc curves presented in Figure 9 for N ≥ 4. (The bcc-fcc curve includes a hard-core contribution (22) which is probably an over-estimate in the light of Dagens’ (25) recent results.) However, we must stress that this is only true provided that the tight- binding hopping parameters are chosen to give a pure d-band width that is close to the final fully hybridized width. Unfortunately it is not possible theoretically to extract a unique tight-binding d-band from the total density of states presented in Figure 8. We can arrive at the same final result by having either a narrow d-band and large hybridization with the nearly-free-electron band or a wider band and smaller hybridization. The d-band structural energy differences depend on the particular choice as is illustrated in Figure 12 for the hcp-fcc case (28), where the splitting parameter β = 1.0 corresponds to a relatively narrow d-band with hopping only to first nearest neighbours whereas β = 0.5 corresponds to a pure d-band width that is closer to the final fully hybridized width but with the possibility of hopping directly out to third nearest neighbours. The choice of β = 0.5 corresponds most closely to the fully hybridized result in Figure 11 and we have, therefore chosen to work (as in Figures 9 and 10) with parameters that most nearly reproduce the final width of the d-band. Nevertheless, the energy differences between hcp, Sm-type, and dhcp are quite a bit smaller than those presented in Figure 9, so that the Sm-type and dhcp structure might easily be lost in the early transition metals where hybridization effects will be a lot stronger than in La which has only ½ an sp-electron.

”

— Pettifor

So, care to guess if hybridisation with 4f, which alone among the elements he considered would be relevant for lanthanum, was included? I remind that the lack of consideration of f orbitals has dire consequences on analysing thorium, for which 5f is about as active as 4f on lanthanum. Well! Six years before Pettifor's article, we had this gem from Coqblin (1971):

“

The relative variation of its atomic volume under a 40 kbar pressure is 12 %, which is larger than that of normal rare-earths. This experiment suggests that the valency in lanthanum is a little smaller than 3 at normal pressure.

”

— Coqblin

Shades of Wittig's model indeed!

Of course, no one seems to be asking: if Lu has the same structure as Y, then that must mean it has a more similar structure to Sc and Y in terms of d occupancy too. And indeed, he notes that Y has about 1.5 d electrons, and so does Lu. So even if you refuse to acknowledge 4f as a possible reason for the dhcp structure of La for whatever reason, the argument still supports Lu under Y. Double sharp (talk) 03:48, 11 May 2020 (UTC)

@Double sharp: Not really. We know La has a larger d-occupancy than Lu. We know from Pettifor's work that this explains the dhcp structure. There is no need to wishfully invoke 4f:

Despite Wittig's similar wishful thinking, he wrote, "This result ends the speculation about a special "f electron mechanism".
We know that Lu is not a superconductor at regular pressure, as is the case with Ce to Yb.
We know it was suggested that the lack of superconductivity in Lu might be attributable to a small 4f character.

We agree on the 5f situation in Th, just as we agree Th-U, and Am show normal pressure superconductivity.

You'll have to do better than Coqblin's unconfirmed paper. Nice cherry picking, but. He adds:

"Only the conduction electrons participate to the superconductivity mechanism and the "normal" lanthanum, i. e. without 4f character at very high pressure [20GPa], has a high superconducting temperature T_c0 of order 12 K. On the contrary, the 4f electrons tend to inhibit superconductivity and, as the 4f character decreases with increasing pressure, T_c increases with pressure and tends to T_co at very high pressure. The basis of this model is in contradiction to previous models which attributed the origin of superconductivity to the presence of 4f electrons.

"The recent discovery of superconductivity at high pressure with a pressure dependent Tc in barium [20 GPa] yttrium [50] and cesium [8 GPa] can lead to some critics against the preceding model. So, the assumption of a small 4f character at normal pressure (or valency of 2.7) has to be checked experimentally and the understanding of a high T_c0 value for "normal" La calls for new theoretical investigation. "

Sandbh (talk) 12:15, 11 May 2020 (UTC)

@Sandbh: LOL. As Wittig pointed out, 4f bands can be conducive for superconductivity. That's why I left out that later-refuted bit of Coqblin's paper, not because I wanted to cherry-pick. Meanwhile, I see you still refuse to consider Wittig's statement "The experiment does not exclude, however, that La may be a 4f-band metal of a similar type as α-Ce", despite all the evidence he marshals for it in the following pages, and yet carry on considering the speculation that 4f is responsible for Lu lacking superconductivity. Nice going. Considering 5f for thorium and not 4f for lanthanum continues to be a silly double standard, especially since in 1978 Glotzel confirmed 4f involvement in La metal just like is known for 5f involvement in Th metal. Double sharp (talk) 12:29, 11 May 2020 (UTC)

@Double sharp: Glotzel deals with FCC La. I continue citing 4f in Lu in the absence of a Wittig-like statement saying "This result ends the speculation about a special "f electron mechanism". There are only 13 other supporting 4f metals, after all, none of them superconducting at normal pressure. I don't pay much heed to the rest of Wittig's (1973) evidence, if he preceded the same evidence with an unequivocal statement dismissing speculation about a special "f electron mechanism". Cogblin (1971) is no better. At least he acknowledged that "4f electrons tend to inhibit superconductivity" and, as the 4f character decreases with increasing pressure, T_c increases with pressure and tends to T_co at very high pressure." Sandbh (talk) 13:26, 11 May 2020 (UTC)

@Sandbh: LOL, I see you ignore that Wittig treats the supposedly debunked "f electron mechanism" quite differently from his 4f-scattering resonance of La. Not to mention that it only requires 310 °C to make La go fcc. And that that state is even metastable at STP, as doi:10.1016/0038-1098(85)90217-0 notes. XD Double sharp (talk) 13:35, 11 May 2020 (UTC)

And of course, what Sandbh does not mention: according to Pettifor, Y has about 1.5 d electrons in the solid metal, Lu also has about 1.5, but La has about 2.5. So this is yet another argument that really supports Sc-Y-Lu. XD

Not to mention that if La through Lu all have at least 1.5 d-electron occupancy, and that at least the earlier lanthanides La-Pm and maybe Sm (see Pettifor's Fig. 10) therefore should have >2 d-electron occupancy, then it sure seems that fⁿds² is not even the correct condensed-phase configuration of the lanthanides. So much for the idea of one d electron hanging up that the La table implies. Double sharp (talk) 05:54, 12 May 2020 (UTC)

R. Lu clearly trumps La in terms of double periodicity, because it means that the tranches "f¹-f⁷" and "f⁸-f¹⁴" in the lanthanides end logically with an exceptional situation at the f⁷ and f¹⁴ elements that is readily explainable as stabilisation from the half- and fully-filled configurations and is totally analogous to the uncontroversial Mn d⁵ and Zn d¹⁰, unlike the weirdness that happens if you move the tranches one element to the right (La table) that destroys the analogy; [note that this argument depends on knowing beforehand that d¹ is not hanging up, but the previous points show that]

No, Lu does not trump La in terms of double periodicity. The dips move around; you have to choose which properties to focus on. Per Sobolev I choose the most obvious ones, which work well enough for most purposes, without having to go into more detail. Sandbh (talk) 08:25, 9 May 2020 (UTC)

I can easily look at second ionisation energies throughout the table, and from there conclude that the natural place to have the period divide is between each group 1 element and the succeeding group 2 element. And I hope we would agree that this is extremely unnatural. Because even if there is no way to pick a constant oxidation state across the entire table and not be unfair about it, one can look at physical properties and immediately see where the natural period divide is. So, just do that for the 3d and 4f elements to get the most obvious natural tranches. Somehow the dips stop moving around the moment you do that, and fix themselves at Eu and Yb just as they do at Mn and Zn. No fine detail required, the pattern is obvious. Double sharp (talk) 10:26, 9 May 2020 (UTC)

S. Lu clearly trumps La in terms of oxidation state periodicity, because similarly +2 should logically be stabilised at the half-filled and fully-filled subshell; as well, the stability of Lr +3 looks especially nonsensical after the whole trend in the late actinides has been towards stabilising the +2 oxidation state;

The stability of Lr⁺³ doesn't look especially nonsensical after the whole trend in the late actinides has been towards stabilising the +2 oxidation state. Neither do the noble gases look nonsensical coming after the halogens. Sandbh (talk) 08:25, 9 May 2020 (UTC)

@Sandbh: You're focusing on form and not analysing what is supposed to cause the trend. Well, why do the noble gases contrast so much with the halogens? Because the halogens are one step away from a stable configuration and the noble gases are at it, no problem. Well, why do the late actinides prefer the +2 oxidation state? Well, because getting to +3 requires dipping into 5f, which is getting drowned into the core rather quickly. Oh, wait, that makes nonsense out of lawrencium. So perhaps we should learn from the group 17 vs 18 situation and suspect that the reason for the different behaviour is because something different is going on: that is, lawrencium is not using 5f to get to +3, and is really part of the next series, in which 6d and 7s alone are used by Lr through Bh to make +3 through +7 their most favoured oxidation states. Double sharp (talk) 10:16, 9 May 2020 (UTC)

@Double sharp: The preferred oxidation state for the Am-Md, and Lr is +3. Your point was? Sandbh (talk) 08:03, 11 May 2020 (UTC)

@Sandbh: You're missing the point. Comparing Cf to Es to Fm to Md to No, every succeeding actinide has a more stable +2 state than the previous one. Which is easily explained because 5f is more buried for each succeeding actinide and going to +3 requires using the 5f shell. That fails completely passing from No to Lr, which obviously indicates that 5f is no longer being used here. Of course not, the extra electron is coming from 6d and 7p now. Seems exactly like what happens going from Fe to Co to Ni to Cu to Zn: every succeeding 3d metal has a more stable +2 state than the previous one, which is easily explained because 3d is more buried for each succeeding one and going to +3 requires using the 3d shell. That fails completely passing from Zn to Ga, which obviously indicates that 3d is no longer being used here. Of course not, the extra electron is coming from 4p now. It's totally analogous. Just like Ga is the start of the next series, so is Lr.

And of course, since more than one oxidation state can be relevant, we easily see that they can increasingly not be neglected, as depending on the conditions in the water the +2 state may be favoured. That's basic chemistry, just look at a Pourbaix diagram instead of asking for one preferred oxidation state as if there was such a thing valid for all sensible conditions. Fermium is already pretty easily reduced from +3 to +2, already Sm²⁺ will do it for you. Double sharp (talk) 09:06, 11 May 2020 (UTC)

T. Lu clearly trumps La in terms of electron affinity trends, where zero electron affinity happens at the end of every block (which makes sense as then all the reasonable vacancies are filled and an extra electron will not be bound);

Ha, ha! I like the EA argument, noting you and Droog Andrey dismissed its relevance based on one irregularity out > 100 data points. Sandbh (talk) 08:25, 9 May 2020 (UTC)

@Sandbh: Nope. We were dismissing the relevance of orbital radii because of Pd. Wrt electron affinity, our dismissal was based on supposed negative EA values. Which I don't refer to here, calling them zero. Double sharp (talk) 10:16, 9 May 2020 (UTC)

@Double sharp: As you said, “The Pd anomaly is, in fact, exactly why I agree with Droog Andrey that this chart shouldn't be used as it is.” As I said, dismissal on the basis of one anomaly out of > 100 data points. Sandbh (talk) 11:59, 10 May 2020 (UTC)

@Sandbh: Which is what I said above. I considered palladium to be the reason why orbital radii should not be used. Whereas we only criticised EA values based on the fact that negative EA values make no sense. And I'm consistent, so I don't refer to them here. Well, as for your consistency: do you think thorium 5f is more akin to cerium 4f or lanthanum 4f? If it's the former then you're creating a double standard about whether configurations that are chemically relevant but not the ground state should be considered (yes for Th, but apparently no for La and Ac), and if it's the latter you're still creating a double standard about whether those are relevant for block placement (yes for Th, but apparently no for La and Ac again). Double sharp (talk) 12:15, 10 May 2020 (UTC)

U. Lu clearly trumps La in terms of term symbol trends, where a block (for similar reasons as the previous point) always ends with a column of nothing but ¹S₀;

The term symbol argument blows up in its own face considering it's less regular than an La table. Sandbh (talk) 08:25, 9 May 2020 (UTC)

Only because of lawrencium. Which is due to relativistic effects that are really strong here and not for La, thus making it a silly way to decide the problem. Of what possible relevance is this to the La situation, which ought to be resolved by properties of La, and not properties of something forty-six atomic numbers away? XD Double sharp (talk) 10:16, 9 May 2020 (UTC)

V. Lu clearly trumps La in terms of pedagogy, because it will not lead to hands raised at the back of the classroom for the one-off perturbation from Madelung's rule (because it doesn't exist anymore); and it also clearly explains that Madelung's rule is the ideal that elements tend to follow even if the ground state is not quite right; and it also clearly explains that the 4f electrons in La through Yb are valence electrons (otherwise one would suspect them to be all divalent from naïvely reading ground-state configurations, which is false);

No, Lu does not clearly trump La in terms of pedagogy. The issue here is a misunderstanding of what the MR is. In fact the La form more closely follows the MR than the Lu form. Sandbh (talk) 08:25, 9 May 2020 (UTC)

LOL. So what is the MR? Note that the conventional MR as given in textbooks simply follows the n+l pattern perfectly and makes no allowance for any funny business at La. So, here the convention must be wrong, whereas when it comes to Sc-Y-La it must be accepted. XD Double sharp (talk) 10:16, 9 May 2020 (UTC)

@Дрейгорич, R8R, and Droog Andrey: Forgot to summon everyone for this exchange, because it is also hilarious. Double sharp (talk) 02:59, 13 May 2020 (UTC)

Sacre bleu! Quite surprising that you'd say that since Pr-Yb all behave regularly in an Lu table, minus Gd. ― Дрейгорич / Dreigorich Talk 17:39, 13 May 2020 (UTC)

W. Lu clearly trumps La in terms of consistency on secondary periodicities, because while Y-La is also a sound piece of secondary periodicity, it is just as strong as Al-Sc or Mg-Zn;

Eh? Do I need to read past Y-La is also a sound piece of secondary periodicity? Sandbh (talk) 12:20, 9 May 2020 (UTC)

@Sandbh: Yes, you do. It's just as strong as Al-Sc and Mg-Zn, neither of which we want to elevate to primary periodicity as something to put in the periodic table. Doing so for Y-La only will create a double standard. Double sharp (talk) 12:46, 9 May 2020 (UTC)

@Double sharp: Ah, now I see. Within my approach I don't have to worry about it, since each of these dyads cross clearly cross different blocks. Sandbh (talk) 10:23, 11 May 2020 (UTC)

And how's that clear, considering that within the first 108 elements (the ones where we have confirmed electron configurations and not just predictions), the following table

H                                                    He
Li                                 Be B  C  N  O  F  Ne
Na                                 Mg Al Si P  S  Cl Ar
K  Ca Sc   Ti V  Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
Rb Sr Y    Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I  Xe
Cs Ba La * Hf Ta W  Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn

has the same number of DE anomalies as your preferred Sc-Y-La + Be-Mg-Ca one, and that Ca, Sr, and Ba have some d involvement in their chemistry? And that it does a better job at keeping similar elements together, as the general group-1-like character only applies to Ca, Sr, Ba, and Ra in group 2, with Be and Mg being more like post-transition metals? Double sharp (talk) 17:00, 11 May 2020 (UTC)

X. Lu clearly trumps La in terms of consistency on delimiting transition blocks, by using +2 everywhere (ionising s electrons only) as the baseline instead of looking for the chimeras of most common oxidation states (you'll never find them for 4d and 5d, and for 5f both +3 and +4 have a majority);

@Double sharp: There is no need to ionise away the outer s2 electrons. As I understand it, the s shell is only weakly occupied; it contributes only weakly to bonding, as in the other f-elements. The more important consideration is to compare like with like i.e. stable oxidation states. That is simple enough to be taught by textbooks in classrooms and realistic enough to be acceptable by practicing chemists. For the 4d series, +4 is the most common stable oxidation state (5 out of 10); 5d is +4 (6 out of 10); and for 5f, +3 is common to all of them and the most stable for 8 out of 14. Sandbh (talk) 12:17, 9 May 2020 (UTC)

@Sandbh: So, first you ask for "stable oxidation states", and then go ahead for cases where not every element involved has that baseline candidate as a stable oxidation state at all! There's nothing comparable to the status of +3 in the 4f elements. Oh yes, the outer s shell is weakly occupied for the 4f elemnets. Care to imagine why? Because it's already been ionised and the charge of each Ln atom in question is about +2, even when its notional oxidation state is +3. Double sharp (talk) 15:14, 9 May 2020 (UTC)

Y. Lu clearly trumps La in terms of regularity, because it avoids creating a totally unprecedented split block (helium is not an exception, it's still an s block element regardless of where you draw it for chemical reasons);

@Double sharp: As you know, the split d-block has been around for many years, and nobody has cared. Indeed, Hamilton (1965), showed a periodic table extract (groups 1 to 11, plus footnoted Ln and An, showing Ce, Pr…Lu; and Th, Pa…Lw) with a split d block (the gap is between groups 3 and 4) and said that—without any fuss—this is "the periodic table as it is usually presented".

@Sandbh: Not a good argument for its unprecedented nature. We are here to examine it, not simply say "this is how it has been". And evidently many chemists have cared enough to support Sc-Y-Lu. Double sharp (talk) 12:56, 9 May 2020 (UTC)

Not a good argument to revisit it, after maybe two dozen chemists in 60+ years have published mostly one shot arguments supporting Lu. And that would be out of how many millions of articles? Sandbh (talk) 10:30, 11 May 2020 (UTC)

Z. Lu clearly trumps La in terms of authority, because most authorities who actually go out of their way to look at how the periodic table should be (instead of just copying it from somewhere else) display their clear support for it (note that if we were writing this in the 1940s and 1950s, the same could be said of Seaborg's actinide concept; the placement with uranium below tungsten was rock-solid in textbooks, but everyone thinking about the chemistry of those elements was leaning against it).

@Double sharp: Most authorities (still) focus on single issue or unbalanced arguments. One of the oldest of these arguments dates from 1958 or over 60 years ago. In contrast, Seaborg won a Nobel Prize in chemistry for his work in synthesizing actinide elements, within six years.

@Sandbh: LOL. Seaborg won the Nobel Prize for synthesising the actinides, not for clarifying the actinide concept. And he only had a single-issue argument based on predicted oxidation states and symmetry for it (cf. pp. 13–14), and nothing about the chemistry of uranium had changed, which still fit badly in group 3. And you do realise that that was not universally accepted in 1950, either? Just see what Paneth wrote in Nature (doi:10.1038/165748a0). Double sharp (talk) 12:56, 9 May 2020 (UTC)

That's already twenty-three. And all of those based on the idea of chemically active valence subshells, whose relevance to chemistry is obvious by definition, and which are my answer to Scerri's clarion call "for a categorical means of settling the issue" (doi:10.1007/s10698-018-09327-y). Double sharp (talk) 03:29, 7 May 2020 (UTC)

Changed the numbers, as three more points have been added (12, 14, and 17, now). Double sharp (talk) 11:52, 7 May 2020 (UTC)

Changed to letters, as with 26 points it is irresistible. Double sharp (talk) 06:00, 8 May 2020 (UTC)

@Double sharp:. I'm about to start responding to these arguments. My first impression is that you've fallen for the "never mind the quality, feel the width" trap. Compared to your first go, with 17 arguments, your subsequent arguments have weakened your position. Sandbh (talk) 08:01, 9 May 2020 (UTC)

@Sandbh: LOL, they weren't 17 separate arguments. They were just a lesson plan with numbered paragraphs, as anyone can see at User:Double sharp/Idealised electron configurations#Lesson plan where they are preserved. Many of them were not even aimed at refuting Sc-Y-La at all, they were just explaining the theory, including why ground-state electron configurations are usually irrelevant for d and f elements. Only point 16 was aimed at that. And it was written from the perspective of the future when Sc-Y-La had already been abandoned, when such a thing would only be required to address why old periodic tables had this strange breakdown of periodicity in group 3. So, do you actually read what I write? XD Double sharp (talk) 09:55, 9 May 2020 (UTC)

@Double sharp: Pot calling the kettle black! They were presented as statements in support of your position. "That's already twenty-three" you triumphantly proclaim. Nice back-pedalling! Do you ever read what you write? Sandbh (talk) 06:21, 11 May 2020 (UTC)

@Sandbh: You put words into my mouth. Let me quote Archive 42: well, before I gave those 17 points, I said: "My approach avoids lying to children at all. We simply tell them the truth from the start. This is how I'd see a lesson go once we finally manage to dump the historical relic that is the La table". Apart from adding that bolding, I have changed nothing from what I wrote then. It is a lesson plan and it was always a lesson plan. So, that's a clearly false assertion from you.

So why don't you productively give a criterion that could possibly falsify your theory as I have? Double sharp (talk) 06:33, 11 May 2020 (UTC)

Appendix (for point Q): structures of the transition metals (predictions for 6d).

Sc	Ti	V	Cr	Mn	Fe	Co	Ni	Cu	Zn
hcp	hcp	bcc	bcc	~bcc	bcc	hcp	fcc	fcc	~hcp
Y	Zr	Nb	Mo	Tc	Ru	Rh	Pd	Ag	Cd
hcp	hcp	bcc	bcc	hcp	hcp	fcc	fcc	fcc	~hcp
Lu	Hf	Ta	W	Re	Os	Ir	Pt	Au	Hg
hcp	hcp	bcc	bcc	hcp	hcp	fcc	fcc	fcc	~hcp
Lr	Rf	Db	Sg	Bh	Hs	Mt	Ds	Rg	Cn
hcp	hcp	bcc	bcc	hcp	hcp	fcc	bcc	bcc	bcc

(Tildes mean distortion from the ideal structure, for Mn and group 12, for which the stable configurations seem to be a reason.) Whereas La dhcp, Ac fcc. Way to go "destroy[ing] a beautiful piece of the harmony of the physics of transition metals whose structure varies regularly with valence, unless they are magnetic" or have strong relativistic effects involved (*), to quote Wittig. Well, obviously Ce and Th don't fit the group 4 trend because of f involvement. Seems very likely that the same is the culprit for La and Ac breaking the group 3 trend. Double sharp (talk) 05:56, 8 May 2020 (UTC)

(*) Special relativity is responsible for the anomalies near the end of the 6d row. Without relativity, darmstadtium would be fcc like platinum. For group 11, Cu, Ag, and Au have small energy differences between the bcc and fcc structure; no doubt relativity helps things along. Copernicium is extremely relativistic and quite noble-gas-like(!!). Double sharp (talk) 04:48, 9 May 2020 (UTC)

Now for one that was missed, until Sandbh(!) raised it below and I corrected it up to later knowledge. I have taken the liberty of using thorn as the 27th letter of the alphabet:

Þ. Lu clearly trumps La in terms of understanding intermetallic compounds of these elements. The first 3d metal that Sc, Y, Lu form an alloy with is Mn. But for La it is Co. Double sharp (talk) 04:58, 11 May 2020 (UTC)

Actinium 5f smoking gun

Actinium 5f smoking gun: (doi:10.1016/0038-1098(81)90572-X) "The present work is a preliminary investigation determining the effect of correlation on the electron energy bands and also it is the first exact calculation for the bandstructure of actinium. Our calculation leads to the following conclusions. The 5f states are more sensitive to the starting potential. The 5f states are itinerant in the Ac metal and their placement in the bandstructure is very important. Because of the importance of the 5f states, the exchange and correlation also become important. If one does not include correlation along with exchange the 5f states may not be placed properly. This shows the importance of the inclusion of correlation term in dealing with 5f states in Ac. One can argue that the 5f states could have been placed properly by adjusting the value of the parameter α, as Koelling and Freeman have done for Th [2]. But compared to this, ours is a more realistic one and no adjustable parameter is employed. In the case of Th the inclusion of correlation definitely has led to a better agreement with experiments [3]. We expect the same thing to happen in the case of actinium also. One cannot say anything more than this regarding the effect of correlation on the bandstructure of actinium at present. Work regarding the density of states, Fermi surface cross-section and determination of other electronic properties is in progress."

(doi:10.1103/PhysRevB.30.6943) "From the band structure and density of states histograms, one can see that the f levels are well above the Fermi level. The picture which has emerged for the band structure of this lighter actinide [actinium] is that of a typical high Z transition metal with itinerant 5f states superposed and strongly hybridized with the 6d7s bands." (I suppose here "transition metal" means the 6d7s bands, now with a 5f band stuck on top of it.)

So, if thorium gets into the f-block because it has itinerant 5f states, which is something that Sandbh recognises (doi:10.1103/PhysRevLett.75.280) – consistency demands the same for actinium.

They also note that Ac has a band structure analogous to La and Pr. ;) Double sharp (talk) 04:01, 7 May 2020 (UTC)

@Double sharp:A careful reading of these papers shows that the first was a preliminary investigation. The second paper, three years later, by two of the same authors, says:

"At normal pressure the band structure is similar to the band structure of Th. The unoccupied 5f states never presented a problem in the present case. For Th, 5f states got mixed up with the d band…Here in the present calculation…the unoccupied 5f states never interfered with the regular s and d bands. As the volume [pressure] decreases, the entire band structure is slowly shifted up. (Some of the bands are incompletely drawn due to nonconvergence in the high energy range for some of the k points. Since these points are well above the Fermi level, convergence is not tried by increasing the number of RAPW's. ) This trend is similar to the high-pressure band structures of lanthanum (La) and praseodymium (Pr).

The band structure at V/Vo –0.5 is entirely different from the band structures at V/Vo –1.0 to 0.6. At…high energies…The 5f states are seen to hybridize with the 6d and the 7s like bands. The overall band structure [i.e. at high pressure] is that of a transition metal but with f bands which overlap and hybridize to give a more complex structure.

The change in the conduction bandwidth at I' may be again due to the strong hybridization of band structure with increase of pressure.

From the histogram, it is seen that the Fermi levels lie near the peak arising from d-like states in band 2 for V/Vo —1.0 to 0.6 [Figs. 4(a) to 4(c)]. But this trend is changed for V/Vo —0.5 [Fig. 4(d)]. It is also seen that the huge peaks arising out of f bands are well beyond E_F.

From the band structure and density of states histograms, one can see that the f levels are well above the Fermi level.

The width of the unoccupied (itinerant) f level increases with increase of pressure. But at E_F the effects of the 5f bands are small."

Here's where the f levels lie, compared to 1st ionization, in % terms, + the level at which the transition occurs.

La    Ce^   Pr
33%   0%    0%
1.88  --    --
Ac    Th^   Pa
72%   15%   0%
3.72  0.96  --

I'm not seeing any significant scope for Ac 5f involvement in ambient conditions. Sandbh (talk) 11:43, 7 May 2020 (UTC)

Notice what you don't underline: "At normal pressure [my bold] the band structure [of Ac] is similar to the band structure of Th." Which has 5f hybridising with the 6d and 7s bands, exactly like I said. Not to mention that even what you quote says that 5f in Ac is itinerant. Indeed, at high pressure f involvement increases. Now, just look at Lu, with no 4f involvement at all even at 202 GPa (doi:10.1016/B978-0-444-59536-2.00004-0), and tell me how much f involvement it must be having at ambient conditions. ;) Double sharp (talk) 12:23, 7 May 2020 (UTC)

And let me quote Wittig about what the Fermi level means here for thorium: "The presence of a hybridizing 5f band above the Fermi surface in thorium has been at the same time theoretically postulated [D.D. Koelling, A.J. Freeman and B.W. Veal, Bull. Am. Phys. Soc. 18,423 (1973)]. In our simplified multiband picture presented here (with separate s, d and f bands) the 5f band is, however, believed to overlap the Fermi surface. Both descriptions have the same physical meaning: the conduction electron distribution on each particular thorium cell is visualized to have a share of pronounced 5f character." And the same would be true of actinium with its 5f orbitals above the Fermi level readily hybridising with the 6d and 7s bands. Double sharp (talk) 13:49, 7 May 2020 (UTC)

Another actinium 5f smoking gun: https://escholarship.org/content/qt4tc1b0xz/qt4tc1b0xz.pdf with ligand-to-metal donation of what seems to be about 0.3 of a 5f electron to Ac in Ac(HOPO). Also note the 0.34 of a 4f electron on La in LaF₃ (doi:10.1039/C3CP50717C). ;) Double sharp (talk) 12:41, 7 May 2020 (UTC)

Lutetium nitride

@Double sharp: What's your interpretation of this(?):

"The GGA and EV-GGA approach has been used to compute the electronic structure in B1 phase at the equilibrium lattice constant which are presented in figure 3 and at high pressure B2 phase in figure 4 respectively. It can be seen from Figure 3 that there is no band gap at the Fermi level. Top of the valence band is matched to zero of the Fermi level (EF). It is observed that top three bands in valence band region are from N p orbitals lying up to -3.28 eV while all fourteen completely occupied Lu 4f energy bands hybridized with N p, s bands."

B1 = the normal NaCl phase; B2 = CsCl phase, at around 250.81 GPa with a volume collapse of 3.75%.

Here. Sandbh (talk) 12:05, 7 May 2020 (UTC)

@Sandbh: See doi:10.1088/2053-1591/ab31c2 (2019 vs your 2015). The band structure of LuN matches ScN and YN; LaN has a different structure with 4f in the conduction region (which makes a nice smoking gun for La 4f involvement, too). Lu 4f is well below the valence band maximum of LuN, which is formed mainly by the N 2p states. Just look at figure 3. Double sharp (talk) 12:28, 7 May 2020 (UTC)

@Sandbh: That kind of hybridization does not mean chemical bonding. See GaN for example. Droog Andrey (talk) 12:42, 7 May 2020 (UTC)

“

In addition, N2s-N2p-Ga4s and N2s-N2p-Ga3d hybridization regions occur at the bottom of the valence band

”

— doi:10.1103/PhysRevB.81.085125

@Double sharp and Droog Andrey: Thank you both.

The LuN figure 3's in each paper are effectively the same. I understand Lu 4f is well below the valence band maximum, yet still within the valence band.

I understood this kind of hybridization does not mean chemical bonding. What does it mean then to say, "all fourteen completely occupied Lu 4f energy bands hybridized with N p, s bands"? I had understood that the 4f electrons in Lu were too core-like to be involved in hybridization; i.e. below the bottom of the valence band. Is that not so?

On the related GaN article, here are some relevant extracts (my numbering and underlines):

[1] "The top of the valence band in GaN is dominated by N 2p states whereas the Ga 4s states are much weaker and located at somewhat lower energy."

[2] "Contrary to the case of the wide band-gap nitride AlN, where the populated Al 3d states…are located at the very top of the valence band, the Ga 3d states in GaN are located at the bottom of the valence band and therefore the N 2p-Ga 3d interaction plays a different role than in AlN."

[3] "However, the electronic structure and chemical bonding of N with Ga is still largely unknown in GaN. This includes, in particular, the Ga 4p states at the top of the valence band, the N 2s hybridization with the Ga 4s states at the bottom of the valence band, and the potentially important role of the shallow Ga 3d semicore states."

[4] "In this paper, we investigate in detail the bulk electronic structure and the influence of hybridization and chemical bonding between the N and Ga atoms of w-GaN in comparison to pure Ga."

[5] "The experimental results are compared to electronic band-structure calculations based on the generalized gradient approximation method of Wu and Cohen, WC-GGA including the optimized Coulomb interaction U which here accounts for the strong electronic interactions of the narrow Ga 3d band with localized electrons."

[6] "Moreover, the role of the N 2p-Ga 3d coupling for the magnitude of the band gap is discussed in comparison to other wide band-gap nitrides such as AlN."

[7] "We distinguished several hybridization regions giving rise to the N 2p-Ga 4p and N 2p-Ga 4s bonding at −1.0 to −2.0 eV and −5.5 to −6.5 eV below the top of the valence band, respectively. In addition, N 2s-N 2p-Ga 4s and N 2s-N 2p-Ga 3d hybridization regions are found at the bottom of the valence band between −13 and −15 eV and between −17 and −18 eV, respectively. The N 2s-N 2p-Ga 4s and N 2s-N 2p-Ga 3d hybridization and covalent bonding are both deeper in energy from the top of the valence band than the N 2p-Ga 4p and N 2p-Ga 4s hybridization regions indicating relatively strong bonding although the intensities are lower."

[8] "As in the case of Ge, the shallow Ga 3d semicore level at −17.5 eV interacts with the 4sp valence band and withdraws charge density that opens the band gap.

Item:
2 appears to suggest d involvement in AlN
5 notes strong electronic interactions of the narrow Ga 3d band with localized electrons
6 refers to N 2p-Ga 3d coupling.

Double sharp, how do you reconcile these items with your table showing Al and Ga limited to sp interactions? And for Zn, I understood you show it as being dsp on the basis of some hybridization of its filled 3d subshell. How is this different from the 4f hybridization occurring in LuN? Sandbh (talk) 02:23, 8 May 2020 (UTC)

@Sandbh: I don't have to reconcile it. As Droog Andrey already mentioned, this use of the word "hybridisation" does not imply actual chemical bonding. You can just look at the spatial extent of the orbitals involved and note that any significant overlap is massively unlikely. I show zinc as being dsp because 3d has some contribution to the explicitly bonding orbitals in compounds like ZnF₂ (just read the paper, doi:10.1021/ic50177a056), which you can also see from the spatial extents of the orbitals involved. And you can look at it for LuF₃, say, and note that 4f in Lu is significantly smaller than 3d in Zn whereas the bond length is longer, and so it has no hope of being used. (Orbital radii: Zn 3d 30.4 pm, Lu 4f 24.6 pm. Bond lengths: ZnF₂ 173 pm, LuF₃ 198 pm from doi:10.1039/c3cp50717c.) Double sharp (talk) 03:08, 8 May 2020 (UTC)

@Sandbh: Why do you compare 3d in AlN and 3d in GaN? That's outer subshell in the former but core subshell in the latter. Droog Andrey (talk) 10:13, 8 May 2020 (UTC)

@Droog Andrey and Double sharp: I had understood the 4f electrons in Lu were too core-like to be involved in hybridization i.e., below the bottom of the valence band. For LuN that is not the case; the 4f sub-shell lies within the valence band. Re AlN and GaN I see the same thing applies there, for 3d, hence my question. Q1. Does this count as 3d involvement in Al (especially) or Ga? A 2. In the case of 3d in GaN why do you refer to this as "core" sub-shell if it lies inside the valence band? Sandbh (talk) 11:05, 8 May 2020 (UTC)

@Sandbh: 4f in Lu is too core-like to be involved in chemical bonding, not in hybridization. Being within the valence band does not make the subshell chemically active, and that's what the example of GaN shows. The comparison of 3d in AlN and GaN has no sense; you may compare 3d in AlN to 4d in GaN, but that has nothing to do with core/valence question. Droog Andrey (talk) 11:34, 8 May 2020 (UTC)

@Droog Andrey and Double sharp: As the article you linked to said, “The populated Al 3d states…are located at the very top of the valence band.” Does this count as 3d involvement? Sandbh (talk) 11:58, 8 May 2020 (UTC)

@Sandbh: No, because there is no 3d involvement to the bonding. The bonding in AlN is only from N 2s and 2p and Al 3s and 3p, as expected. And the paper carefully contrasts hybridisation and bonding. Double sharp (talk) 12:34, 8 May 2020 (UTC)

Some wonderful quotes supporting Sc-Y-Lu

That article I linked (doi:10.1039/c3cp50717c) has some wonderful quotes supporting Sc-Y-Lu, which I will share below with my bolding at the risk of being accused of word-count bombardment:

“

The trends are very similar, with a nearly linear lanthanoid contraction of 14 pm from La to Lu (same as Neese²²), comparing well with the ‘recommended’ values for the fluorides of 13 or 14 pm. ...

SOC in the Ln(4f) shell might play some role for the geometries. The 4f orbital level splits into j = 5/2 and 7/2 spinor levels with capacities for 6 and 8 electrons. The first 6 f-electrons (La to Eu) predominantly occupy the slightly more contracted j = 5/2 spinors. Therefore, one may expect a more pronounced lanthanoid contraction from La to Eu, and then a reduced one from Eu (k = 6) to Lu. ...

The highest bond energies are obtained for the spherical f⁰, f⁷ and f¹⁴ Ln³⁺ ions of La, Gd and Lu. The bond energies decrease, on average, with increasing number of f-electrons from k = 0 to 6 and from k = 7 to 13, i.e. from La to Eu by about 1.4 eV per step, and from Gd to Yb by about 1.5 eV. A quadratic fit in k⁷⁴ would be better, though statistically insignificant. The somewhat ‘irregular’ variation, in particular in the 2nd half-period, is due to the diﬀerent variations of correlation and SOC energies in the free Ln⁰ atoms and in the formal Ln³⁺ cations in the fluorides.

”

Just look at those beautiful values showing sensible double periodicity only with La-Eu and Gd-Yb tranches (taken from the paper):

	La	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb	Lu
LnF₃ homolytic atomisation energy	22.37	22.26	21.05	20.02	19.11	18.82	17.38	21.20	20.33	19.47	18.78	18.03	17.40	16.74	21.25
Ln–F bond energy	6.67	6.59	6.39	6.23	(6.0)	(5.7)	5.39	6.50	(6.5)	6.12	6.15	6.21	5.82	(5.5)	(6.4)

“

It had been noted by various authors^5,25,75 that the heterolytic dissociation energies for LnF₃ → Ln³⁺ + 3 F⁻ vary much more smoothly. This is so because both Ln atoms, the free LnF₃ ions as well as in the trifluorides, have the same dominant 4f^k configurations with similar electron correlation and SOC. However, most free neutral Ln atoms have a 4f^k+16s² configuration, while La⁰, Ce⁰, Gd⁰ and Lu⁰ have 4f^k5d¹6s², and among them, the Ce⁰ ground state is strongly ¹G₀–³H₀ mixed.⁷⁶ Accordingly, the homolytic bond energies comprise contributions from diﬀerent orbit–orbit and spin–orbit couplings, i.e. from complicated differential configuration mixings in LnF₃ and Ln.

”

As we can see, you can't get anything useful done without at least understanding that many configurations are involved. Of course, the philosophy of the Lu table handles this completely: exact occupancies don't matter, what matters is total occupancy of the chemical active subshells. So much simpler, since you get to write lazy configurations like La = [Xe] (4f5d6s6p)³ instead of memorising all the useless Madelung exceptions. ;)

“

The chemically active valence shells of the LnF₃ molecules contain 3·3=9 occupied F⁻(2p) type MOs and the Ln³⁺(4f,5d,6s) shells. The latter contain k electrons in the inner valence f-shell, while the 5d, the 6s and possibly also the unoccupied 4f AOs stabilize the dative s and p pairs from the three F⁻ ligands.

”

Guess what, in figure 5 they plot MO levels of Ln 4f and F 2p. Guess for which element Ln 4f suddenly takes a plunge to under F 2p instead of above or matching it. No prizes for guessing lutetium. ;)

“

For the early lanthanoids, the Ln(4f) orbitals give rise to a higher and rather narrow band, being only split a little due to electrostatic perturbations and weak orbital overlap interactions. The band width does not change from La to Lu, indicating little change of these interactions. However, in the later half of the lanthanoid series from Gd to Yb, the Ln(4f) type orbital has decreased in energy so much upon increase of the nuclear Ln charges that they become near-degenerate with the F(2p) and even the F(2s) bands. At the end of the Ln series, at Lu, the two bands begin to separate again, the Ln(4f¹⁴) shell becoming a closed core shell below the F valence band for the subsequent transition metals.

”

And indeed, in table 3 they plot effective orbital and total atomic charges. LaF₃ already has 0.34 of a 4f electron on La. And Ir has somehow more 4f involvement than Ho through Lu, though these are all pretty tiny anyway. And La has the biggest 4f–2p bond order of all the Ln (0.057), nearly matched by Ce (0.055), exactly corroborating what I say about how pre-collapse elements like La and Ce or the early An are likely to show the biggest direct (rather than indirect) involvements of the f subshell. ;)

“

The effective atomic charges are rather constant throughout the series, F ~ −0.6 and Ln ~ +1.8 (Table 3). This is consistent with an ionic picture Ln³⁺ F⁻₃. The Mayer bond orders indicate constant dative F⁻(2p) bonding into the Ln(5d) shell, and also a little bonding into the Ln(4f) shell at the beginning of the lanthanoid series.

”

Wow, they said it again!

Not only that, but this corroborates what DA said: in a real chemical environment, the atomic charge of notional Ln³⁺ is more like Ln²⁺. So, orbitals filled due to ligand-metal charge transfer should count fully as occupied chemically. But of course, that means there is no problem at all with accepting La 4f and Ac 5f anymore.

“

The question then arises whether the energy degeneracy will only cause Ln(4f) AO mixing into the canonical MOs, or whether it will also contribute to some additional energetic effect of the bonding or anti-bonding type. These two different issues must be distinguished.

”

And there you have an explanation of the difference between just energy degeneracy and whether the orbital is actually bonding or not. ;)

“

From La to Eu, the spin on Ln is k + δ, δ increasing from 0 to 0.11; from Gd to Yb it is 14 − (k + δ), δ increasing from 0.06 to 0.18. The surplus δ over the integer value is compensated by spin-polarization of δ/3 of each F(2p) shell, a common phenomenon called spin-borrowing.

”

Yet another demonstration of how double periodicity is so much better with the f-block starting at La.

“

The Ln(5d) orbitals are populated by nearly 1 electron with maxima for La (0.90), Gd (0.97) and Lu (0.88) and minima just before at Eu (0.86) and Yb (0.80).

”

And again!

“

The small spin polarization of the Ln(5d) shell by an amount of about 1% of the spin of the Ln(4f) shell indicates Ln(4f) polarization by a little Ln(d) admixture. If there should be some Ln(4f) bond contribution, it should decrease along the series from La to Lu since the Ln(4f)–F(2p) overlaps S decrease significantly (namely, for LaF₃ at R_La–F = 211.7 pm: S_σ = 0.105; for GdF₃ at R_Gd–F = 204.1 pm: S_σ = 0.028; and for LuF₃ at R_La–F = 197.7 pm: S_σ = 0.005 only). The small additional f-populations above k describe the central atom’s core and valence shell polarizations. The Mayer bond orders indicate a rather constant Ln(5d)–F(2p) covalent contribution of about 0.15 and a smaller Ln(4f)– F(2p) contribution that decreases from La (0.06) to Lu (0.03). All other overlap populations are smaller.

From gadolinium onwards till ytterbium, there occurs severe Ln(4f)–F(2p) orbital mixing (see Fig. 5 and 6). ... The significant Ln(4f)–F(2p) mixing at the canonical MO level for the later lanthanoid fluorides does not imply observable Ln(f)–ligand(p) covalency eﬀects.

”

Till ytterbium. Not lutetium. Even for this mixing without covalent bonding. In fact as usual the ones with the most 4f involvement in the bonding despite the contraction are La and Ce because they partially precede it. ;)

There are other interesting things here, including some core holes due to the decreased nobility of [Xe] compared to the lighter noble gases, also maximised at La. ;)

“

EuF₃ and YbF₃ show heterolytic decomposition energies which are higher by 1.4 eV per Ln–F bond than their neighbors. In contrast, their homolytic decomposition energies are the smallest among all LnF₃. The spin-averaged orbital energies of the 5d acceptor-orbitals of the Ln³⁺ ground states (~19.3 + 0.08k eV, ±0.2 eV) and other Ln³⁺ bonding parameters do not exhibit any particularity for Eu³⁺ and Yb³⁺, except that the 3rd ionization potential, which is the electron affinity of Ln³⁺, increases from La (19.2 eV) to Eu (24.9 eV), from Gd (20.6 eV) to Yb (25.1 eV), and again from Lu (21.0 eV) onwards. One might argue that the resonance stabilization of F⁻Ln³⁺F⁻₂ ↔ F⁰Ln²⁺F⁻₂ also increases from La to Eu and from Gd to Yb.

”

So, DA's 3rd IE argument is totally corroborated by the experts. And at the end, as a last farewell by this article, we see an example of the charge-transfer 4fⁿ ↔ 4fⁿ⁺¹ motif that permeates 4f chemistry. Not only does it show double periodicity only with the Lu table, it also doesn't make sense for the La table because then you're not comparing like with like anymore as 4f plays no role at Lu. Lutetium fits completely naturally only with hafnium through mercury. ^_^ Double sharp (talk) 03:48, 8 May 2020 (UTC)

Rare earth alloys

Here's a nice extract from Gschneidner, speaking on the insignificance of 4f bonding involvement in rare-earth metals:

"Although 4f involvement in the bonding probably occurs in all systems, its contribution to the total bonding is generally quite small and is over-shadowed by the other contributions (electronic, space filling, lattice, etc.). But in ~10% of the compound series examined it appears that the 4f bonding is one of the important parameters in governing the crystal structure eg RAl₃, RRu₂, RAs₂, because the other contributions balance out each other.

Gschneidner KA 1980, "Phase relationships in rare earth metal alloy systems", in EC Subbarao & WE Wallace (eds), The science and technology of rare earth materials, Academic Press, pp. 51-75 (68)

--- Sandbh (talk) 07:28, 10 May 2020 (UTC)

So by that logic, I suppose there are no 4f elements at all. Nope: consistently, there is 4f bonding, even if it is usually not the most major direct effect. Except for Lu, where there never is any. And I see from Gschneidner and Wittig that lanthanum is behaving exactly like the early lanthanides Ce, Pr, and Nd with their irrefutable f involvements. Double sharp (talk) 07:32, 10 May 2020 (UTC)

@Double sharp: As you know, there certainly are 4f metals. The question is what degree of relevance do you assign to 4f bonding? As you know, we can apply the pragmatic and effective 90% rule:

"It works this way: if something is true about 90% of the time or more, state the generalization as true and indicate that there are exceptions that will be dealt with later (perhaps even in another course); further indicate that even though the textbook may deal with these exceptions, you will not test students on them." doi:10.1021/ed800164k

"It will be appreciated that simplicity has been achieved…at some expense in accuracy. It is not possible, in a single account, to present all its modifications and limitations; several descriptions, from different angles, are necessary fully to appreciate the structure of the Periodic Table…" doi:10.1016/0001-6160(79)90104-4

Or, as you know, we can have the tail wag the dog, so to speak: "A minor or secondary part of something controlling or dominating the whole or the main part." Sandbh (talk) 08:15, 10 May 2020 (UTC)

@Sandbh:. LOL. Of course, if you do that, since direct 4f valency is rarely the major factor, you still end up with no 4f metals. I prefer to note something that happens to be true 100% of the time, is simple, and dominates everything about the chemistry of La-Yb starting from why they like the +3 state in the first place: La-Yb have 4f bonding contributions, whether direct (like this) or indirect (charge transfer from 4f to 5d), whereas Lu never does. It is indeed true that direct valency of 4f is rare, but indirect valency is ubiquitous in the series La-Yb and controls every part of their chemistry and physics. And that's obviously simpler, because I simply ignore the distinction between direct and indirect valency. Any form of valency is fair game. If you want to give the students a little bit more, just tell them that deeply buried subshells like f and g tend to be indirectly valent except at the beginning of the series where they haven't finished collapsing. Of course, that's still not enough to give Lu any 4f valency at all. Double sharp (talk) 09:30, 10 May 2020 (UTC)

@Double sharp: Remind me again why the 0 4f electrons in La explain why it prefers the +3 os? And, obviously, we do have 4f metals as can be discerned by e.g. the configurations of the trivalent cations. As your luminary Wulfsberg says, focus on the configurations of the ions. Sandbh (talk) 11:34, 10 May 2020 (UTC)

@Sandbh: Because lanthanum doesn't have zero 4f electrons. In chemical environments it can have more than that. The important thing is the interplay between 4fⁿ and 4fⁿ⁻¹ states across the lanthanides. That's wholly general and simple based on uniform close-to-ground-state Madelung-following configurations, Johnson explained that perfectly well already. And it helps you do what you should really be doing to predict oxidation states: find the lattice energies of the compounds that will result. The fact that in the ground state La happens to favour the minority one is no big deal, the important thing is that every lanthanide changes between them. Then there's no reason to wonder why most lanthanides, which don't have that 5d electron outside, don't become divalent instead.

Just because the cations have the electrons does not mean they are the ones being used. Lu³⁺ is [Xe]4f¹⁴, sure. It never goes beyond that and digs into the 4f shell. That's exactly like Hf⁴⁺ with the same configuration, which is obviously not a 4f metal. To be a 4f metal you have to use your 4f electrons. And you can find that involvement in the metal itself, or in how the subshell is used in compounds. Oh, and Cs⁺ and Ba²⁺ are both [Xe], no 6s electrons at all. That doesn't mean there are no 6s metals. Yes, Wulfsberg has said something here that isn't right, so be it. Just because I think he's right in some cases doesn't mean I think he's right in all cases. Double sharp (talk) 12:00, 10 May 2020 (UTC)

Pending. Sandbh (talk) 11:32, 11 May 2020 (UTC)

@Double sharp: Stone (1979) doi:10.1016/0001-6160(79)90104-4 discusses alloy systematics in the periodic table.

On group 3 and the REM he writes that they behave similarly to one another in alloys with d-metals, and that Mn is the first element with which they usually form a compound. However, going down group 3, Y doesn’t form a compound until Fe is reached; La not until Co; and Ce behaves the same as Y.

+-----+
|Sc:Mn|
+-----+
|Y:Fe |
+-----+-----+-----+
|La:Co|Ce:Fe|Pr:Mn|
+-----+-----+-----+

The Y-La-Ce corner triad then appear to be a bit stand-offish compare to their REM brethren. It's an interesting pattern.

Stone offers no further explanation. Sandbh (talk) 04:43, 11 May 2020 (UTC)

Just ask the Miedema Calculator. Just select "enthalpy of mixing", put Sc/Y/La/Lu as your first element, and then march through the first transition series for the second element. Notice how the curve switches direction at Mn for Sc, Y, and Lu, but only at Co for La. Then start wondering how this possibly can be turned into a La-supporting argument. And maybe look at the Y-Mn system (doi:10.1007/BF02645974, dating from 1991) and see that there actually are indeed such compounds. XD Double sharp (talk) 04:52, 11 May 2020 (UTC)

Here is reality:

        +-----+
        |Sc:Mn|
        +-----+
        |Y:Mn |
+-----+ +-----+
|La:Co| |Lu:Mn|
+-----+ +-----+

Double sharp (talk) 07:40, 11 May 2020 (UTC)

Pending. Sandbh (talk) 11:24, 11 May 2020 (UTC)

d-involvement in NG halides

From here (p. 2701):

"…the calculations reported here suggest that the d orbitals are involved to a degree which is chemically significant"

@Double sharp: Will you need to add "d" to group 18 of your table?

@Sandbh: LOL. The source is from 1969(!). d-orbital explanations of hypervalence have since been debunked, which oddly enough has never stopped them from persisting in textbooks as errors. Exactly analogous to Sc-Y-La. Double sharp (talk) 07:45, 10 May 2020 (UTC)

Pending. Sandbh (talk) 11:21, 11 May 2020 (UTC)

@Double sharp: Our article on hypervalence nevertheless refers to later studies referring to minor but significant d involvement in e.g. XeF₂. What’s the status of these studies? Sandbh (talk) 11:00, 10 May 2020 (UTC)

@Sandbh: The study being cited is actually not that enthusiastic about expanded octet explanations for hypervalence, despite what the article makes it look like. Here's a quote (doi:10.1038/nchem.1619):

“

The XeF₂ molecule, a classical prototype of hypervalent compounds, has been studied by using a VB-QMC method to gain detailed insight into the root causes for its amazing stability relative to its separate atoms. One side result of this study is a quantitative measure of the contribution of the old expanded octet model, which was thought long ago to explain hypervalency through sp³d hybridization. It is shown that the VB structures corresponding to this model account for 11.2% of the wavefunction, and bring a stabilization energy of only 7.2 kcal mol⁻¹, much less than the total bonding energy. These results demonstrate, in a more quantitative way than has been done before, the deﬁnite superiority of the Rundle–Pimentel model over the expanded octet proposal.

”

— https://hal.archives-ouvertes.fr/hal-01627883/file/BraHib%20Hypervalence%20NChem%202013_sans%20marque.pdf

The study also notes that a more useful explanation for XeF₂ is Rundle–Pimentel/charge-shift, no d orbitals on xenon required. So I see no need to change my table. Double sharp (talk) 12:14, 10 May 2020 (UTC)

@Double sharp: There is some more to that article:

"However, it has been shown by many researchers that, even if d orbitals are necessary to provide quantitative bond energies in hypervalent species, these orbitals have occupancies of only 0.3 electrons at most, and therefore do not act primarily as valence orbitals but instead as polarization functions or as acceptor orbitals for back-donation from the ligands. Accordingly, the energetic contributions of sp³d hybridization to hypervalent bonding are expected to be small (amazingly, to our knowledge, such quantities have never been estimated, even approximately)."

Here, the authors distinguish between orbitals that do not act primarily as (a) valance orbitals but instead act as (b) polarization functions or as acceptor orbitals for back-donation from the ligands. Whereas, as I understand it, you do count (b) orbitals, as (a) orbitals. Is that right?

As you note, the article says the VB structures corresponding to this model ("the sp³ d expanded octet model") account for 11.2% of the wavefunction, and bring a stabilization energy of only 7.2 kcal/mol, much less than the total bonding energy (64 kcal/mol). So there is some d contribution. Why do you exclude this from your table? Sandbh (talk) 13:03, 10 May 2020 (UTC)

a_2u orbital in La(CO)₈⁻. Analogous orbitals in the Y and Lu complexes have no overlap and no bonding.

@Sandbh: Wrong. I do not count (b) orbitals. 4f in lanthanum is a valence orbital of the (a) sort: they are not just polarisation functions needed, there is actual occupancy and overlap with the ligands that causes real bonding (just see Droog Andrey's pictures for a graphic demonstration). The sort of orbitals I also consider are (c) orbitals that act as reservoirs of valence electrons, even if they prevail in non-bonding MOs, like 4f in Yb. Well, as Droog Andrey wrote in Archive 33:

“

@Double sharp: you've just catched a beautiful idea: 4f-electrons is more of a reserves area, so they are indirectly valent (prevail in non-bonding MOs), while 5d6s (and sometimes 6p) are directly valent (prevail in bonding MOs), but both are significant for chemistry because of electron correlation between the subshells. Such a situation is observed mostly from La to Yb, so that's another fruit in my bin :P

”

— Droog Andrey

Of course, for La 4f not even this apology is required. It's a full-fledged member of the totally legitimate valence orbitals club of the same order as 5d6s6p there. Lanthanum is undeniably an f metal, with a level of direct involvement of the 4f orbitals only matched by cerium.

As can be seen, the stabilisation energy given from d occupation is utterly negligible. Of course I should exclude it. XeF₂ is a standard example, you can easily Google many sites where MO theory is applied to it, with absolutely zero need to invoke 5d involvement. As can be seen from reading the paper, the major contributor that makes XeF₂ stable is charge shift: you get 82.9 kcal mol⁻¹ just from resonance energy (F·–⋅Xe⁺F⁻ ↔ F⁻Xe⁺⋅–⋅F, coming from the charge-shift character of the Xe⁺–F⁻ bond), and another 44.3 kcal mol⁻¹ from the diionic structure F⁻Xe²⁺F⁻. The minuscule stabilisation energy sp³d hybridisation structures give when added cannot even hold a candle to these huge figures and strongly indicate what the major effect here is: one that requires no octet-expansion.

And of course, this theory suggests that at issue is the 2nd ionisation energy, therefore perfectly explaining why KrF₂ is more unstable than XeF₂, and why NeF₂ and ArF₂ are not known. So much simpler, saying "octet rule all the time in the main-group elements" and pointing to partial ionic character of the electron-poor bonds involved, rather than trying to invoke high-energy d orbitals. Of course: the first excited state of Xe with a 5d electron is [Cd]5p⁵5d¹ at 9.890 eV. Way to go suggesting 5d involvement in Xe, and yet strenuously trying to deny 4f involvement in La with the [Xe]4f¹6s² state at just 1.884 eV. XD Double sharp (talk) 13:10, 10 May 2020 (UTC)

@Double sharp: As you note, the later article says the VB structures corresponding to this model ("the sp³ d expanded octet model") account for 11.2% of the wavefunction, and bring a stabilization energy of only 7.2 kcal/mol, much less than the total bonding energy (64 kcal/mol). So there is some d contribution.

1. Why do you refer to this as "utterly negligible"?

2. The same article does not treat (b) ligand acceptor orbitals as (a) valence orbitals. Why do you treat (b) ligand acceptor f orbitals as f valence orbitals? Sandbh (talk) 11:21, 11 May 2020 (UTC)

1. Just read my previous comment carefully, paying especial attention to the numbers. 2. I do that because they can additionally contribute to the bonding, as confirmed by cubic complexes of La whose shape is unexplainable without 4f involvement. And for LaF₃ above. Double sharp (talk) 12:23, 11 May 2020 (UTC)

Is Th a double standard

There are 42 references to a double standard on this page, most of them made by Double sharp, and most of them to do with counting Th as a 5f metal, but not counting La as a 4f metal.

So here's what I've said about this.

On Th, this is only a question of degree, and bang-for-buck. Ce and Th are the first metals where we see a significant impact of f involvement. We don't see anything on that scale in La and Ac.

I also addressed this as follows:

This is from Johansson and Skriver 1997, in DF McMorrow et al. (eds), Magnetism in metals: A symposium in memory of Allan Mackintosh, Copenhagen, 26-29 August 1996 : Invited review papers, Kgl. Danske Videnskabernes Selskab, Copenhagen:

"This firmly establishes that there is a profound change in the behaviour of the 5f electrons when proceeding from Pu to the next element Am."

"Another point to notice is that the atomic volume for cerium in the α-phase deviates considerably from the general behaviour of the lanthanide elements. Later we will show that this is due to itinerant 4f electrons, a property which is in contrast to all the other lanthanides where the 4f electrons are localized with an integral occupation of the atomic-like f level, 4f n."

"Once more we emphasize that at zero pressure there is a profound difference between the early and late An metals, in the sense that the 5f electrons are itinerant (metallic) for the elements up to and including Pu, while they are localized and non-bonding (atomic-like) for the elements beyond Pu (Johansson, 1975). Thus in this respect the later (heavier) An and their 5f electrons behave like most of the Ln with their localized 4f n atomic-like configurations. On the other hand, among the Ln the first element with a substantial occupation of the 4f shell, i.e. cerium, shows already at rather low pressures or at low temperatures a behaviour very reminiscent of the early An (Johansson, 1974)…

"We illustrate this by arranging the An relative to the Ln introducing a displacement in atomic number (Johansson and Rosengren, 1975a):

           Ce Pr Nd Pm Sm Eu Gd
Th Pa U Np Pu Am Cm Bk Cf Es Fm

(The physical reason for this displacement is the larger spatial extent of the 5f orbital as compared to the 4f orbital for the corresponding element.) This suggests a most interesting connection between the 4f and 5f series, but this has not yet been fully explored."

See also Johansson and Li (2009) doi:10.1080/14786430902917632:

"For the rare earth metals (the lanthanides), it has been long known that the 4f n atomic configuration remains essentially intact when introduced into a solid (metal) phase."

"Thus, thorium is a genuine 5f metal, since, without the presence of 5f electrons, it would otherwise be a normal tetravalent hcp metal."

I see good support here for the Ce to Gd tranche, and Th as an f-metal, as well as bringing Gschneidner, and Wittig, into question. Not to mention the irrelevance, in this context, of La, Ac, and Lu.

--- Sandbh (talk) 04:21, 10 May 2020 (UTC)

For convenience I've transcluded this earlier contribution by Double sharp:

LOL. Without the presence of f electrons, La and Ac would similarly be totally normal hcp metals. Yet they are not. Funnily enough, what you quote directly supports my tranches, because as usual the crash into more localised f electrons happens at Am. The congener of Eu. Double sharp (talk) 05:46, 10 May 2020 (UTC)

My response:

Not so. "…they are localized and non-bonding (atomic-like) for the elements beyond Pu (Johansson, 1975). The first localised tranche is, in your terms, Ac-Th (2); the second itinerant tranche is Pa-Pu (4); the third localised tranche is Am-No (8).

We further know from from Pettifor's work that La has a larger d-occupancy than Lu, and that this explains the dhcp structure in La. Sandbh (talk) 13:09, 11 May 2020 (UTC)

Funnily enough, a sudden increase in localisation on 5f at Am accords perfectly with the idea that the half-filled subshell is reached there. Because, the same thing happens to 4f at Eu, which explains its divalence as a metal. In actuality we have two tranches: Ac-Am, where oxidation states increase, stay put for a while, and then fall down at the half-filled subshell; and then Cm-No, which is rather more like La-Eu than Ac-Am. Again, Johnson's paper on quarter-periodicity explains why. In this sense, you can think of 5f as somewhat analogous to 3d.

So how are you going to rationalise away Glotzel's 1978 confirmation (doi:10.1088/0305-4608/8/7/004) of La 4f being populated by the exact same mechanism as Th 5f (hybridisation)?

“

The f bands in La and Th are essentially unoccupied, but through hybridisation the number of f electrons at the observed volume amounts to 0.17 (0.56) per atom for La (Th), whereas in a Ce the f band is partially occupied and the number of f electrons is 1.2 per atom. For all three metals the number of f electrons increases slightly under compression. The bonding f contribution to the pressure is essential in determining the equilibrium radii as well as the bulk moduli in all three metals and, in Ce and Th, it is of the same order of magnitude as the bonding d contribution. The outermost p core bands are approximately 2 eV wide, and yield a small binding contribution as in a noble gas. Self-consistency of the outermost p core states is important, e.g. the calculated bulk modulus for La at the observed volume is 240 kbar with, and 350 kbar without, core relaxation as compared with the experimental value of 248 kbar. Numerical results for all three metals are given in table 1.

”

— Glotzel

They are all fdsp metals. With lanthanum being analogous to thorium in its small but very present f involvement.

And here's something you quoted above from Jørgensen (1988, doi:10.1016/S0168-1273(88)11007-6):

“

It is evident from the neutral atoms reviewed that 5f electrons play as minor a role in thorium as 4f do in lanthanum, but that 5f electrons are at least as important in uranium as in cerium.

”

I repeat: double standard! Double sharp (talk) 13:14, 11 May 2020 (UTC)

Ah, I see above how you tried to rationalise Glotzel away, by noting that it was for fcc La and not dhcp La. Never mind, of course, that fcc La is metastable even below the transition temperature of 310 °C, with a tiny free-energy difference between it and the dhcp state (doi:10.1016/0038-1098(85)90217-0). XD Double sharp (talk) 13:46, 11 May 2020 (UTC)

Orbital radius, EA, and isodiagonality

Two properties
While researching double periodicity, I happened upon an obscure article, which simply correlates electron affinity (EA) with orbital radius, and in so doing reproduces the broad contours of the periodic table (p. 362). Having never thought much about the value or significance of EA, and its absence of easily discernible trends, I was suitably astonished.

Godovikov AA and Hariya Y 1987, "The connection between the properties of elements and compounds; mineralogical-crystallochemical classification of elements", Jour. Fac. Sci., Hokkaido Univ., ser. IV, vol. 22, no. 2, pp. 357-385.

The authors left out the Ln and An and stopped at Bi. They were sitting on a gold mine but provided no further analysis.

Development
I added the data up to Lr, updated the EA values, and redrew their graph. It's a thing of beauty and wonderment in its simplest sufficient complexity and its return on investment.

I’ve appended 39 observations, covering all 103 elements.

Isodiagonality
The authors refer to the following new diagonal relationships (pp. 370-372):

Chemical

Na-Ca-Y
La(Ln)-Th: "This aids in explaining the isomorphism between the named elements in the complex oxides, thorianite." [?]^
Ga-Sn
Zn-In

^If so, this would be congruent with Ca-Y-Ce; according to us, thorianite was so named on account of its high percentage of Th; it also contains the oxides of U, La, Ce, Pr and Nd (weird!)

Solid solution

Mn-Ru
Fe-Rh-Pt
Ru-Ir
Co-Pd

Mineralogical (and retrograde at that)

S-As
Se-Sb
Te-Bi

Conclusion
So there it is, just two properties which account for nearly everything, and possibly eleven new diagonal relationships.

Observations

Very good correspondence with natural categories
Largely linear trends seen along main groups; two switchbacks seen in group 13; also falloffs (6p sub-shell) seen in groups 14-17
First row anomalies seen for Li (in amphoteric territory), Be (ditto), C (misaligned), N (in noble gas territory), O (misaligned), F (ditto) and He (ditto)
For group 13, the whole group is anomalous, no doubt due to the scandide contraction impacting Ga and the double whammy of the lanthanide and 5d contraction impacting Tl
Nitrogen was called a noble gas before the discovery of the real noble gases and appropriately enough falls into that territory

Rn is metallic enough to show cationic behaviour and falls just outside of noble gas territory
F and O are the most corrosive of the corrosive nonmetals
The rest of the corrosive nonmetals (Cl, Br and I) are nicely distributed, across the border from F
The rest of the simple and complex anions, funnily enough, comprise the intermediate nonmetals
The metalloids are nicely aligned; Ge falls a little outside of the metalloid line, being still occasionally referred to as a metal; Sb, being the most metallic of the metalloids falls outside the border; At is inside; Po is just outside

Pd is located among the nonmetals due to its absence of 5s electrons; see https://pubs.rsc.org/en/content/articlelanding/2013/dt/c3dt50599e#!divAbstract
The proximity of H to Pd is astonishing given the latter’s capacity to adsorb the former
The post-transition metals (PTM) form an "archipelago of amphoterism" bounded by transition metals: Ni and C to the west; Fe and Re to the south; V, Tc and W to the east; noble metals to the north
Curiously, Zn, Cd, and Hg are collocated with Be, and distant from the PTM and the TM proper (aside from Mn)
Zn is shown as amphoteric, which it is. Cd is shown as cationic but is not too far away from amphoteric territory; it does show amphoterism, reluctantly; Hg is shown as amphoteric which is the case, weakly, for HgO, as is the congener sulfide HgS, which forms anionic thiomercurates (such as Na2HgS2 and BaHgS3) in strongly basic solutions

The ostensibly noble metals are nicely delineated; Ag is anomalous given its greater reactivity; Cu, as a coinage metal, is a little further away
The proximity of Au and Pt to the halogen line is remarkable given the former’s capacity to form monovalent anions
The ferromagnetic metals (Fe-Co-Ni) form a nice line
The TM from groups 4-12 form switchback patterns e.g. Ti-Zr and the switchback to Hf
The refractory metals, Nb, Ta, Mo, W and Re are in a wedge formation

Tc is the central element of the periodic table in terms of mean radius and EA values; V is close, Cr is a little further away
Ti is just inside the basic cation line; while Ti(IV) is amphoteric, Ti3+ is ionic
Sc-Y-La shows a main group pattern up to La, when there is a switchback to Ac
Sc-Y-Lu-Lr shows a TM switch back pattern
La, and to lesser extent Ce are rather separated from the rest of the Ln, consistent with Restrepo

Sc and Lu are close to the amphoteric territory and are both in fact, weakly amphoteric
The post-cerium Ln and An (but for Th) all fall within basic cation territory
EA values for the An are estimates and need to be treated with due caution
The light actinides (Th to Cm) occupy a tight locus, with the exception of Th, where the 5f collapse is thought to occur, and Pu, which sits on the border of 5f delocalisation and localisation
While the light actinides U to Cm are shown as being cationic they are all known in amphoteric forms

The heavy actinides, Bk to Lr, are widely dispersed
All the Ln, bar Tm, are located within close proximity of the light An locus; Tm is the least abundant stable Ln
The gap between La and Ce, and rest of the Ln is consistent with Restrepo’s findings
Nobelium in this edition of the chart falls off the bottom, having a radius 1.58 (cf Es) and an EA of -2.33
There is an extraordinary alignment between He and the Group 2 metals

Magnesium is on the cationic-amphoteric boundary; some of its compounds show appreciable covalent character
Li, being the least basic of the alkali metals, is located just outside the alkalic zone; Li compounds are known for their covalent properties
The reversal of the positions of Fr and Cs is consistent with Cs being the most electronegative metal
A similar, weaker pattern is seen with Ba and Ra.

I'll add this to our EA article in due course. Sandbh (talk) 05:56, 13 April 2020 (UTC)

Feedback

Looks interesting, but the data should be carefully checked. Orbital radii of transition metals are hard to calculate, and the values from reference books are questionable as a rule. Negative electron affinities are also unclear because they have no physical sense; they go closer to zero when more diffuse functions are added to the basis set. I would not recommend to use this chart as it is. Droog Andrey (talk) 07:55, 13 April 2020 (UTC)

@Droog Andrey: Sigh. The article giving the orbital radii has been cited 514 times. Only 77 times since 2016. The EA values are from our own article, every single source of which I personally checked. Just what level of evidentiary support do you expect? Do you feel I post these things without doing due diligence? Do you feel I'm a pissed off by your Holier-than-thou attitude? I sure am. Sandbh (talk) 08:09, 13 April 2020 (UTC)

I feel I'm more willing to believe Droog Andrey's misgivings because he is a computational chemist and neither of us are. So, @Droog Andrey:: could you explain to us why orbital radii are problematic for the transition metals?

P.S. If you are going to draw trends, I suggest again what Wulfsberg does: predict degree of hydrolysis of cations from what are basically the generalised Fajans' rules I have been advocating. Double sharp (talk) 10:09, 13 April 2020 (UTC)

@Sandbh: It is not a matter of due diligence. It is a matter of understanding whether or not the things you are diligently plotting make chemical sense. I was doing the same thing until Droog Andrey explained the problems with our old Sc-Y-La approach, for example. And I feel that in this case I want to learn from him, and not just count citations, when I bet you can find tons of citations for the d-orbital explanation of SF₆ that is totally wrong. Double sharp (talk) 10:11, 13 April 2020 (UTC)

@Double sharp: I was recently asked by a well-respected chemist/physicist for some help for them and their colleagues correcting an article. They and their colleagues don't get how we work in that they make some edits and then get reverted. They don't understand that reputation without citing sources won't work. It's a good thing to learn from people like Droog Andrey, and I welcome his participation. On the due diligence thing, I do it with much more care and effort than a professional saying something on the basis of their discipline—since I have no science qualification—and that includes checking with professionals in the field.

What I don't respect in this forum is professionals saying trust me, I'm an expert (not that Droog Andrey has done this) or making assumptions about how much work and research I may have conducted before posting. Amateurs have made significant contributions to chemistry. When a chemist says, "that can't be done" they do so from within their frame of reference, whereas non-professionals have no such blinkers, and say, "why not?".

Cross-discipline academic expertise (which I have) can bring fresh thinking to the table, and that can only be a good thing

On "whether or not the things you are diligently plotting make chemical sense". Really? You're familiar with my work here and my two FA. I gave the details of the article in which the original plot appeared. I checked Google Scholar for other items by Godovikov and saw he has written a lot in this field. I looked at his and my plot and asked myself: is there anything here untoward? Not to my eye. I checked the works of Sneath; Restrepo; Leach; and Schwarz. I couldn't find any inconsistencies. Hell, I even checked my own peer-reviewed work. Again, nothing untoward. I saw the Pd anomaly, and hunted down the explanation.

You know I've been published in peer-reviewed academic journals. I do my research. The same goes for my edits to Wikipedia.

All this counts for nothing in Wikipedia. So I cite my damned sources.

I've never looked for citations for the d-orbital explanation of SF₆ but I've read of the controversy and would check my sources. Sandbh (talk) 11:46, 13 April 2020 (UTC)

@Sandbh: The Pd anomaly is, in fact, exactly why I agree with Droog Andrey that this chart shouldn't be used as it is. Because chemically speaking, Pd is no different from any other 4d metal: 4d, 5s, and 5p are all active. The ground-state electron configuration is just an accident that is partly brought on by the higher 4d-5s gap compared to 3d-4s, and is easily corrected in actual chemistry. Much better to look at atomic or ionic radii when this totally disappears; that should give better results.

Citing sources is important, but there is also a need to understand the material so that you know which sources are likely to be more accurate. That's why when I know I don't understand something that comes up here, I ask someone who's likely to know more. As happened for taking into account orbitals in computational chemistry and for intermetallics in archive 42. Double sharp (talk) 12:46, 13 April 2020 (UTC)

One anomaly

@Double sharp: Words almost fail me.

There's one friggin' anomaly out of 118 = < 1%. I provided a reference explaining the anomaly. Here's another: "The Pd-anomaly is clearly seen experimentally…The small radius of Pd, relative to all its neighbors in the Periodic Table, is a consequence of its outermost electron density deriving predominantly from d-levels, instead of s-levels."

Never mind the other > 99% of data points. Never mind the explanation. In bullet #12 I said, "The proximity of H to Pd is astonishing given the latter’s capacity to adsorb the former." Of course, there is nothing going on here! Professors Andrey and Sharp know better.

Anomalies prompt curiosity and inquiry. That's interesting. What might be going on here? "Bah, humbug" says Scrooge McDouble sharp. "Move on!" "There's nothing to see here!" Never mind my 38 other dot point observations.

While we're at it, let's remove the MP cross EN chart from the post-transition metal article, since that contains at least one anomaly. Oh, and let's remove the EN v standard reduction potential chart from the nonmetal article, since that contains one anomaly. Even better let's have dumbing down project to remove all other interesting perspectives we attempt to add to our articles. Yeah, that'll be good for the world.

Hey! Let's remove the periodic tables from our periodic table article, since each of those tables contains at least one anomaly!

You've done this to me before when you argued for Sb as a metal rather than a metalloid. Never mind the 194 references making up the list of metalloid lists showing Sb was included in 87% of these. Never mind my peer-reviewed article on metalloids published in JChemEd, now with 21 citations. And hey, the EA cross OR chart supports Sb as the most metallic of the metalloids. Did you say anything about that? No, of course not, the important thing is to immediately side with Droog Andrey.

You did it to me again when I mentioned the "magic thread" running through the intermediate nonmetals. You undermined that.

You did it to me again when I suggested N should be part of the intermediate nonmetals. You disagreed.

What happened subsequently?

Each of these three items formed part of my peer-reviewed article published in Foundations of Chemistry, with > 800 accesses to date.

More recently you unilaterally removed my contribution to our periodic table article, on La and Lu in group 3, referring to it as "fringe science". Really? Never mind I provided a reference from a well-respected chemist writing in a well-known chemistry textbook. Never that the composition of group 3 is of topical interest to IUPAC. Never mind that there are other sources supporting this option. Did you do any research to see if there were any other such sources? No. Did you add a disputed/discuss tag? No. You decided to unilaterally remove my contribution. Never mind that our periodic table article seeks to provide a good survey of the options on offer for the various controversies. Thanks a lot for imposing your righteousness view upon the world, not. Do you know what self-knowledge is? You need some of that to appreciate how you came over.

As a fellow member of this project I feel your agreement with Droog Andrey, in this instance, is beyond belief; unreasonable by any standard of Wikipedia reasonableness, let alone an ordinary reasonable person; disrespectful, and incivil. How about stepping back, taking at look at what you wrote, and asking yourself how that contributed to mutual respect and camaraderie among project team members? Sandbh (talk) 08:01, 14 April 2020 (UTC)

@Sandbh: As I explained in archive 42: the single source putting both La and Lu in group 3 (and not all the other Ln as well) that you mention (Silberberg) is not even consistent about doing that in his own periodic table. (Yes, I actually looked at the book!) And Silberberg was the only source mentioned as doing this. It certainly seems fringe to me.

The Pd 5s band is also occupied and contributing in the metal, and that is why it is paramagnetic. "The low-lying levels [of PdH] are hybrids of s-like states with s and d-like Pd states" (doi:10.1016/0038-1098(80)90218-5). (So much for the idea that the proximity of Pd to H on this chart explains Pd's astonishing ability to take up H, when that proximity only comes about apparently because of that weird gas-phase configuration that chemically means nothing, as usual for gas-phase configuration anomalies. I agree that that situation is interesting, but as an explanation this doesn't seem to work based on what I see from papers.) And I suggested alternative measures that get rid of such anomalies and look more closely at what is universally recognised as significant since Fajans: atomic and ionic size.

Why can't I agree with Droog Andrey if he gives a well-argued reason for his disagreement with you? Not to mention that me disagreeing with you about N as part of the intermediate nonmetals had nothing to do with Droog Andrey's opinion, as I recall. Not to mention that I pointed out to him that Sb and Bi were semimetals and had weak metallic chemical properties (and he agreed that Sb and Bi were not true metals); the point which I agreed with him on was that they were both closer to metals than nonmetals. I don't agree with him just because he said something, but because his arguments convinced me. When I argue for Sb as a metal, that is in the context of a metal-nonmetal dichotomy (without metalloids): if you include metalloids, I would include Sb as one indeed, recognising that a metalloid category surely just means elements around the border between more metallic and more nonmetallic behaviour. It's not a dichotomy, there are more metallic elements and more nonmetallic elements, each have characteristic properties, and you have some that are close to the border like Sb really is; there's a difference between placement decisions for a three-way split and a two-way split. I have the right to my own analysis, particularly if it is backed up by actual chemists and actual texts. Which it always is. And I have the right to disagree with you, pointing to understanding of chemistry from the literature to back up my stand, just as you have the right to disagree with me. Please remember what R8R mentioned to us: the truth is born in argument.

If you seek to characterise my actions this way, and if this is going to be your response to disagreement – well, that is regrettable. In that case I think further discussion between us in the near future will not be productive since tempers are clearly flaring on both sides. So, I suggest we both cool this discussion off, stop trying to summarise our things in a TL;DR (because it seems abundantly obvious that we are not going to be able to agree at the moment), and resume this when I do a July RFC that should bring more people in to comment. Double sharp (talk) 09:48, 14 April 2020 (UTC)

@Double sharp: Time is a friend so I'm not as annoyed now as I was yesterday. What riled me was the work I put into checking the article and updating the chart, only for the two of you to more or less immediately dismiss all of it based on one anomaly, never mind the other merits. Normally I'm quite diplomatic. Yesterday I decided I'd had enough of the kind of behaviour that's caused me to feel the way I felt, and for the first time decided to let rip as if to say, "enough BS, no more Mr nice guy; I'm not putting up with this crap anymore."

Anyway. Back to business.

I raised about two dozen items in my post setting out my feelings on, and giving examples of, your behaviour towards me.

As usual you adopt a defensive mode, choosing to ignore twenty of these.

You couldn't even bother to acknowledge the unilaterality of your removal of my edit re Silberberg. Nice way to treat a fellow project member.

For Pd, and as usual, you misquote me and go into defensive mode. I never said "the proximity of Pd to H on this chart explains [italics added] Pd's astonishing ability to take up H". I said, the proximity is interesting and that I wondered what was going on. No acknowledgement of the extra citation I provided explaining the smaller size of Pd.

You are of course entitled to disagree with me. That said I was stunned by the rapidity with which you agreed with DA (not a citation in sight). On the N question, and the Sb question I was complaining about your consistent pattern of "self-righteousness" behaviour, which never goes anywhere. Meanwhile my positions appear in the peer-reviewed academic literature.

The truth is not born in argument. It's born in discussion to find out what is right.

All that said, I've found our argument-discussions to be a worthy and richly rewarding learning experience for me, and I hope for you, and our contributions to Wikipedia. Don't read too much in my venting. I hope you can learn something from me as to my feelings on how to work collegiately and respectively. I look forward to continuing to work with you.

Please don't feel undue concern about what I've said. We're nowhere near FJ's unacceptable standard of behaviour. I only ask for respect from a fellow project member. Sandbh (talk) 03:21, 15 April 2020 (UTC)

Orbital radii and negative EA

@Sandbh: please get us rid of hysterics and complaints.

Orbital radius is defined as the last inflection point on the curve of radial distribution of total electronic density. The accurate computation of the latter for atoms with many low-lying configurations require multi-reference methods like CASPT3 and large atomic basis sets like ANO-RCC (using relativistic hamiltonian of course). I'm not aware of such computations being done systematically over the entire PT.

Negative atomic electron affinities has no physical sense unless some excited metastable states are encountered (like 1s2s2p for helium anion). The most of negavive values cited appear to be computational oddities upon careful examination. Droog Andrey (talk) 11:11, 15 April 2020 (UTC)

@Droog Andrey: Nice to hear from you. Happy to oblige. Could you please get rid of posting your assertions without supporting citations. Could you please get rid of your juvenile jibes such as that's one more fruit in my bin, or that Sc-Y-Lu will crush Sc-Y-La. If you have concerns about the accuracy of data in an article could you please offer a better alternative. Could we please engage in a mutually respectful discussion on what is the truth rather than who is right?

The orbital radius figures come from JT Waber & DT Cromer. "Orbital radii of atoms and ions." Journal of Chemical Physics, volume 42, number 12, 1965, pp. 4116–4123. doi:10.1063/1.1695904.

I'd normally be cautious about such an old article. That said, it has 514 citations, and I figure if there was something better, people would be citing that instead. Godovikov & Hariyaand (1987) used it. You can find the same figures in RJ Silbey et al. Physical chemistry, 4th ed. Hoboken, NJ: John Wiley & Sons, Inc., 2005, p. 882. For Lr I got the orbital radius from Li et al. 2002, "Theoretical study on Lr atomic ground state", Chinese Journal of Atomic and Chemical Physics, vol. 19, no 2, 2002.

For electron affinity I checked all the supporting citations, including those with negative values. AFAIK nitrogen is widely regarded as having a negative electron affinity. Weller et al. 2010, Inorganic chemistry, 5th ed., Oxford University Press, pp. 28-29, list precise negative EA values for the noble gases, without any fuss. They also list EA values for X^2- from X^- values for O (−780 kj/mol); and S (−492). Their value for N is −8 which is what I see elsewhere.

Do you have a citation supporting your concerns about negative electron affinities?

The chart corresponds to all known patterns in the periodic table. Even the position of Pd is explicable, based on the two citations I gave. The results of a scatter plot of EA and orbital radius looks truthful to me. What is it about that approach that you'd regard as not being a true outcome? Thank you. Sandbh (talk) 12:20, 15 April 2020 (UTC)

I'm not good at making citations, but I'm quite experienced with computational chemistry. You know, 10.1063/1.1695904 use pretty low level of theory to compute orbital radii.

O^2- and S^2- do not exist in gas phase, the second electron has no bound states at all.

You may either use my warnings or throw it out. I have no resources right now to publish an article with correct computations you need, sorry. Droog Andrey (talk) 12:42, 15 April 2020 (UTC)

The point is that negative electron affinity means that the added electron has no binding energy, that's not a different situation from zero electron affinity. At the most it stays there for a few microseconds or milliseconds before autodetaching again if the energy it went in with is enough to excite a resonance. It's quite common to consider them as zero; and in fact, they are probably not all that far from zero in reality:

“

It used to be common to see large negative electron affinities for many elements, when all we had to depend on were extrapolation processes. I assume that no EA is (much) below zero, i.e., endoergic to a significant extent. The logic is that the screening constant for an atom cannot be (much) larger than the atomic number. No set of screening constants has ever suggested such extremely high values.

”

— R. Thomas Myers, doi:10.1021/ed067p307 (1990)

Anions like O²⁻ and S²⁻ are unbound in the gas phase, salts with such anions only form because the electrostatic forces between the cation and the anion is sufficient to overcome that. (Which is, incidentally, why N having a barely negative electron affinity is not actually all that relevant for its chemistry, for which the high electronegativity common to 2p elements is more important.) Double sharp (talk) 13:50, 15 April 2020 (UTC)

No worries about making citations. Just give us a pointer to the source; no need for formatting niceties, if that’s what you mean.

We know:

doi:10.1063/1.1695904 uses a pretty low level of theory to compute orbital radii
it has been cited 514 times
if there was some better data people would be using that instead

@Sandbh:There is: doi:10.1063/1.1712084, used in Atomic radius. Still too low level of theory, however. Droog Andrey (talk) 05:45, 16 April 2020 (UTC)

the scatter plot of EA and OR yields a result which is very close to the broad contours of the periodic table
negative electron affinities are commonly quoted

@Sandbh: quotation means nothing. Droog Andrey (talk) 05:45, 16 April 2020 (UTC)

It's also common to quote all those electron affinities as zero, in practice. Not that the quotations are in themselves a good argument in the first place (they need justification), but they cut both ways. Double sharp (talk) 06:50, 16 April 2020 (UTC)

We know that:

quotations are widely used with the scientific literature
they usually represent scientific practice or consensus
the quality of Wikipedia rests on supporting citations
quotations enable us to stand on the shoulders of giants
negative electron affinities are commonly listed as such and just as commonly as zero
Double sharp acknowledged that N has a (barely) negative EA.
that N has a negative EA was predicted as long ago as 1945

--- Sandbh (talk) 07:45, 16 April 2020 (UTC)

Myers assumes EA's can be below zero, even if not by much.

On negative electron affinity Double sharp and I agree N has a negative electron affinity.

As another example, let us consider the negative electron affinity of helium.

We know:

this was experimentally measured as −0.08 eV. doi:10.1103/PhysRevLett.19.737 (128 citations)
this article gives a calculated figure of −0.0774, adding "Good agreement with the less-precise experimental values is obtained." doi:10.1103/PhysRevA.19.452 (62 citations)
this article says, "Our calculated electron affinity for He 3^S (Is2s) with this basis is [−]64.9 meV as compared with the best experimental and theoretical estimates of [−]79 and [−77] meV, respectively doi:10.1103/PhysRevLett.52.1413 (35 citations)

@Sandbh: do you ever analyse what you quote? Droog Andrey (talk) 05:45, 16 April 2020 (UTC)

@Droog Andrey: Yes, I do. Why do you ask? The best experimental estimate those authors refer to is: "Thus, we believe the affinity of He(2³S) is known to be 80.0 mV with about 2 mV probable error doi:10.1103/PhysRevLett.19.737. If what I quote is not right I'm happy to move on and learn. That's what the purpose of discussion is; to establish what is right. Sandbh (talk) 07:45, 16 April 2020 (UTC)

@Sandbh: You quoted positive EA for an excited (1s¹2s¹) helium atom. You know, I calculated it myself (as 76 meV) back in 2012. In the same way there are positive EA's for 2s¹2p¹ Be, 3p⁵4s¹ Ar and so on. And I even googled some sources for you: doi:10.1063/1.556047 and doi:10.1021/cr990044u. Droog Andrey (talk) 17:45, 16 April 2020 (UTC)

@Droog Andrey: Yes, I see. I quoted the wrong entity. Sorry. There still seems to be some sign convention confusion. Thus, the article I quoted from says "The calculated electron affinity is 0.233 eV [for the diatomic He molecule] compared to 0.077 eV for the He⁻[⁴P°] ion." The latter figure is effectively the same as the experimental measurement of −0.08 eV given by doi:10.1103/PhysRevLett.19.737 but using the reversed sign. That is the convention used in the research literature https://pubs.acs.org/doi/pdf/10.1021/ed074p123 and in Wikipedia. Yet the same article from which I misquoted gives 64.9 meV for He 3^S (Is2s), implying they are referring to −64.9 meV. Thank you for those citations. I didn't seen any egregious discrepancies compared to our current values. Sandbh (talk) 04:17, 17 April 2020 (UTC)

We know anions like O²⁻ and S²⁻ exist and have measurable properties.

On nitrogen, we know this article says that despite having a high electronegativity, its chemistry is largely covalent in nature; anion formation is energetically unfavourable owing to strong inter-electron repulsions associated with having three unpaired electrons in its outer valence shell, hence its negative electron affinity. doi:10.1007/s10698-020-09356-6 (849 accesses)

--- Sandbh (talk) 03:27, 16 April 2020 (UTC)

Those anions do not exist in the gas phase as bound entities. They only exist in solid salts and solutions because then there is enough energy released to overcome that. Which is exactly why the negative electron affinity is not actually that much of a big deal for nitrogen, it can easily take up a strong partial negative charge in a bond like C≡N. Anyone can see that the presence of such a bond makes the molecule very polar, just compare melting points of propionitrile (EtC≡N, 96–98°C) with butyne (EtC≡CH, 8.1 °C). The high electronegativity is what matters, you really need to be strongly electronegative to make N have a partial positive charge. (Special case being Cl, where the electronegativity is not much higher than N but it is more polarisable and gets the negative charge.) That you don't much see totally ionic N³⁻ is just because of the really high negative charge; anions have the double-whammy problem that smaller anions find it difficult to support strong negative charges, but bigger anions are not electronegative enough. It's more important to note the similarities between N- and O-donor ligands. Nitrogen's unreactivity as a pure element is just because the triple bond N≡N is so strong, which again is due to high electronegativity (by itself, it wants to avoid interelectronic repulsion that F₂ suffers); once that is broken, it reacts as violently as one could wish. And that's not a strike against it, otherwise sulfur is stronger than oxygen. Double sharp (talk) 03:39, 16 April 2020 (UTC)

Zero electron affinity

Indicates block ends (He-Be-Mg; Ne-Ar-Kr-Xe-Rn; Zn-Cd-Hg-Cn; Yb-No) or sometimes halfways (N, Mn), with only Fl standing apart because of relativity. Droog Andrey (talk) 17:22, 15 April 2020 (UTC)

Yes, agree; sort of as a rough boundary. Corresponds with the closure of an s or p sub-shell on top of full underlying sub-shell. There are nineteen such end of block elements: s = He-Be-Mg-Ca-Sr-Ba-Ra (7); d = Zn-Cd-Hg-Cn (4); p = Ne-Ar-Kr-Xe-Rn-Og (6); f = Yb-No (2). 5 of these have positive EA: Ca-Sr-Ba-Ra; Og predicted. Compliance = 73.7%. A little on the low side. That said, the positive values are quite low, so there is definitely a pattern. Chemistry relevance? Not completely sure yet. Sandbh (talk) 04:34, 16 April 2020 (UTC)

Oganesson is an anomaly only because of relativistic effects, so it's not terribly important. (At stake is the low 7p-8s gap.) Ca⁻ seems to have accepted the extra electron into 3d and 4p, so that the heavy alkaline earths can be seen as a manifestation of the s block issue where the higher orbitals are open (unlike any other block), so that you have to consider the np and (n-1)d orbitals as well (under pressure, (n-2)f too). So the non-compliant values in fact seem to indicate the same deeper underlying pattern as usual, or relativity eating into the pattern for Fl and Og. Double sharp (talk) 06:06, 16 April 2020 (UTC)

(P.S. I would like to note that counting anomalies is not everything there is. Yes, you need the anomalies to be a minority, or you have the primary and secondary effects mixed up. But there's a difference between a theory that randomly fails in one quarter of the cases and one whose failures can be explained by a secondary effect that was not taken into account in the original analysis.) Double sharp (talk) 12:52, 18 April 2020 (UTC)

Negative electron affinity

Nobelium, perhaps, has the lowest EA at −223 kJ/mol. Chlorine has the highest at 349 kJ/mol.

Here’s a much clearer explanation of EA:

"The energy change involved in adding an electron to an atom to form an anion is known as the electron affinity of that element (EA). Due to an unfortunate tradition regarding the signs of electron affinities, they are better regarded as the energies required to remove the electron of a gaseous anion of −1 charge to produce a gaseous atom of that element. Hence we list them in Table 6.8 (p. 366) as ionization energies of the −1 ions; they could also be called zeroth ionization energies:

Cl^– (g) → Cl(g) + e^– ΔH = EA = IE(0) = +348.8 kJ mol^–1 "

--- Wulfsberg G 2018, Foundation of inorganic chemistry, University Science Books, CA, p. 362

In the case of No, then, it apparently requires a fair bit of energy to attach an electron to it and form No⁻. Look at the electron configuration of No: [Rn]5f¹⁴7s². All its sub-shells are full. It’s happy as is, no room for lodgers.

For Cl⁻ it takes a rather large amount of energy to remove an electron and form plain Cl. Look at the electron configuration of Cl⁻ i.e. [Ne]3s²3p⁶. All its sub-shells are full. It wants to keep its e⁻ lodger! Sandbh (talk) 03:14, 6 May 2020 (UTC)

@Sandbh: But there is no such thing as a ground-state No⁻ anion in the gas-phase, the electron will not stay there. The only way you can force nobelium to accept an electron is to give the incoming electron so much kinetic energy that it excites a resonance state. Which will then promptly autodetach again after not so much as a second. So putting these kinds of things on the same footing as normal negative ions is not comparing like with like.

You can only talk about such anions in a situation where energetically it stops being worth it to get rid of the added electron(s), like O²⁻ and S²⁻ in salts. In particular, this is why the negative electron affinity of nitrogen has about zero relevance for its chemistry. The better reason to look for as to why it seems so docile at first glance is the strength of the N≡N triple bond, that must be broken first. That's exactly why oxygen is surprisingly restrained with its O=O double bond (you usually need a flame or spark first to get things going). Just look at what happens when these are not factors. (And no doubt the fluorine-breathers on the planet Skyron are looking at us disapprovingly, clicking their equivalents of tongues and calling us the local equivalent of "wusses". ^_^) Double sharp (talk) 04:31, 6 May 2020 (UTC)

P.S. And this statement about the highest EA being for No, with a value well below zero, even after I pointed to Myers' article explaining why this doesn't make any sense. XD Do you have a mental block against information as long as it comes from me, even if I cite it with sources? Just look at archive 42, and how I kept fighting against the nonsensical idea of "predominantly ionic" vs "predominantly covalent" for a whole element's chemistry(!!), quoting Greenwood and Earnshaw, to no avail. At least until you found Rayner-Canham and Overton, which you kept quoting only the simplification on p.29 on, adding the sensible nuances I was noting on pp.99 and 109. And only then did you say "Quite so." XD Double sharp (talk) 04:41, 11 May 2020 (UTC)