Wikipedia talk:WikiProject Elements/Archive 46

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Very serious questions for Sandbh

Sc-Y-La lack consensus

@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)

@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)

Question A

@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)

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)

Chemistry is quantitative and qualitative

@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)

All the other vectors

@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)

For your amusement

@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)

I have a bridge to sell the two of you know-it-alls

The scientific method

@Double sharp and Droog Andrey: I get asked some odd questions in the thread. I know what the scientific method is. If there was a scientific method that could be applied to the group 3 question it would've be done by now. There'd be no IUPAC project. I get asked to come up with a falsifiable hypothesis or theory. There isn't one. If there was one it would've been done by now.

Now, here's a noteworthy quote by Double sharp:

"…literature, which is full of people arguing for the Lu table…"

Two dozen authors in 100 years? Why, that must mean the literature is full of people arguing for the Lu table! If you believe that I have a bridge to sell you.

Not all arguments are logic. Good examples are politics, economics, philosophy, and ethics, and the many qualitative aspects of chemistry. I do wonder if the two of you understand that. It seems not. Sandbh (talk) 05:11, 14 May 2020 (UTC)

@Sandbh: Politics, economics, philosophy, and ethics are not natural science. Chemistry is. Droog Andrey (talk) 12:09, 16 May 2020 (UTC)

@Droog Andrey: Not all arguments in chemistry are based on logic. "In many respects, computational chemistry is still an art, and relies upon a delicate mix of physical intuition, pragmatic cleverness, and practical know-how." Sandbh (talk) 13:11, 16 May 2020 (UTC)

@Sandbh: And how exactly do you think the results are interpreted? Surely you know that effective integration is also an art and relies on a delicate mix of intuition, pragmatic cleverness, and practical know-how? And does that put the foundation of mathematics on logic in jeopardy? Double sharp (talk) 13:29, 16 May 2020 (UTC)

(P.S. An admittedly extreme example backing up my point about integration may be found here.) Double sharp (talk) 12:33, 24 May 2020 (UTC)

Since I am quoted, and I admit I phrased it badly above: what I meant is the relevant literature, focused on group 3, has certainly significantly more Lu proponents than La proponents. Which is what I say immediately below. As for the rest, I will let others write what they think of Sandbh's comment.

Anyway, my policy from now onwards will be that I will not respond to anything Sandbh has to say, unless he edits or quotes my posts. What I think of what he has to say can mostly be found by perusing the archives. Double sharp (talk) 07:40, 14 May 2020 (UTC)

Retracting this for now, since R8R has intervened. Double sharp (talk) 10:17, 23 May 2020 (UTC)

R8R's views

I have always regarded this problem as a problem of definition, rather than that of a hidden truth somewhere. This has greatly influenced my vision on it; not just in this discussion, but also in the previous discussions.

So naturally, when Double sharp began to speak about how a scientific hypothesis should be falsifiable, I have eventually come to ask myself if this applies here. My hunch was that Popper talked about facts, rather than interpretation thereof. Group 3 indeed does not exist; it is a mind construct that we use to emphasize some similarities or progressions that we want to emphasize (in electron configurations, mp/bp, etc.). That Sc has a mp of 1541 °C, Y 1526 °C, La 920 °C, and Lu 1652 °C (provided that we have agreed to consider the standard pressure) is a matter of fact; what to make of that and other facts like that is a matter of interpretation. Some interpretation may seem obvious to one person and another to a different person; what we have in the end in a convention.

Consider the statement: "every object thrown falls back on Earth." Sounds legit, but then in the end you realize there is still some room for ambiguity that's hidden in the word "falls." If a Sun were to meet the Earth, would that be considered a fall to the Earth? Hardly so. What about light from it? What about quanta? The big takeaway from this little consideration is that ambiguity may hide well, and sometimes problems are not problems of fact; they are sometimes problems of definition. (This takeaway is easily projected onto our problem at hand.)

From there, I remembered my old idea: what if this is not a question of reality, but rather a question of what we think of reality? Perhaps Popper did not include that in his thinking? You may recall the old chicken or the egg philosophical problem. If we were to answer that question literally, we would note that some time ago, there were non-chickens than mutated into chickens. Let's say we have found a specific non-chicken that mutated during its lifetime to become the first chicken. So chicken first? Or could it be that we will say the egg came first because that's the egg that gave us a chicken? There is no right answer to that; it's only a matter of convention. And this also goes for our group 3 problem.

Then I realized that we were not looking for the truth indeed; we were looking how to categorize that truth. The last question that remained was whether categorization was science at all. And it appears that the process of categorization itself is not a part of the realm of science, which was limited in scope to finding the truth to be categorized. This came rather as a shocker to me; to say that this was counter-intuitive is to say nothing at all. Science is unthinkable without categorization. But then I realized science is equally unthinkable without mathematics. And yet, we don't think mathematics is science.

Now back to the statement of Sandbh's: "There is no logical provable answer." I agree; there isn't one. We would have to agree what we even mean by "group 3": what do we seek to emphasize? We would also have to agree on how to look for the answer, and what can be considered as midpoints in our thinking (recall, for example, Sandbh's statement on how every late actinide except No still preferred +3 vs. Double sharp's statement on how stability of +2 increases all the way up to No: both statements are correct). If we seek to apply logic, we would have to agree on premises first (which is outside of the realm of logic, hence the notion of the lack of a logically provable answer), which would not only include basic truths, but also conventions on how to interpret them. This way is the best way forward, but it is hard; very hard, in fact. The worst of all is that it's so hard that we humans have repeatedly shown ourselves unable to grasp the complexity of it. This is particularly noticeable for the intellectual types, who think they've grasped it and who think that their logic is infallible and that everyone can be like them.

I have put some special effort to understand Sandbh's thinking because it was not obvious to me where the consistency was in it. However, I have managed it; I do see a consistency there, that's a valid way to go forward. Not necessarily that I always like, but definitely not something I'd consider corrupt to the core in an irredeemable manner. It takes an effort to understand something you don't understand and don't agree with, but sometimes, that effort is worth making, and this is a case when it is. This doesn't make you have to agree with it; just try to think why he'd try that.

tl;dr Sandbh is indeed not being scientific; that's not a reproach, however, since there's no way to be scientific here in the first place, and that's something worth realizing.--R8R (talk) 11:15, 15 May 2020 (UTC)

@R8R: OK, so for example: what do you think the consistency is in Sandbh allowing thorium into the f-block, with no 5f electrons in the ground state, no known compound in which its ground state is 5f¹, and no 5f occupancy that is not coming from charge-fluctuation hybridisation or ligand-metal charge transfer; but not allowing lanthanum and actinium, which are in the same boat for 4f and 5f? As opposed to my and Droog Andrey's approach, which is to note that all three elements may use 4f/5f as a valence bonding orbital with positive occupancy on average, and that the ground state does not really matter when so many excited states are really close for most d and f elements?

Maybe we have to indeed agree how to look for the answer indeed, but it seems to me that if, say, something (ground-state configurations) seems to correlate quite badly with chemical variation, and something else (Madelung-following averages) correlate much better, it ought to be pretty uncontroversial scientifically that the second one is a better base to stand on. Well, let's say you have a bunch of facts; then OK, it's true that the categories don't exist, nonetheless it's true that there are more and less natural ways to categorise, and that a categorisation is more natural if it conforms to and is based on something that really exists. That's essentially my argument for why "f element" should imply f orbital usage.

It seems to me that the second one wins on consistency hands down (because it doesn't treat Ac [Rn]5f⁰6d¹7s² and Th [Rn]5f⁰6d²7s² using a double standard), and also on naturalness of categorisation precisely because it focuses on something that correlates well with chemistry ("fuzzy" configurations like (5f6d7s7p)⁴ for Th) and has some explanatory power, rather than something that doesn't ([Rn]5f⁰6d²7s² for thorium wrongly predicts a lack of f involvement for thorium). But I'm ready to be enlightened on how Sandbh's argument may possibly be considered to have consistency in it. Double sharp (talk) 11:36, 15 May 2020 (UTC)

Well, that part of the discussion came after I made that realization :) I don't want to be the devil's advocate here as I'm not sure I could sell it to myself. However, I can give you a way that would probably make you feel easier about this.

This actually comes back to the logic bit. There is no logical contradiction in what Sandbh says (at least I don't recall anything; I may have forgotten something); things sometimes may look like they don't sit very together, but logically, that doesn't mean they contradict each other. And if you find anything in Sandbh's thinking (or you can use that idea outside of the group 3 discussion, too) that makes you think that then consider that there at least some way they could stand together' even if that way couldn't appeal to you, surely there are other ways of looking at it?

Is the f-block defined by f-involvement? What about the d-block, what is it defined by then? There is d-involvement in La? Hmmm, we're not getting very far from this idea alone. Not any further than the idea that a 7p electron in lawrencium is an argument against its membership in the d-block, if you see what I mean there.

Again, I really hope that I was able to any extent help you change your perspective from looking for what's right to the understanding that there are possible way of looking at it and you may choose the most suitable one from there while having the rest in mind, and if I was, then my participation wasn't for nothing.--R8R (talk) 21:18, 20 May 2020 (UTC)

@R8R: The type of the block corresponds to subshell with the lowest orbital symmetry. E.g., for La-Yb there are 4f5d7s7p active subshells, hence they belong to f-block. Droog Andrey (talk) 22:18, 22 May 2020 (UTC)

@Droog Andrey: +1

@R8R: It's really very simple. La has f but not g involvement, it goes into the f block. Lu has d but not f involvement, it goes into the d block. You pick the chemically active orbital of highest angular momentum. And that works perfectly except for the s block. But that was already the symmetry break: the s block is unusual in lacking secondary periodicity, not having its electrons fall into the core after being used (so each other block starts with trivalency), and fraternising with the wrong n+l value (you have as one unit "4s 3d 4p", not "3p 4s" as pure n+l implies). So there's no problem with the idea that the s block should be somehow different, it matches real chemistry. They are already quite well defined as elements with only one or two valence electrons. But why should La and Ac follow that?

I accept that there are different ways of looking at it, but all of them agree that thorium is a double standard. Suppose f electrons are needed in the ground state. Then thorium has none, neither does La and Ac. Suppose f electrons are needed in compounds. Then thorium has them, so do La and Ac. Suppose we insist on excluding orbitals filled by back-donation from the ligands for whatever reason. Then thorium lacks f electrons, so do La and Ac. Suppose we insist on f bands being itinerant and influencing the properties of the bulk metal. Then thorium has f involvement, so do La and Ac. Suppose f electrons are completely irrelevant to block placement. Then what is left to distinguish Th from La/Ac? Double sharp (talk) 10:02, 23 May 2020 (UTC)

Scerri (2009, JChemEd) said something that goes much to the heart of all this:

"The possession of an outer f electron is clearly not a requirement for an element to be placed in the, nominally named, f-block."

If you accept this, noting he has written at some length about the group 3 question, and more-or-less single-handedly convinced IUPAC to set up the group 3 project, then the la-de-dah about Th and Lu, and La and Ac for that matter, and whether or not they do or do not have the required "electron du jour", goes away. Other factors then come into play, presumably. --- Sandbh (talk) 04:09, 16 May 2020 (UTC)

And do you know why Scerri says this, instead of taking one sentence stripped of all context? Surprise, surprise, it is exactly because of thorium as I mention:

“

Better still, consider the configuration of thorium, [Rn]6d²7s². This element follows actinium, and nobody disputes placing it in the f-block even though it does not possesses any outer f electrons. The possession of an outer f electron is clearly not a requirement for an element to be placed in the, nominally named, f-block.

”

— Eric Scerri

So, that indeed proves that the la-de-dah about this is irrelevant as long as it focuses on ground-state configurations. Because, as Scerri noted, thorium destroys the consistency of Lavelle's "pair out of place" argument. That's exactly what I have been saying, but maybe Scerri saying it too is necessary for it to be accepted here. This argument is irredeemably inconsistent. Can we agree on this? And, once we do, can we please drop this irredeemably inconsistent argument once and for all?

My stand, however, is different. As luminaries going up to Seaborg have noted, ground-state configuration anomalies don't mean anything in chemistry. It is the same idea as looking to condensed-phase configurations as Scerri has recommended on the grounds that gas-phase configurations are when the atom is not in a chemical environment; this just goes a bit deeper by noting correctly that the same atom may have a different configuration depending on what compound it is in. This problem is most acute for d and f elements. Can we agree on this?

@Double sharp and Droog Andrey: Bear in mind that, in the case of Scerri, he is known to change his mind from time to time. He too recognises how hard it would be to take on the chemistry establishment wrt to changing from gaseous to solid configurations. I presume that is why, in 2018, he referred to distinguishing blocks on the basis of the predominant differentiating electron which, to my mind, represents an example of simplest sufficient complexity. As long as you choose to ignore the nature of the chemical establishment, including its history and culture, you'll continue to experience exasperation. Sandbh (talk) 08:00, 23 May 2020 (UTC)

@Sandbh: There is no "tak[ing] on the chemistry establishment" from either of us. Expert chemists have known for years that the important thing is the configurations of the elements in compounds rather than as gas-phase atoms. The only thing there is to take on is textbook errors.

Here are some old quotes from expert chemists, with my bolding:

Jørgensen (1988):

“

The two major reasons why this series intended for gaseous atoms strongly bewilders chemists is that undue emphasis is made on irrelevant irregularitie (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.

”

Seaborg (1991):

“

It is important to realize that the electronic structures listed in Table 6 are those of the neutral (unionized) gaseous atoms, whereas it is the electronic structure of the ions and compounds that we are chiefly concerned with in chemistry. The relationship of the electronic structure of the gaseous atom of an element to that of its compounds can be rather complicated.

”

Schwarz (2010):

“

The qualitative behavior of chemical elements can be rationalized with the help of the dominant electronic valence configurations of the atoms embedded in a molecular or crystal environment. These may be correctly called the “electronic configurations of the chemical elements”. However, what is listed in respective tables of chemical textbooks under this headline is something else, namely, what physicists call “the configurations from which the J-level ground states of free unbound atoms in vacuum derive”. ...

it is misleading to present free atoms as prototypes for the microscopic description of chemical elements in compounds. The common qualitative textbook explanations of the atomic ground states (correctly: J levels) are incorrect. Therefore, we plead for teaching the correct atomic-orbital order (sequence 6) together with the regular exception, sequence 8, for the s block. One need no longer apologize for irregularities.

”

Focusing on the ground-state configurations instead of configurations in compounds is really taking on the chemical establishment. Which are these experts, not the textbooks, which, as Scerri notes below, "inevitably present impoverished accounts of the particular fields that they are describing".

And I cannot accept as "simplest sufficient complexity" an ill-defined approach that has no connexion to real chemistry. Such as differentiating electrons. Ill-definedness and lack of connexion to real chemistry implies that the approach lacks sufficient complexity. Double sharp (talk) 09:53, 23 May 2020 (UTC)

Perfect, another one from a source you yourself cited (my bold, again):

Fernelius (1986): (10.1021/ed063p263)

“

It is fair to say that most chemists agree that the periodic table today, no matter what form it may have, must reflect electronic configurations. However, complete consistency is difficult to attain. [And then a quote of Jørgensen in a footnote, no less.] The regular order of fillings, p, d, and f orbitals throughout the whole array of elements is followed so closely that it may be easy to overlook the irregularities even though those irregularities do have chemical consequences. One must always keep in mind that the electronic configurations one finds in the usual tables apply to the "normal" atoms-those separated in space and thus not influenced by surrounding atoms and at such a temperature that there is no radiation of energy from the atom. This condition is seldom realized in chemical compounds and even in the free element in solid or liquid condition. [Not very "normal", are they?] ...

(One must remember that orbital distributions are for the "normal" atoms as defined above. These conditions do not hold for palladium metal because it is an electrical conductor and conduction takes place only when electrons have been promoted to a conduction band.) [Perfect example of how the lack of occupancy of 5s in an isolated Pd atom means nothing. Now, we also agree on this for 5f in Th, maybe it is not so surprising anymore for 4f in La and 5f in Ac?]

”

That is: although irregularities can have chemical consequences, those will be irregularities in chemical environments, not the completely irrelevant irregularities of an atom sitting on its own far away from everybody else minding its own business. Double sharp (talk) 10:21, 24 May 2020 (UTC)

On the electron configurations: doi:10.1002/chem.200500945 Droog Andrey (talk) 12:05, 24 May 2020 (UTC)

@Droog Andrey: Wow, thank you! Double sharp (talk) 14:30, 24 May 2020 (UTC)

@Droog Andrey and Double sharp: I think what you're saying is suggestive but not sufficient to make it a final solution by itself. I think we need to sort out first what a block is.

I think I mentioned that there are, in principle, two ways to look at it. One way is to start with a general picture (like what follows from Aufbau) and have all your knowledge fit it. The other way is to look at each element individually and assess it based on the examination. Unlike the former way, the latter is not strictly defined by itself; it is defined by the elements, and that assessment can in principle give different results based what properties the elements (for instance, it can mean that there would be blocks of variable length; saying this is not possible is exactly the pre-definition that I have mentioned in the first case).

So if we decide we want to follow the second approach, that is fine. So there's an element that has three (6s4f5d6p) orbitals which are the orbitals that are involved in bonding. I cannot see why that would make that element would definitely be in the f-block if we don't consider the other elements to see it doesn't have any room in any other place in a sort of predefined picture, which is something we have in the other case, actually. A phrase like "the orbital of the highest angular momentum defines a block" is possible but seems like a deliberate choice rather than something natural (or maybe it even is natural, but as you recall, "natural" is relative). It may look so excellent, but it, too, could be challenged.

@R8R: The highest angular momentum is natural just because mathematically "lower symmetry" × "higher symmetry" = "lower symmetry". Droog Andrey (talk) 19:59, 23 May 2020 (UTC)

@Droog Andrey: Maybe I haven't worded it well enough. My point is, you can find it most natural indeed but the concept of "natural" is relative: different people think that of different things, by the very nature of this word. It's absolutely possible that this is what you or Double sharp or some other people find it natural, if you want to use that word, and that's fine as far as I am concerned. But as I have argued on this page, "natural" in this kind of context is in principle relative because it depends on axioms in your thinking. My argument here is not for a -La-Ac table, but rather for challenging your own arguments and for being able to listen to arguments you don't agree with without dismissing them before it's become clear that you can legitimately do that, and you often can't at all; I have argued this problem in the end of the day depends on how you look at things in this problem in particular, and the concept of "natural" also depends on how you look at things.

If you meant to make a clarification, fine then, point taken but it doesn't run contrary to my argument (note the "maybe it even is natural" part).--R8R (talk) 20:37, 23 May 2020 (UTC)

Another consideration of mine is how this approach could be challenged by extending the scope from the current 110 or so elements. If you recall my question about the superheavy elements, I find that your angular momentum approach gives a result that I don't like, which makes me question the excellence of the approach. It does look strange to me because in our common 118 elements, those two approaches can often coincide and both seems fine choices for defining a block, but here, they don't and you have that "what if" situation, where you make a preference for either only at the expense of the other. Either choice is an arbitrary decision. For one, from here I would prefer to have a predefined picture and have results suit it; I like the Pyykko table, which has elements 121-138 in the 5g series, 139 and 140 in 8p_1/2 and then 14 elements in 6f and 10 in 7d. You said you had a different idea with a 22-element g-block. Which only shows you that the data is up for interpretation. (I hope that it gives you some idea of how if "differentiating electron" is ill-defined, then so is "block." Yes, there is a definition you like; doesn't mean everyone will accept it, other people may have their own ideas.) And as long as there is no ultimate interpretation everyone has settled on, there is enough room to consider the question not solved or at least not yet claim there is nothing in the way barring textbook errors; for you maybe, but not necessarily for a wider community. It doesn't necessarily mean that nothing should be done right now, but it's a good sign you may need to think some more to find a solution.

@Sandbh: in response for your question about what I find important to be reflected in the solution to this question; I'd say exactly this: electron configurations are very suggestive but are not necessarily the answer by the virtue of that alone. I'd also say that it's important to decide upon what one would want to reflect in a "block"; I'm not sure how to formalize my thinking on it but I hope that this message is insight enough into what I think about it. I'd also note that the periodic trends in Sc-Y-Lu are a better match to the rest of the early d-block and I think this is suggestive but not decisive too. I hope this is satisfactory. I'd write it as a reply to the question but the section it was in is already archived.--R8R (talk) 17:09, 23 May 2020 (UTC)

You say there is no particular 3-4 divide. I also don't think there's a divide particularly worth highlighting. Sandbh may think differently; that's fine and valid, it really is.

I pretty much think that as long as you understand that there is room for a different idea to have its way, you can argue for anything you like. I have reacted positively to many arguments you have raised (though not all of them) and I'd often say the same. I will note that what you quote doesn't highlight any errors; it highlights what I'd call unfortunate interpretations, and there's a difference, because what I find unfortunate someone else may not, and they may not be mistaken.

So depending on what you want to say to me: yes, if there were no other considerations (such as Wikipedia house rules or tradition), I'd pick a -Lu-Lr table myself, or no, it's not just errors that are in the way.

Here's a piece of advice that I really consider valuable: if there's a choice between A and B, then you always have at least three options: A, B, or I don't know. You don't have to make a choice until you can, and the same goes for the wider chemical society. Probably until there's readiness to settle of a definition of a block everyone could accept (note that our article block (periodic table) does not give a clear definition, for example), there's not going to be a solution and we'll have the status quo. I believe, and I get some confirmation from Sandbh, that if it were easy, Scerri would've done it already even though IUPAC is heavily bureaucratic and foot-dragging (as I have heard from Oganessian), the task was established. Note how some of your arguments, not only in the message I'm responding to (I made this observation some time before), revolve around you: in this message, for example, you have "I cannot accept as "simplest sufficient complexity" an ill-defined approach that has no connexion to real chemistry"; and what if other people can and it's just you? A solution is supposed to be universal, not just work for you.

But speaking of Wikipedia house rules, Scerri's taskforce has produced this graph. I suppose that it's going to become an argument in an encyclopedia that is supposed to follow sources; I'd actually expect it to be among the strongest arguments, if not the strongest argument of all, the -La-Ac side could employ to keep the -La-Ac table in Wikipedia in absence of other recommendations from IUPAC. This was mentioned before in this discussion, but I suppose that if Scerri considered those sources authoritative enough to be worth noting, then a guess from a Wikipedia editor that those sources maybe should have not been counted will probably not beat it.

It's not really very simple; if you want it to be, then yes, but the same won't necessarily work for everyone. It's important to take your own ideas with some skepticism.--R8R (talk) 17:01, 23 May 2020 (UTC)

From Essays in the Philosophy of Chemistry (also Scerri, with my comments in square brackets):

“

It could be argued that there are in fact no anomalies [in electron configuration; he is using 3d as an example] since one is merely observing the result of the variation of two energies, those of the s² and s¹ configurations, which happen to cross at a certain point along the first transition series. [So you have to consider multiple configurations, as usual. In some cases they are so close that ligand effects can easily switch which one is the ground state!] Moreover, and perhaps more relevant to the present project, the energies of these configurations can be computed from first principles via the Hartree-Fock method and they too show very similar trends, including a crossing of energies at more [or] less the same point along the transition series. [So what happened to not being able to get the Aufbau of chemical activity from first principles?]

Conclusions

This study illustrates the fact that the philosophers of chemistry, especially those influenced by the prevailing anti-reductionist zeitgeist, can too easily conclude from episodes in the history of chemistry and physics that reductionism fails. This is in fact how my own work until recently can be characterized, although I like to think I have been consistent in adopting a cautious approach and have stayed close to the scientific facts.

In the case under discussion one can only conclude that the periodic table has not been reduced to quantum mechanics if one restricts oneself to represents a serious omission since the condensed phases are overwhelmingly more relevant to most of chemistry and physics. Second, there is the related fact that by restricting oneself to gas phase atoms one is only considering isolated atoms of the elements rather than atoms that are bonded and present in compounds.

Third, let me make a general comment about philosophy of science which has been made many times before but which is especially pertinent in the present case. There is a tendency for philosophers of science to obtain their knowledge of science from textbooks, which inevitably present impoverished accounts of the particular fields that they are describing. Of course it is not difficult to understand this tendency, which stems from the fact that philosophers are generally not sufficiently technically proficient to cope with the latest research on the subject and prefer to fall back on the version of the science that they themselves learned during their earlier scientific education.

”

Exactly. Now that I have quoted Scerri as saying it, can we move on to something else, and drop DEs based on anomalous but nearly completely useless ground-state configurations once and for all? And maybe stop referring to textbooks as the wisdom of the masses or the chemistry battleship, when they are full of pedagogical simplifications, generally have focuses that are not very related to group 3, often don't justify why they picked their group 3 composition, and shoot themselves in the foot by often giving ambiguous Sc-Y-La / Sc-Y-* tables and always giving the Lu-supporting Madelung rule? Or if you'd like to do that, then carry on and plaster d-orbital explanations of hypervalence all over Wikipedia and see how long it takes editors at WP:CHEMISTRY to revert you. They are even in Greenwood and Earnshaw, you know. Page 685:

“

For descriptions of the bonding [in SF₆] which involve the use of 3d orbitals on sulfur, a net positive charge on the central atom would contract the d orbitals thereby making them energetically and spatially more favourable for overlap with the fluorine orbitals.

”

A very standard, often taught explanation of SF₆ involving sp³d² hybridisation by the sulfur atom. It's also completely wrong as studies have been demonstrating for decades. We listen to the studies, not the textbooks. Same for group 3.

Except that you then have to note that this is still not quite it, because an element may show slightly different configurations as a solid than it does in a chemical environment, so looking at just condensed phases in the pure elements alone will not be enough. You must look at all La compounds. Therefore you must simply ask what orbitals can be used by a La atom in any chemical environment as the proper generalisation following the spirit of what Scerri has suggested. Can we agree on this?

Thorium uses its 5f shell like a perfectly respectable f metal. Lanthanum and actinium do the same with 4f and 5f; lutetium and lawrencium never do. There is no consistency problem there. Outer f electrons in the ground state are indeed not necessary for an element to go into the f block, but some kind of f involvement in chemistry surely is, or else the name means nothing. Can we agree on this?

And, BTW, Scerri says the same thing (my bold):

“

More generally, electronic configurations represent a first-order approximation. An atom does not possess an electronic configuration in a literal sense assumed in general chemistry but exists in a superposition of many different configurations. In addition, electrons in any particular atom cannot be distinguished, which means that speaking of an atom as actually having this or that d electron for example is also strictly an approximation.

”

You see? There are many relevant configurations. Not only is it irrelevant which one is the ground state when many are so close, but also these many different configurations may include those with 4f occupancy and chemical activity for La! We cannot, for the reason of the last sentence, talk about the differentiating electron either. (Reminds me of the one-electron universe postulate, BTW.) The only thing that will remain consistent is chemically active subshells: all else is irrelevant la-de-dah. Can we agree on this?

I appeal to Scerri's cogent reply:

“

It is natural to ask what the long-form might look like in using Lavelle’s favored grouping as opposed to the one favored by the present author (9). The answer is that Lavelle’s grouping presents us with a choice between two options. Either the d-block must be split so as to insert the f-block elements between groups 3 and 4 or, if the f-block is inserted between groups 2 and 3, the sequence of increasing atomic numbers is violated. While the first choice is possible, but undesirable, the second one is a nonstarter. Splitting the d-block is undesirable because it only serves to accommodate the wish to group together scandium, yttrium, lanthanum, and actinium. To justify this ad hoc move would require an independent argument, but one that is especially not available to authors such as Lavelle who maintain that the d-block perfectly reflects the filling of five d orbitals by ten outer electrons. Why should there be a break only between the first and second of these electron-filling processes?

”

Why would anyone want to split the d-block, when it is abundantly clear that lanthanum may use its 4f electrons for chemistry and that the collapse has started there already, and that Sc-Y-Lu-Lr gives a more homogeneous d-block rather than having to create ad hoc arguments for La when it inevitably acts abnormally for a d element? The only argument we ever had for one d electron hanging up was condensed-phase configurations which we thought erroneously mostly showed fⁿds². But now we know that they don't. Actually they have lots of terrible irregularities and fractional orbital occupancies! Not to mention that by their logic, not only is La more of a d metal than Lu (2.5 d electrons vs 1.5, which already torpedoes the "one d electron hanging up" idea), it is also more of an f metal than Lu (0.17 f electrons vs 0; no, I am not interested in complaints that this is for the wrong allotrope, because that allotrope is metastable at STP too), and Lu fits better under Y (both have about 1.5 d electrons) than La (which has 2.5)! Can we agree on this?

So, if condensed-phase configurations don't work (because just because an atom shows one configuration in the metal doesn't mean it'll show the same one in a compound) and gas-phase configurations don't work, we are forced to use the most general form: all possible chemically relevant configurations. This is not something I made up, it is following Scerri's call against focusing too much on ground-state configurations!

Then it is utterly obvious that the Sc-Y-Lu form is better because 4f may be occupied and contributing as a valence orbital for La, just like 5f for Th! Can we agree on this?

And the n+l rule, while it fails quite badly if you insist on following the order "6s < 4f < 5d < 6p" for this reason, is actually quite correct if you note that the big breaks happen before each s subshell (whence the s-block symmetry break): (1s), (2s 2p), (3s 3p), (3d 4s 4p), (4d 5s 5p), (4f 5d 6s 6p), (5f 6d 7s 7p), with free ordering within each set of parentheses depending on the element involved and its chemical environment. But we see absolute n+l regularity in terms of when every subshell but the s ones become inactive.

And condensed-phase configurations were the very argument that convinced you to Sc-Y-La in the first place! Shouldn't you be convinced back if it later emerges that they don't work and the proper relevant thing to look at supports Sc-Y-Lu? Especially now that we can see from the quotes that it's not only me saying all this, but tons and tons of reliable sources, including some you quote yourself?

This is very much a "last chance" to see if further argumentation is worthwhile. The points where I ask "can we agree on this?" are so clear from the literature that they can hardly be refuted anymore. Including from sources you yourself cite. Well, in the past, regarding the elementary lack of understanding of "predominantly ionic/covalent", you have been at loggerheads with me, no matter how much reason and how many times I gave sources explaining the situation, until you found your own source saying the same thing that I did. Well: now I have quotes from your own source saying what I and Droog Andrey have endlessly been saying back at you. Are you going to accept them now, or are you going to persist in going for arguments that are contradicted by reality as even your own sources agree it is? Double sharp (talk) 06:14, 16 May 2020 (UTC)

Naturalness of conventions

@R8R, Droog Andrey, Дрейгорич, and Sandbh: Actually, let me just explain my attitude re conventions, with some examples from mathematics that I hope can be followed. (Dreigorich, I am afraid this will be rather a long read, but I think you will like it. I have tried to be as clear as possible, so that I can write something and not have to issue too many follow-ups explaining it.)

As for whether mathematics is a science, I will just quote Vladimir Arnold: "Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap." And if you want a philosophical perspective on this, read Imre Lakatos' Proofs and Refutations.

In principle, one did not have to define the primes the way we do now. We could have carried on with the old definition that 1 was a prime. After all, it is divisible only by 1 and itself. And everything would be self-consistent. It is just that if you did that, then the way mathematics ends up being, you find yourself having to special-case out p = 1 all the time. (Just think of the fundamental theorem of arithmetic: with 1 as a prime, prime factorisation is no longer unique.) And that's what makes you realise it's a reasonable categorisation.

And in principle, there was no reason to come up with the notion of a normal subgroup: it is simply that they are the answer to a very natural question "what can the kernel of a group homomorphism look like", and if you don't invent them, then the development of group theory basically grabs you by the throat and forces you to. And that's what makes you realise it's a reasonable category to define.

Well, so it is here. Is it reasonable to define "lanthanide" to exclude lanthanum, and "actinide" to exclude actinium? No, and the reason for that is that if you try doing that you will end up saying "lanthanum and the lanthanides" all the time. Because when Nd does something, say, odds are good that La does it too. So that's not a reasonable definition. And if you look at electronic structure of compounds, it's also not terribly useful because La and Ac both have f involvement in their compounds, just like Ce-Yb and Th-No. In fact thorium is the biggest argument here: if you did exclude La and Ac, it becomes a double standard if you don't go ahead and exclude Th as well, even though it does the exact same thing as they do. And doing so is basically a great big warning sign that your categorisation is artificial. It is like talking about "the primes and 1", or (even worse) "the primes and 57". You are creating an excuse to insert an element into your set with vastly different properties. You may get away with imposing that on Nature, but Nature will have Her revenge, and that wrongly included example will impose itself as a knife twisting deeper and deeper into every generalisation, as an exception that you will always need to check and treat separately. And it is not even going to form a fruitful generalisation of your original definition for you, if it is that alone.

And that is why: even if we may in principle make up categorisations as we wish, there are natural and non-natural categorisations.

Now, is it reasonable to define "lanthanide" to exclude lutetium, and "actinide" to exclude lawrencium? For the lanthanides, indeed it would be a bit awkward chemically. But not physically, where we can immediately see that La-Yb have a stark difference from Lu: the first fourteen have f involvement, the last doesn't. And I trust I have referenced enough papers here arguing about why this is important for physical properties. So, let's call it a draw for the Ln. For the actinides, it is without question reasonable. And why can I say that? Simply because lawrencium stands as a reproachful counterexample to many, many, generalisations you can make about the late actinides. The late actinides are divalent in the condensed phase: yes, but not Lr. The late actinides have significant redox chemistry with the +2 and +3 states: yes, but not Lr. They are for this reason generally predicted to have lower densities than the preceding elements: yes, but not Lr. They are also for this reason generally predicted to have lower melting points than the preceding elements: yes, but not Lr. They show an increasing stability of the +2 state as you go across the series: yes, but not Lr.

The last one may be countered by noting that even so, the +3 state is still the more stable one with the sole exception of nobelium. It is true, but: this is throwing away useful information. As is common knowledge, the species predominating in aqueous solution will depend on the conditions. What is the pH? Is the environment oxidising or reducing? This will all affect the more stable species and sometimes the more stable oxidation state. Why do you think people are worried about acid rain? Why do you think people are worried about hexavalent chromium, seeing as trivalent chromium is the more stable oxidation state? And why do you think already fermium and mendelevium may be separated from the other heavy actinides specifically by reducing them somehow to the +2 state? (Shades of Sm, Eu, and Yb indeed!) Asking for only one most stable oxidation state to treat as a generalisation reduces this richness to "Main screen turn on!", as if we were composing all functions with sgn, and provides an impoverished and non-general approach to chemistry that does not further understanding. And that's why I claim: while the statement of mine that R8R refers to above is correct, and so is the one that Sandbh refers to above, they have different levels of explanatory power, and the first is clearly superior.

It is true that Lr³⁺ elutes in the sequence where you would expect it, standing in relation to Md³⁺ as Lu³⁺ stands in relation to Tm³⁺. But this is surely not enough to claim a significant connexion. Yttrium acts like a lanthanide in every respect thanks to the lanthanide contraction ensuring it falls within their range in variation, and scandium is like a lanthanide even smaller than lutetium (which therefore gains some exceptional properties). No²⁺ elutes between Ca²⁺ and Sr²⁺, but that doesn't make it an alkaline earth metal, earlier. And good luck getting the early actinides like thorium and uranium to appear in the +3 state in the same conditions that will let mendelevium be in the +3 state as well, for instance! Similarity of chemistry extends beyond groups and is not limited to elements in the same group. Yttrium vs lanthanum is not out of place as such a similarity; I will note in fact that the similarity Al-Sc is in some ways chemically stronger than Al-Ga (mostly because Ga is, thanks to the 3d contraction, more acidic than Al). Tungsten to uranium was another such that was the chemistry battleship, as Sandbh has put it, until Seaborg came along. (No doubt, if we were having this dispute in the 1940s, I would be arguing on Seaborg's side and getting dismissed on the grounds of the dominance of U below W. Which would have, amusingly, been more real than the dominance of La below Y, which has always had to compete with * below Y even when Lu below Y was not so common an option!) Just compare these with the often rather worse resemblances from the 5p to the 6p elements, which are real congeners!

No, we must go further than that when describing the periodic table. Mendeleev used chemical resemblances, and physical properties, but he had no choice. He did not understand electronic structure. No one did at the time, the electron not having yet been discovered! Bohr made a better go at how electronic structure explained chemistry, but he did not fully understand it either then. They have excuses. Now we know, and we have no excuse not to use it and go deeper. Similarly, maybe it was reasonable to call 1 a prime before much number theory was developed. Once enough was developed to make our way to the fundamental theorem of arithmetic and beyond, it stopped being reasonable.

And indeed, it turns out that these are reasonable, self-consistent sets united by a single, amazingly simple property: they are respectively 4f and 5f elements. When you examine the chemistry of the Ln and An, you're always going to have to take into account that 4f is completely drowned into the core at Lu and 5f is completely drowned into the core at Lr. These two always are special cases among the Ln and An. And that explains everything! Just as the fundamental theorem justifies why you don't want 1 to be a prime, the significant distinctiveness of Lr from the rest of the late actinides is totally explained by the fact that the other late actinides are using 5f to get to +3, and Lr doesn't need to. The dawn of electronic periodic tables has been a sweet breath of generalisation. We would be insane not to take it. It has let us put to rest such annoying goblins as B-Al-Sc and Be-Mg-Zn. Why not let it speak its mind on group 3 too?

In some specialised contexts, where some primelike behaviour from the units is the important thing (i.e. noting that Q viewed as a multiplicative group is generated by the primes and the unit −1), the units are sometimes treated as primes. No problem: this is about the same thing as referring to "rare earth elements" as a category. There are important similarities there, that go beyond the block labels. And in this case, we are well justified in referring to "the 4f elements and group 3". As well as things like Ac and Lr, indeed, which mostly get overlooked purely because of their strong radioactivity (see for instance how Pm is kind of ambiguous as a rare earth because it is almost totally absent from nature). But the basic category, suitable for use by the beginning students, is pretty clear: we are talking about the aufbau, we see when each subshell is chemically active, and the regular pattern is not only mathematically pretty and symmetrical, but it also fits exactly with reality: 4f has its activity between Z = 57 and 70 only (it may be pushed to 55 and 56 under high enough pressure, but never to 71), and 5f has it between Z = 89 and 102 only (maybe to 87 and 88 under pressure, it hasn't been checked AFAIK, but never to 103 according to predictions). So simple, so beautiful! Stuffing Lr in with the 5f elements will have Nature twisting the knife into your generalisations until you repent of the idea.

Ah, but not only that. Not only does Lr never fit in with the 5f elements to create a self-sufficient category alone, but it fits in perfectly with the 6d elements. Lawrencium acts exactly like an early 6d element (up to bohrium): strongly preferring the group oxidation state, not having its expected increase in size totally destroyed by the actinide contraction (it is reduced a bit, like for Rf-Bh, but by a nonzero amount, unlike Ac), and in general being what 5d "should have been" without the lanthanide contraction destroying that size increase and the expected electronegativity decrease! It follows the trends perfectly. Just try to fit actinium onto them, it will forever be the bane of your generalisations. The same is seen to a lesser extent with lanthanum vs lutetium with the 5d elements. While it's true that Lu makes a reasonable trend continuing down from Y or to the right from Yb (which cannot be said analogously for Lr), between La and Lu, there's only one element that makes a homogeneous d block: lutetium. Including lanthanum instead results in it being the bane of generalisations. We may look for instance at physical properties: just examine melting points, densities, superconductivity. Then go on to chemical properties like coordination ability, reactivity, hardness, etc. Lanthanum is just not a natural member of the "5d elements" category. If you force it in there, it will chafe at its chains like 1 forced together in the primes, and it will wreak havoc on all your careful generalisations that were so fruitful for explaining crystal structures, superconductivity, and almost everything you would look at that would otherwise show a perfect, crystal-clear regularity.

Is there a mathematical analogy for this? Why yes, I think there is. After realising the distinctive properties of 1, and cutting it out of the primes, mathematicians gave a name for things with such properties. They're called "units". ±1 are the units of the integers, for example. There it has found a new home with similar objects in its category, and Nature smiles at us again and lets us generalise fruitfully.

The La table is inconsistent, in how it treats actinium vs thorium: that is the death knell of naturalness for a categorisation, just as much as it was for forcing 1 in as a prime under slightly different criteria. (For primes must have two factors, and 1 has but one.) Quite a few texts have abandoned it; many luminaries have argued for it; most authorities arguing about the issue argue for Lu; and many texts who have not abandoned the issue at least show the Lu-supporting Madelung rule anyway, therefore creating a self-contradiction. Curiously, despite that Lu-supporting Madelung rule being even more of a convention than the La table (which is often presented ambiguously in a way that also suggests * below Y), Sandbh does not see fit to keep that. Indeed in this case he seems totally willing to take on the chemistry battleship. Just look at item V in my alphabet of Sc-Y-Lu arguments, readily available now in archive 44:

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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); [Double sharp (talk) 03:29, 7 May 2020 (UTC)]

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)

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Well, I shall not speculate as to why. The convention is inconsistent; reliable sources focusing on the question have made up their mind. It is our job to follow them. Not even something like Greenwood and Earnshaw, which for all its glory never addresses the topic of which element should go below yttrium with solid argumentation, but treats it as a given that La and Ac should be there. Why should people unaware of the raging controversy, visible the moment you ask Google Images for a periodic table, matter more than the luminaries, crowned by Landau and Lifschitz, who actually looked at the issue? Double sharp (talk) 15:56, 15 May 2020 (UTC)

Your argument is not unreasonable but think about the argument itself. So if we go about what's natural and what isn't, then a careful reading of that will yield the idea that what's natural and what isn't is, in the end of the day, relative. I mentioned this in a previous discussion, but look at this article. It argues about how we think with different sets of basic concepts in mind, in this case, the concept of colors. I think it's been apparent enough from the discussion that has unfolded that you and Sandbh have different concepts of what to value. With that knowledge in mind, it is much easier to progress properly in a discussion.

Now you're talking about what's better rather than what's right. I like that; I think that's precisely what the talk should be about if we want to get anywhere. But think about this: every sequence of logical implications has to start somewhere, with some axioms. If you value different things differently, that could be thought of as different axioms if we feel the need to stay within the realm of logic. But in that case, you can't logically prove anything to Sandbh (and neither could he to you) as you have different axioms. This means you need to agree on your axioms first if you want to get anywhere. What axioms are better cannot be chosen within the realm of logic itself, so Sandbh is right when he says there is no logically provable answer. Not to mention that when we choose our axioms, we normally do that in a backtracking way that somehow corresponds to what those axioms would yield. Moreover, translating everything into the terms of logic would be so tedious that a) we usually don't even realize how tedious that is, and b) we don't have the patience to do that, so we either give up or declare those little things unimportant to get somewhere, and that is if we even acknowledge them in the first place. Moreover, if we were somehow able to distance ourselves from the results (to make it truly logical), why would we want to recognize such abstract results? This is why Sandbh is absolutely correct to say "there is much more to the world than logic."

And if you think about it some more (which is not a realization that comes naturally in the first place), you'll notice that there is always a component of relativity in any discussion. "Inconsistent" in your discussion is really "doesn't sit very well together but still not in an principally irreconcilable manner," because you make your own assumptions there. That is, in fact, correct even for scientific discussions (this is also why the border between mathematics and science includes theoretical physics in the mathematical category, rather than in the scientific one). And that again brings us to the question of how to think about it. I hope this consideration of mine will help you reconsider the general proceedings of this discussion.--R8R (talk) 14:14, 17 May 2020 (UTC)

@R8R: I can accept to some extent that what we choose to focus on is a choice, but it seems to me that:

(1) asking for f elements to use f orbitals for chemistry is somehow the obvious idea, and;

(2) since the d-block elements are precisely what is under dispute as well (at stake is whether La or Lu is the first element in the 5d series), I note that in almost every way lanthanum is a clear outlier for the d-block. It never fits the trend significantly better than lutetium (boiling point is where it comes the closest, but then the difference is small compared to the jump to Hf anyway), and often fits worse. We may start with the properties table I quoted:

property	La	Lu	Hf	Ta	W	Re	Os	Ir	Pt	Au	Hg
m.p. (K)	1193	1925	2506	3290	3695	3459	3306	2719	2041.4	1337.33	234.43
b.p. (K)	3737	3675	4876	5731	5828	5869	5285	4701	4098	3129	629.88
specific heat capacity (J/(g*K))	.195	.154	.144	.14	.132	.137	.13	.131	.133	.129	.14
EN (Pauling)	1.1	1.27	1.3	1.5	2.36	1.9	2.2	2.2	2.28	2.54	2.0
EN (Kulsha-Kolevich)	1.11	1.31	1.38	1.46	1.54	1.55	1.67	1.75	1.84	1.93	1.81
Density	6.145	9.84	13.31	16.654	19.25	21.02	22.61	22.56	21.46	19.282	13.5336
Young's modulus	36.6	68.6	78	186	411	463	???	528	168	78	???
Bulk modulus	27.9	47.6	110	200	310	370	462	320	230	180	25
Resistivity (nΩm, close to r.t.)	615	582	331	131	52.8	193	81	47.1	105	22.14	960
Brinell hardness (MPa)	350-400	893-1300	1450-2100	441-3430	2000-4000	1320-2500	3920-4000	1670	310-500	188-245	???
Heat of fusion (kJ/mol)	6.20	22	27.2	36.57	52.31	60.43	57.85	41.12	22.17	12.55	2.29

And then we can note that putting lanthanum into the d-block makes it the extreme in hardness, reactivity, in high coordination numbers, but putting lutetium in there does nothing of the sort as it is even less basic than yttrium. If you try Ac vs Lr, actinium emerges even worse from the predicted 6d properties we have:

property	Ac	Lr	Rf	Db	Sg	Bh	Hs	Mt	Ds	Rg	Cn
m.p. (K)	1323	1900	2400	???	???	???	???	???	???	???	283
EN (Kulsha-Kolevich)	0.97	1.29	1.34	1.41	1.49	1.59	1.72	1.83	1.92	1.99	1.91
Density	10.07	15.6	23.2	29.3	35.0	37.1	40.7	37.4	34.8	28.7	14.0

And clearly the principle of increasing basicity as you descend the table is impacted by kainosymmetry (the even-odd period divide as a result of orbitals without radial nodes); Ga³⁺ is less basic than Al³⁺. So, it is not problematic at all that Lu³⁺ is less basic than Y³⁺.

The only excuse is if you claim that 4f contracts only after La and therefore that the first d element should precede the Ln contraction and not suffer it. But that's just plain against the facts: Hamilton's 1965 paper shows that in H-Ba, the 4f orbitals are hydrogenic because they are far enough from the nucleus that it can be treated as a point potential, but La has rare-earth-like 4f orbitals. Condensed-phase configurations won't save you either. Not only does fcc La (metastable at STP) have 0.17 of an f electron per atom (Glotzel), but I also note that you do not have "one d electron hanging up": in the condensed phase configurations, Y and Lu have 1.5 d electrons per atom approximately (Pettifor as Sandbh cited, but it undermines the La points in reality), but La has about 2.5(!). So that argument for breaking the 5d block also doesn't work.

This period divide by parity is normal for elements in the even periods outside the s-block; just look at the Madelung rule graphic, with the s column moved to the left like it usually is in the periodic table:

1s
2s       2p
3s       3p
4s    3d 4p
5s    4d 5p
6s 4f 5d 6p
7s 5f 6d 7p

Well, we know the first orbital of each given angular momentum value (1s, 2p, 3d, 4f) is smaller than expected, the contraction will appear for the first time and counteract the expected increase. So for that reason we see an even-odd distinction in periods, at least before relativistic effects mess it all up. The 2p elements are small and highly electronegative, being strong oxidisers in their highest oxidation states from N onwards; the 3p ones, significantly less so. The 4p ones move a bit backwards towards the 3p ones (compare Cl(VII) and Br(VII), among other things) because of the 3d contraction; the 5p ones can increase again.

The same thing is going on with the d elements. 3d vs 4d mostly acts like 2p vs 3p. With the 5d row we have an almost exact cancellation of atomic size increase by the 4f contraction, but we also have relativistic destabilisation of 5d, so we end up almost perfectly recreating the 4d motif at the beginning. And that generalisation only works with Lu under Y: only then is the general motif of the early d-block preserved. That is: one distinct 3d element, two very similar 4d and 5d elements, and a 6d element that acts like a natural continuation of the trend from 3d to 4d that got stalled. (Lr acts perfectly reasonably there, like Rf through Bh, too; this is thanks to relativistic 6d expansion.) There's no reason to compare it with the s-block when something completely different is happening there: the 4f contraction comes right after Ba, not La.

And in the s-block it is mostly absent, further cementing my point that this block should be treated separately. But you can see it passing from 1s to 2s of course; and because of the worse shielding of 2p compared to 1s, which is admittedly still very good, you can see that the increase of reactivity and alkalinity from Li-Na and Be-Mg is somewhat attenuated compared to the pairs Na-K and Mg-Ca. But it's a small effect, and after this it stops because the important bits of the core are still the p orbitals of the previous shell from then on. You start getting relativistic effects only later for 7s because 6p_3/2 relativistically expands and 7s contracts, but that is a different regime.

I know Sandbh has pointed to Restrepo, but I think we can obviously see that the facts of physical and chemical properties unanimously proclaim that putting La in the d-block makes it a clear outlier. Lanthanum is not more similar to transition metals than lutetium by any obviously relevant metric. Not stoichiometry as Restrepo uses, which will of course make it impossible to compare Lu with Hf due to differing oxidation states.

As has been noted: Sc-Y-La usually gives trends like the s-block groups (it is like K-Rb-Cs and Ca-Sr-Ba), whereas Sc-Y-Lu usually gives trends like the d-block groups (it is like Ti-Zr-Hf and V-Nb-Ta). But the old argument that group 3 is more like groups 1 and 2, than groups 4 and 5, is simply against the facts. Well, if you want to look at "forms aqueous cations", then group 4 has Zr⁴⁺ and Hf⁴⁺. Well, if you want to look at "hard bases" (prefer N-, O-, F-donor ligands to heavier p elements), then not only group 4 but also 5 and 6 are like 1–3. Well, if you want to look at organometallic chemistry, group 3 and 4 do not act very differently! Not to mention that the lanthanides clearly have properties ranging from the more s-like lighter ones to the more d-like heavier ones, and the actinides clearly have similarities to both s metals (in reactivity) and d metals (in variety of oxidation states). The whole idea of "keep similar elements together" actually supports Sc-Y-Lu, because it puts the f block between the s block and the d block.

So: if we plead for "follow relevant configurations" as I do, we get Lu. If we plead for "make the blocks more homogeneous", we get Lu. If we plead for "make the physical trends more homogeneous", we get Lu. If we plead for "make the chemical trends more homogeneous", we get Lu. If we plead for "make the condensed phase configurations more homogeneous", we get Lu. If we plead for "show the regularities", we obviously get Lu. If we plead for "show the irregularities", we also get Lu (because the only such is the s-block). So even if what's natural is relative, the vast majority of concepts if applied as criteria either support Lu in group 3 or get bogged down in inconsistencies (the usual litmus test being "see what it says about Be-Mg-Zn or B-Al-Sc"). And I've already done the same thing above for Lr, pointing to lots of properties that Es through No have that are not shared by Lr. That seems to be a powerful argument that Lu in group 3 is natural independently of your criteria!

Meanwhile, the only thing Sandbh has is appealing to convention; appealing to ions (Ce³⁺ to Lu³⁺) that obviously don't work anywhere else (the 4f issue is a one-off, it might not even happen for 5g because of relativistic expansion of high-angular-momentum orbitals; and periodicity is basically the opposite of one-offs); going on ground-state configurations that expert chemists (there is no other word for Seaborg) understand are not everything for chemistry and create the thorium problem (well, thorium was discovered first, put below hafnium, and is the first element to have 6d²); and noting that nothing changed in the chemistry of Lu after the configurations were discovered. Well, as for the latter – nothing changed in the chemistry of uranium when Seaborg moved it to the actinides, nothing changed in the chemistry of beryllium and magnesium that is still more similar to zinc than calcium. But Sandbh does not propose to move them back.

So apparently all there is is convention, as that is the only thing that separates the issues of uranium and beryllium from the issue of lanthanum. A convention of authors who often show their table ambiguously between Sc-Y-La and Sc-Y-* and then ally it with a Madelung rule that supports Sc-Y-Lu. This does not seem like a sound basis for judgement, whether scientifically or on Wikipedia weighing the sources. Double sharp (talk) 04:09, 19 May 2020 (UTC)

Well, you were there some time ago, you must see why, say, it took Droog Andrey a year (as you said) to change your mind back to -Lu-Lr. You see, some people can be rather stubborn in their thinking and there is also not a Droog Andrey available for everyone. While I am sympathetic with your argument in itself, I find it important to always try your opponent's shoes so that you can argue better and you actually increase your chance of convincing them. Not to mention that they can be the right ones sometimes :) it's not that Sandbh has nothing, it's that you don't recognize the power of what he has; whether you do that rightly or wrongly (this is where that "people can have different starting points" bit comes in), there's a distinction between the two. Ideas can in principle be wrong but at the same time powerful and alluring, and that's important to keep in mind in particular because if your opponent doesn't feel neglected, you have a better discussion if for nothing else. Also, ideas can in principle be wrong but at the same time very valuable as they help you move on from there or they give a lot to think about and reflect on, if you need any help finding worth in an idea you don't agree with; it may not necessarily also have to do with you personally.

But as long as you don't devalue other positions, you're very free to think what you want to think and try to convince anyone in that, too. There is a good reason why we generally perceive people who stay calm and listen to their opponents even in hearty discussions, even when they say the stupidest things as people who are reasonable and command charisma and this makes people like them. Granted, their attitude also sometimes may need to be changed to retain that outlook when things really go south, but we're clearly not in that kind of debate.--R8R (talk) 21:01, 20 May 2020 (UTC)

@R8R: The main reason it took a year is that I wanted to reserve judgement until DA's calculations were ready, if you recall. ^_^ You may notice that I was almost convinced during the discussion itself in Archive 33. And that thereafter I was sitting on the fence and reserving judgement till I found out more, mostly. And that my response to him refuting arguments that don't work was not to keep using them as if nothing had happened, but moving to other ones.

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@Droog Andrey: You're convincing me more and more back to -Lu-Lr. ^_^ What's doing it for me is the paucity of f-orbital involvement in Lu and Lr, where they seem like core subshells, which is different from the still-present 3d helping of the bonding in Zn even if it cannot be ionised. The La and Ac problem is then a sort of "delay" in the heavy elements (especially for Ac), and while I don't like how neither has an f-electron in the ground state, I prefer the "pre-f" character of La to the "non-f" character of Lu. (We also see a delay in the 6d metals; Rf does not seem to show many transition metal chemical properties, so that the 7th period of transition metals chemically looks like Db–Cn instead of Rf–Rg as extrapolation would predict, although physically the row would indeed look like Lr–Rg like Lu–Au; Cn after all is probably a gaseous metal and acts like a more extreme version of Hg plus relativistic effects allowing +3 and +4 oxidation states.) The "pre-d" character of the heavy group 2 metals is an irritant but I think the "supporting d" character of the group 12 metals (blossoming into full-blown d-character at copernicium) should beat it. Most of all, the simple blocks work pretty well, and the differences between La/Ac and Lu/Lr are minor besides those of He to Be or those of E164 to Pb. ^_^ (What convinced me away from the block-starting argument is the absolute mess it would create in the 8th period as well as the lack of f-involvement in Lu and Lr; I agree that Occam's razor should be used here.) Then we see this confirmed by the analogous positions of Eu to Mn and Yb to Zn.

I still think that making the case for Lu/Lr is not that simple. While Lu/Lr is the position of Jensen and Scerri, I'm absolutely not conviced by Scerri's arguments for it. (I'll note that he's also the one who suggested using condensed-phase configurations; but I'm inclined to think now that you can rationalise the promotion to and ionisation of 5d6s2 in a similar way to how you rationalise the occupancy of 4s in the 3d metals despite the changes they make to the Madelung order. I am inclined to say that TM, Ln, and An chemistry is essentially that of inner orbitals and that that is its main difference from main-group chemistry. As a result a good argument against condensed-phase configurations is that they would have the d-block end at group 10 with Ni, Pd, and Pt. ^_^) Jensen's arguments are a better start but I feel they are incomplete without looking at the relative d- and f-involvement of Ca/Sr/Ba/Ra vs. Zn/Cd/Hg/Cn and La/Ac vs. Lu/Lr as you have done. Indeed, the only reason I haven't changed my mind totally yet is a desire to go research this a bit more first. ^_^

BTW, when you say 'the term "d-element" is used wider than "transition metal"' in the Russian literature, does that mean that "d-element" is more common (say, in referring to things like Fe), or that both terms are in use but that "d-element" has a wider scope (which would be something like how in some English-language usage Zn is a d-element but not a transition metal)? Double sharp (talk) 03:24, 15 March 2018 (UTC)

”

(BTW, I am still curious about that last question.)

Well, the next time it was raised was in Archive 36:

“

@Double sharp: I was re-reading Jensen’s article on the treatment of group 12, ref: [8]. Spectroscopically and chemically he observed that Be and Mg are more like Zn, as Mendeleev showed them, but they eventually ended up in group 2 on the grounds of their electron configs being similar to Ca etc. Is that how you understand it?

I presume this is the same reason (i.e. similarities in electron configurations) why La and Ac have so far remained below Y in group 3? [Sandbh]

I believe electron configuration is a valid reason, though periodic trends such as atomic radius and electronegativity in the alkaline earth group may also be important to consider when grouping elements. ComplexRational (talk) 16:07, 11 November 2018 (UTC)

ComplexRational's answer is closer to how I see it; there are many factors all playing a role here, but electron configurations are preeminent among them. Be and Mg are closer to Zn, but that is because they are small. We expect an increase in size if nothing intervenes, so Be-Mg-Ca is preferable. To show that nothing intervenes, you then have to show that the d-block hasn't started yet (as otherwise the d-block contraction is a good enough reason to put Al above Ga instead of Sc). The "pre-d" behaviour of Ca, Sr, and Ba is then something like the "pre-f" behaviour of La and Ac. So you then have to look at how active the 4f shell is in La vs Lu compounds (i.e., if you neglect the 4f contributions in the calculations of analogous La and Lu compounds, which one ends up looking closer to reality?). I recall we went through a lot of this with Droog Andrey early this year, though that discussion is paused and not quite finished. Double sharp (talk) 00:27, 12 November 2018 (UTC)

”

And, as you know, then came Archive 38, and the great split between me and Sandbh started because I now knew enough to realise that differentiating electrons are not too relevant for chemistry (which were doubts that he apparently "hadn't considered"). And that's when I first made a statement going back to Sc-Y-Lu on the grounds that if the difference between La and Lu was this small, there was no point in block-breaking and overselling the difference as if it was something as big as He:

“

So the only reason this last argument didn't quite convert me back to Sc-Y-Lu again then is that the MP2 test I linked to showed a case of La and Lu both with around equal 4f involvement. (I'd leave the actinides out of it now, because otherwise we get a very awkward problem in the early superactinides.) But rereading that thread, I am of a mind to accept Sc-Y-Lu now even so due to the Occam's razor argument; if the case is so complicated that chemists have been wringing their hands about it for so long, then it's not worth splitting the block based on a smidgen on one side or the other. We can just have a simple rectangular d-block and worry about the fine details later. In other words: it might as well be Sc-Y-Lu, as it looks simpler that way, and no heads will explode like they would for He-Be-Mg. Double sharp (talk) 16:05, 6 January 2019 (UTC)

”

Well, at that point I still gave Sc-Y-La some credit for reflecting the delayed collapse of the 4f orbital; but then I read more and now understand that this means absolutely nothing for actual chemistry (not to mention thorium 5f), so I don't even give it that now. And, indeed, I realised that period 8 already is a strong argument against it over a year ago:

“

Well, I like my criteria to be as simple as possible, but not simpler. If going strictly by differentiating electrons leads to putting He over Be, then my conclusion is not "well, maybe He should be over Be", my conclusion is "well, maybe what we have is too simple". Also, looking at the chemically active orbital with the highest ℓ only demands that we examine one element; looking at differentiating electrons demands that we look not only at the element in question, but also the one before it (pleading common sense for hydrogen, of course), so in a sense a one-element criterion beats a two-element one on parsimony.

But I think I need to make one more point clear: I do not dispute that helium is an s-block element, as that is obvious. I just do not think that mandates that we place it with other s-block elements. Period 1 is in any case not a big precedent for anything, as nowhere else is there only one shell available with only one orbital (or, in hydrogen's case, with only one electron). But the "delayed collapse" problem in periods 6 and 7 and the "supervalent hybridisation" problem in group 2 has the potential to wreak real havoc in the superheavy region. Lv is expected to be able to show supervalent hybridisation with 8s, and Og even has a positive electron affinity. Of the expected mess of delayed collapses in period 8 – our current extended table template is pretty inconsistent in this respect. To my mind now, if you want to put E121 in group 3 with Sc, Y, La, and Ac because [Og]7d18s2 is such a low-lying state for it and 5g isn't active yet, you also need to put E122, E123, and E124 below Th, Pa, and U by the same logic, and no one is going to do that because you literally won't be able to draw it all the way to E172 without either putting two elements in the same place, putting elements out of atomic-number order, or going for a more fluid interpretation of how electron configuration should inform periodic table placement. But if we are going to have to go for such a fluid interpretation, then why not do it for La and Ac as well? Double sharp (talk) 16:27, 12 January 2019 (UTC)

”

Here we go. Roadmap to the current situation, where I am fed up with the double standard of not applying criteria anywhere else:

“

Hmm. When I made the D/E suggestion I never considered it'd be called on to make a ruling on group 2/12.

I note that atomic numbers don't resolve the placement of He. Cleary, at least for chemists, there is an extra criterion that largely decides in favour of HeNe, rather than HeBe. I'd guess, at least for physicists, that the common core argument (set out elsewhere) justifies BeMg in group 2. Sandbh (talk) 02:05, 19 January 2019 (UTC)

If a criterion is supposed to be global enough to answer the question of group 3 without looking into the finicky details of group 3 chemistry, then it strikes me that it ought to be test-driven on other cases. That was what I was aiming to do when I brought the group 2/12 question into the equation.

Sure, atomic numbers don't resolve the placement of He. They do on the other hand firmly tell us that wherever it goes, it must appear between H and Li, so it fixes horizontal placement without any further questions; differentiating electrons have some way to go before fixing vertical placement with anything like that certainty. Incidentally, I think physicists may not find the question of Be and Mg that clear, because Cu and Zn have spectra analogous to those of the alkali and alkaline earth metals respectively, and not those of their chemically transition-metal predecessors Sc through Ni (Jensen mentions this in his paper on group 12). Knowing that Ca, Sr, Ba, and Ra have empty low-lying d-orbitals, while Be, Mg, Zn, Cd, Hg, and Cn do not, a spectroscopic criterion might well put Be and Mg atop Zn. Double sharp (talk) 03:11, 22 January 2019 (UTC)

”

And I was already starting to refer to chemically active orbitals!

So what does Sandbh have, if not what I mentioned in the last paragraph? I don't see any power in arguing "this is the convention" if the convention is this inconsistent in the first place. And if applying that argument historically would lead to the conclusion that Seaborg should obviously not have been listened to for the actinide concept. Double sharp (talk) 03:53, 21 May 2020 (UTC)

P.S. Re "there is also not a Droog Andrey available for everyone" – not in general, but in this case he certainly commented. A lot. And explained way back in early January things that we were still fighting over not too long ago(!):

“

In fact, the table is parsed into blocks according to chemically active subshells in atoms. Differences in ground-state configurations have little sense, especially in d- and f-blocks where a lot of low-lying excited states are observed for the vast majority of the elements. Droog Andrey (talk) 11:19, 7 January 2020 (UTC)

”

And Sandbh just carried on with his citation, in spite of all the warnings from me and DA about how the concept of differentiating electron makes no sense to use here, backed up with citations ranging all the way up to Seaborg about how ground-state electron configurations are not everything for chemistry. Not only is this chemically irrelevant for the d and f elements in particular, it also doesn't even make sense looking at many ground state electron configurations. At the risk of repeating myself 9001 times: just tell me, what is the differentiating electron between vanadium [Ar]3d³4s² and chromium [Ar]3d⁵4s¹? The question makes no sense, as there is more than one.

I hope this adequately explains my obvious frustration above even if doesn't excuse it. Double sharp (talk) 03:39, 22 May 2020 (UTC)

Landau and Lifschitz

I feel the need to place L&L into context.

Double sharp, you wrote:

"Why should people unaware of the raging controversy, visible the moment you ask Google Images for a periodic table, matter more than the luminaries, crowned by Landau and Lifschitz, who actually looked at the issue?"

L&L's "look" at the issue comprises a footnote in a 600+ pp book on quantum mechanics:

"In books of chemistry, lutetium is usually placed in the rare-earth elements. This, however, is incorrect, since the 4f shell is complete in lutetium; it must therefore be placed in the platinum group, as in Table 4."

I don't count this as crowing look; I'd regard it as a passing comment made without sufficient understanding of the chemistry-based subject matter. As Scerri (2020) observes, "Several of the authors who proposed Lu should replace the element La in group 3 were physicists, a factor that may have contributed to their being ignored by the chemical community." It's like saying physicists know better than chemists, never mind chemists have their own priorities.

There are ways and ways of bringing physics into chemistry, and L&L's 37-word footnote isn't (necessarily) one them. Sandbh (talk) 03:26, 16 May 2020 (UTC)

There is exactly the required understanding. 4f has already been completed, Lu cannot use its 4f shell for chemistry. That's exactly the decisive argument. And, BTW, it surely beats any number of books who present a form, do it inconsistently with their own Madelung rule (which is invariably the Sc-Y-Lu one), and never give any analysis at all why they do it. Double sharp (talk) 03:28, 16 May 2020 (UTC)

How conventions are established

In terms of how this occurs there is, as yet, no justifiable need for change.

To this end, here's a fine PhD dissertation (2018) by Robinson on Creating a symbol of science: The development of a standard periodic table of the elements. Robinson writes:

"The sociologist Lawrence Busch notes that 'the emergence of standards is almost invariably the result of conflict or disagreement,' after which a consensus emerges."

Robinson continues:

"There was certainly much disagreement over which form of the periodic table was best. As I show in this dissertation, this was particularly true in the case of pedagogical use, where the disagreements between and emerging consensus among chemical educators resulted in the current standard form of the periodic table."

I have some appreciation of the disagreement Robinson is referring to. The pages of the Journal of Education archive are full of articles proposing improved periodic tables. Whole books have been written about this (Venables; van Spronsen; Scerri etc).

On a scale of magnitude there has been no comparable disagreement wrt La or Lu. It was not until 1983 that Jensen sparked a flurry of interest in the question. His arguments (described by Scerri as "too selective") did not gain traction.

Some three decades on, we now have an IUPAC project (chaired by Scerri) considering the question. Luminaries such as Jensen; Philip Ball (past editor of Nature, no less); Scerri; and Restrepo are members of the project. Even Lavelle, a UCLA colleague of Scerri, is there.

Ahead of the recommendation of the IUPAC project I see no case for change. Sandbh (talk) 02:08, 16 May 2020 (UTC)

In fact, there is. Prior to 2016, we were going on with Lu on WP. The consensus for La succeeded because we gave scientific arguments that we thought were true at the time, but which we now know don't work: either their premises are false or the argumentation simply does not work. That's a very strong case to reopen the discussion: the old consensus has become invalid. Double sharp (talk) 06:38, 16 May 2020 (UTC)

Sorry that I just got around to this. Reading the discussion, I can see using nature as an argument against La and its analogy to using 1 as a prime number. The concept might have worked back then, but when more is known and the fundamental structure exposed, it stands naked with nowhere to hide, like a round peg in a square hole. No excuses. ― Дрейгорич / Dreigorich Talk 19:17, 16 May 2020 (UTC)

Straw poll among participants

@Sandbh, Droog Andrey, R8R, and Дрейгорич: No scientific arguments here, please, to stop going through the same cycle yet a third time. Under comments, we can maybe have arguments about the weight that should be put on different sources.

For a switch to Sc-Y-Lu

Strong Support. Double sharp (talk) 06:32, 10 May 2020 (UTC)
Strong Support. Droog Andrey (talk) 12:47, 11 May 2020 (UTC)
Support. ― Дрейгорич / Dreigorich Talk 06:35, 10 May 2020 (UTC)

For retention of Sc-Y-La

Support. Sandbh (talk) 07:28, 10 May 2020 (UTC)

Abstentions

Comments

I do not understand what the question of the straw poll is very well, and it makes a big difference to me. I would be opposed to a change in English Wikipedia right now, since Wikipedia is a tertary source, and it needs a good precedent for a change that could not qualify as original synthesis (or, as the local terminology goes, original research). I do think that a decision from IUPAC could be authoritative enough to overrule that if editors agreed on that; importantly, because the decision was made by somebody else, someone we could consider authoritative. I will also note that the current version was fixed in a RfC, which has a wider scope than a vote in our relevant but small project, and we'd need an RfC to override that decision. There are house rules here in English Wikipedia, and we have to respect them. At the same time, if I were writing my own self-authored book and were not subject to any house rules, I'd be very fine using a -Lu-Lr table.

Also, generally, it goes that there should be a consensus for a change in Wikipedia, not for retention of an existing policy, which is the status quo, after all.

Sandbh, I am thinking on your question. Will try to post some reply in a few days--R8R (talk) 20:50, 11 May 2020 (UTC)

@R8R: Well, my question is basically "what should be the default form of the PT on en.wp?"

And I get what you're saying, but IMHO this is not actually OR that WP policy would oppose. The reason being that the most reliable sources, by Wikipedia policy itself, are the ones that focus on the issue:

“

Information provided in passing by an otherwise reliable source that is not related to the principal topics of the publication may not be reliable; editors should cite sources focused on the topic at hand where possible.

”

— WP:CONTEXTMATTERS

I think we can agree that many introductory textbooks, even if they display a flyleaf periodic table that has La under Y, are not in fact focusing on group 3. Actually, many of those textbooks that seem to show La under Y either contradict themselves by putting the asterisk in the La cell (thus making it a Sc-Y-* table really), or by showing the completely unchanged Madelung rule that literally supports Sc-Y-Lu. For example, Gonick and Criddle's The Cartoon Guide to Chemistry does exactly all three: in fact, it even says on page 37 that La is the first element in the 4f series, and on page 38 says that the 4f series starts after La. And, while that is annoying for a vigilant reader, it indeed does not matter because this is basically a beginner's primer for chemistry where the chemistry of the inner transition metals matters not at all. (Although it already on pages 62 and 63 explains polarity and the ionic-covalent continuum that Sandbh had so much trouble understanding in Archive 42, LOL.) But, with respect to Gonick and Criddle, who successfully wrote a book that I think every bright kid interested in chemistry will love as a first chemistry book, I think they would agree that as a source this simply cannot be weighted alongside papers explicitly focusing on the chemistry of group 3. At the very least, textbooks that don't even mention that there is a controversy and yet still contradict themselves with Sc-Y-La + Sc-Y-* + Madelung following Sc-Y-Lu can hardly be considered reliable sources here.

And it is not, in fact, terribly hard to find texts and reliable websites that show the Lu option. WebElements has probably by itself greatly increased the visibility of Sc-Y-Lu, and if Wulfsberg is maybe not the most common text around, Clayden, Greeves and Warren more than makes up for that with its Sc-Y-Lu table.

Now, my key point is that most authors who are moved enough to write something focusing on the group 3 issue in their reliable books and journal articles (which are themselves already secondary sources when they analyse the data) support Sc-Y-Lu. The roll is impressive:

Lu supporters (15): Bury (1921),^[1] Shemyakin (1932)^[2], Landau and Lifschitz (1958),^[3] Hamilton (1965), Merz and Ulmer (1967),^[4] Chistyakov (1968), Wittig (1973),^[5] Jensen (1982 and 2015),^[6] Holden (1985), Fang et al. (2000),^[7] Horovitz and Sârbu (2005),^[8] Ouyang et al. (2008), Settouti and Aouragi (2014), Alvarez (2020), Scerri (2020)
La supporters (6): Trifonov (1970), Shchukarev (1974), Ternstrom (1976), Shriver & Atkins (2005); Lavelle (2008, who never responded to Jensen's most significant criticism), Restrepo (2015, who only considers the matter in one short paragraph)

Contextual notes

1. 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.

2. Shemyakin does not specifically discuss the group 3 problem but does very briefly mention "close similarities between Jt and Lu," without any elaboration. The subject of the article is about placing the Ln into the 8-group table (noting Russian chemists are still keen on the Mendeleev's original format, not to say back in the 30s). The author lists what we call group 3 as Sc-Y-Lu-Ac. The series La–Eu and Gd–Yb are then spread across groups 3–9.

3. L&L argue for group 3 membership of Lu on the basis of its complete 4f shell. They do not satisfactorily resolve the group 3 question. They effectively show Lu as a period 6 d block element, in the position immediately to the left of Hf, but also show La occupying a position immediately above Lu and below Y (p. 256). While they were not specifically addressing the group 3 question, such a configuration appears to be at odds with the general principle of one element per periodic table position or, at best, leaves the question of the constitution of group 3 unanswered. They apply the same approach to Cu-Ag-Au, and to Zn-Cd-Hg, resulting in these metals being treated as main group elements belonging to groups 1 and 2, respectively (p. 255). However, groups 11 and 12 are always considered to be d-block groups, since the ten columns from group 3 to 12 correspond to the filling of the ten vacancies in a d subshell. Furthermore, the chemistry of group 11, with the d electrons readily ionised, seems to further weaken such a possibility.

4. 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.

5. The low mp and superconductivity of La can be explained by by a high density of states at the Fermi level, as is typical of d-transition metals, and by a strong electron-phonon coupling and a relatively soft phonon spectrum: Goncharova VA & Il'ina GG 1984, "Anomalies in the elastic properties of polycrystalline lanthanum at phase transitions under pressure", Soviet Physics JETP, vol. 59, no. 5, pp. 995–998

6. Scerri, who is an Lu supporter, has called into question Jensen's argument on the basis of their selectivity

7. Fang et al. (2000), in discussing the spectra of Sc, Y La and Lu X₂ dimers, and those of some other period 6 transition metals, conclude that Lu is more like the other transition metals and is therefore a better fit under Y than is the case for La. This is factually correct but incomplete as an argument since Fang et al. do not say anything about the spectra of the group 2 or 1 metals, or the other lanthanides.

8. On the basis of 18 mainly physical properties Horovitz and Sârbu (2005) argue that Sc and Y are rather dissimilar to the lanthanides and that since Lu is similarly an outlier among the lanthanides, it should be assigned to Group 3 as a homologue of Y. Analysis: In fact, among the lanthanides, Horowitz and Sârbu found that Yb, Lu, Eu and La were outliers, whereas Pm, Dy, Tb, Nd and Ho could be regarded as "typical" lanthanides (p. 482). To some extent this finding does not surprise us since the outliers are found at either end of the lanthanide series whereas the typical lanthanides have mid-range lanthanide atomic numbers. What does surprise us is that the authors appear to have "seized" on Lu—based solely on its outlier status—as their preferred homologue of Y absent of any consideration or comparison of the merits of La, which was also identified by them as an outlier lanthanide, albeit not quite as peripherally. In contrast, Jensen (2009; 2015, p. 25) repeatedly argued for "verification of the validity of…group assignments through the establishment of consistent patterns in overall block, group and period property trends." While Lu may be somewhat more of an outlier than La, the shortfall is insignificant in comparison to broader trends. Indeed, when Jensen's approach to verification is applied to Lu and La, as set out elsewhere in this submission, we find a sound case for La, rather than Lu, as a successor to Y.

9. Restrepo confirmed his position (pers. comm. 20 Apr 2020) with Sandbh

The above notes were added by me. Sandbh (talk) 08:03, 15 May 2020 (UTC)

I have already addressed all of the criticisms Sandbh (yes, it was him, even if he didn't sign) gives regarding the Lu arguments elsewhere here, except for Bury and Shemyakin. (Those obviously are not the strongest, as they were writing so early before important things were understood; but it shows the historical pedigree of the Lu form and rams home the point that the La form has never had an uncontested reign, having always had significant challenges coming from Sc-Y-Lu and Sc-Y-*.) Pardon me if I am not terribly interested in doing so again, aside from issuing a statement here that I have done so. Double sharp (talk) 07:44, 14 May 2020 (UTC)

So I put it to you that Sc-Y-Lu cannot possibly be considered original research, when:

it is the predominant form advocated by authors who focus on the issue;
it has had some very prominent authors taking it up;
the "majority" of Sc-Y-La tables are found in sources that do not focus on the issue and in fact contradict themselves.

[And of course, by the discussion here, we clearly see its scientific superiority as well, but we are not supposed to be arguing about that here. If you want a TL;DR of that, open the edit window and see the hidden text here.]

By the logic of WP:CONTEXTMATTERS, the most reliable sources for this issue should be the relevant ones, and they generally support Lu. There is nothing against making the Lu table default in Wikipedia policy, and in fact reading it carefully supports doing so. Of course, we will continue to treat the La table in articles where the composition of group 3 is at issue; it just means that by default, if it doesn't matter (e.g. the article for chlorine, say), we will show a Lu table like we used to before that discussion from 2016, when I argued to the best of my knowledge using arguments that I now know (thanks to Droog Andrey) completely don't work: the premises they are based on are completely false.

So, now that that's out of the way: in principle, starting a second RFC after this straw poll finishes is perfectly logical in order to make sure the new consensus has a sort of "clout" that can surpass the old one. It's just that I am really tired of repeating the same thing 9001 times to Sandbh (who almost certainly won't listen anyway, given that his approach seems to be unfalsifiable per the above) in order to make it obvious to the closer that not just the consensus of reliable sources but also the scientific logic is against the La table. As such, in the interest of not going around the block a 9002nd time, I would like to at least plead that

the consensus of the previous RFC must be considered superseded for the reason that one of the main drivers behind it (me, with the old La arguments) has since found out that the scientific bases for his arguments were false (and therefore he no longer supports that line of argumentation);
the major part of that RFC was basically a Project-internal discussion; and
the major point of it listed also by a non-WP:ELEM participant (that was to support La) was the "more common in the literature" argument, which must also be considered in need of a relook at.

The old consensus must be considered superseded based on the three above points, a new one is required, and this is a reasonable one with an exceptionally high quality as well (because of all the scientific papers brought in to support the cases).

So, although I agree that this is not the best approach: I plead for the somewhat lazier approach to be taken, because I am really tired of refuting Sandbh's inconsistent La arguments as they pop up after the rain like mushrooms, and also because at this point this discussion bloats so large that I am not sure any outsider will want to come and look at it. (Yes, since Sandbh's arguments are unfalsifiable I am absolutely sure that if we start an RFC the discussion will bloat this hugely as well, and go round the exact same threads again anyway. Just look what happened to the above thread, which was supposed to be a summary of the previous one, oh my.)

So: does that seem reasonable? Double sharp (talk) 03:20, 12 May 2020 (UTC)

Re WP:CONTEXTMATTERS: I will bring up this quote again: "Information provided in passing by an otherwise reliable source that is not related to the principal topics of the publication may not be reliable; editors should cite sources focused on the topic at hand where possible." This is worded in a manner that leaves room for editorial judgment. I would, for example, not consider that that G&E mentions that group 3 is Sc, Y, La, and Ac a mere mention "in passing"; I think that this merely excludes cases like a hypothetical mentioning of that in a Greenwood obituary in, say, The New York Times. A majority of sources that are concerned not with the composition of group 3, but still concerned with the elements more generally, include La and Ac as the final group 3 members. Fortunate or not, that's how it is.

I do generally believe that editorial consensus can override other conventions. Not that it were such a unique thought, but still. I do, however, also believe that an old consensus has some value, and that people should generally be mindful of that when casting an opinion. I find it honorable to go without an opinion on a question when you don't have enough knowledge on it to have a qualified one rather than to seek to get one for the sake of having it. There's gotta be a pretty good reason to go against an old consensus. It could be said that this discussion has unearthed some new arguments and new sources that were not available back then, and that possibly could be a reason enough for a re-discussion. Maybe. But in that case, there has to be a re-discussion. Given the small size of our project, it's safe enough to say that a discussion here is a lower-tier discussion compared to a RfC. We could even put a RfC header right here and that would give us some new opinions. New opinions would be a good thing, especially when our "consensus" is three to one, and a single new participant could change the picture substantially, and when there is a standing decision already.

Re "I am really tired of repeating the same thing 9001 times": with all due respect (not in a way that belittles you), why should other editors that would participate otherwise not be given an opportunity to do so because of that? In all seriousness, you've run a small (in terms of the number of participants, not character count) discussion here endlessly; its lengthiness doesn't make it reach out any more widely. Not to mention that Sandbh mentioned himself that he was a couple of dozens of points behind you at some point, which shows that nothing really made you repeat that 9001 times. I honestly think that if a quarter of the time you devoted to this discussion in February and March had been devoted to hassium, we would've easily gotten one more bronze star already in our PTQ by now. Yet we are where we are. (On a related but off-topic note, hence the parentheses, how do you think I should have reacted upon seeing you spend so much time here, especially when it was already clear a consensus was not on the horizon, when I knew that had you invested a fraction of it into our common project, we would've finished it already? I thought about it and I decided I wouldn't hold a grudge. Why not? We all spend time here as a hobby to enjoy ourselves, and so I figured I wouldn't take it very much to heart because nothing really big depends on it, like, say, money or housing, in which case I'd have all the right to be as worried and agitated as possible, and so I wouldn't make of it a bigger deal than it is. We will be there, hopefully sooner than later. What I'm leading up now is that it could be a great idea to reconsider the grudge you got against Sandbh. Socrates valued truth over his friendship with Plato, but he still did value his friendship with Plato even in disagreement. I take it as a sign of a strong character.)

To round up this message, I'll say that I'd like to see a response to my Cold War message on your talk page before you decide to start an RfC.--R8R (talk) 12:54, 15 May 2020 (UTC)

For some answers re Greenwood and Earnshaw's value here, see the previous section. :)

Thank you for the idea of putting an RFC tag at the top of the page here: it is a good one and will eliminate the need for me to repeat the arguments again, since I can point to the earlier discussion that way. I will respond to your Cold War message and work on Hs tomorrow before doing that, though.

Also: I am terribly sorry to keep you waiting. Maybe part of this is that I was rather instrumental in getting the previous RFC to skew towards La, as you may remember with the scientific discussion. And that's also why I think the consensus needs relooking at if someone who participated that much in it now thinks he was completely wrong. And in fact I also feel pretty guilty now about it, especially since I was the one who initially convinced Sandbh to Sc-Y-La because I, if I remember correctly, pointed out a problem with a/some Sc-Y-Lu argument(s). But now there are much stronger and much more correct ones. (I wish Droog Andrey was here in 2016...) Maybe wanting to right my old wrong here is part of why I have skewed my WP time towards this instead of the Hs and Al collaborations, and I really do apologise for it. I will fix that tomorrow. m(_ _)m

But I will just note: I do not have a grudge against Sandbh, just his argumentation. I still think they are absolutely problematic, but that is not against him as a person. Double sharp (talk) 16:03, 15 May 2020 (UTC)

I re-read that bit a bit more closely. It says, "A very standard, often taught explanation of SF₆ involving sp³d² hybridisation by the sulfur atom. It's also completely wrong as studies have been demonstrating for decades. We listen to the studies, not the textbooks. Same for group 3." It's not very accurate. Consider these two quotes:

“

Wikipedia articles should be based on reliable, published secondary sources and, to a lesser extent, on tertiary sources and primary sources. Secondary or tertiary sources are needed to establish the topic's notability and to avoid novel interpretations of primary sources. All analyses and interpretive or synthetic claims about primary sources must be referenced to a secondary or tertiary source, and must not be an original analysis of the primary-source material by Wikipedia editors.

”

— Wikipedia:No original research

and

“

However, representing a majority viewpoint as such does not equal considering it true, and it is possible that "everybody" is indeed actually mistaken. For example, before Pasteur, everybody considered the spontaneous generation theory to be true, and they were mistaken. Even so, if Wikipedia had existed before Pasteur, it would have treated it as an accepted theory because the majority of experts (scientists in the relevant fields) thought it was true.

”

— Wikipedia:Verifiability, not truth (not formally a policy but isn't one user's essay, either: it was written as a consequence of a change of WP:Verifiability)

It may, of course, be that the scientific foundation of bonding in SF₆ has changed, and we objectively know that there is no d involvement there. That's a genuine scientific question, and we can say that we do know the truth; perhaps we could credibly override what consensus in the literature there is with that. There problem is, this is not the case for the group 3 question: there is no objective answer and there is no truth to be known; instead, there are different answer that may differ in how fit they are for purpose, and that's up for interpretation, too. That's why if we're going to try to override the common view in the literature, we need a wide consensus here for that, or if that turns out not to be available, we have to at least sincerely try to get that.

Very glad to hear we're back on track with hassium. I think we are indeed one step away.--R8R (talk) 16:09, 17 May 2020 (UTC)

@R8R: Well, my point is that the "common view in the literature" is hardly a common view if it's not even self-consistent. It is almost as easy to find Sc-Y-* tables as Sc-Y-La tables. Especially since literally speaking putting the asterisk in the same cell as the "La" means that you're still implicitly putting the lanthanides in group 3 and making it Sc-Y-*, as DePiep will surely tell you. ^_^ And these usually end up being allied with Madelung rules that support the Lu form as the ideal one by making no exception for 4f. Instead we can see the same situation as with hypervalence: textbooks presenting a form, not actually giving an explanation for it, and lots and lots of primary and secondary sources who focus on the issue, either by coming up with new arguments from their own investigations (primary, e.g. Merz and Ulmer) or secondary sources that summarise all the data (e.g. Jensen), who in the majority ask for Sc-Y-Lu to be adopted. So, we need a wide consensus indeed, but I don't agree that it's "the most common view in the literature". Simply putting something out inconsistently and not defending it is not much of a "view" IMHO.

Maybe the answer is not objective, but I still think there is a most natural one, per the above. And for that I appeal again to the complete absence of f involvement in Lu and Lr, and its presence for La and Ac that is just as sure as that for Th, which is an argument that has appeared many times in the literature. That, at least, is a genuine scientific question: the presence or absence of f involvement. And although we can in principle draw the blocks however we like, I think, as do many of the authors who I cite, that it is a very powerful argument for naturalness of some specific ways we draw the blocks. And maybe we can still argue that we start with different basic concepts in mind, but I think the fact that (1) we call this the "f-block" and naturally should expect f orbitals to have something to do with it, allied with the fact that (2) on almost every physical and chemical property, La fits badly with Hf-Hg, should tell us that something is deeply unnatural about Sc-Y-La independent of what we choose to be important. Double sharp (talk) 16:56, 17 May 2020 (UTC)

P.S. You may read the origins of this in Archive 11 of my talk page. I was mainly going for condensed-phase configurations and the more main-group-like behaviour of group 3 to support La. Of course, now I know both don't work, so. Double sharp (talk) 17:30, 15 May 2020 (UTC)

The beginning: how Sandbh switched to La

In fact, this is why I find the situation utterly strange. Prior to this, Sandbh was a Lu proponent. This whole thing started because I found some Lu arguments wanting, and noted that some things seemed to point to La instead. So let's analyse that initial thread and its arguments.

(1) The arguments that Lu creates an additional atomic number triad (Y-Lu-Lr), and that Sc-Y-La without a split d-block destroys the sequence of increasing atomic number order.

Well, indeed I still think those are silly! Atomic number triads, absent of any explanation of what causes them, are simply plain numerology. Sc-Y-La is also an atomic number triad; the question is whether it should be that one, matching K-Rb-Cs and Ca-Sr-Ba, or Y-Lu-Lr matching Zr-Hf-Rf and Nb-Ta-Db. In vacuo there is no way to decide that without referring to the actual chemistry and physics. And the second is a silly argument because everybody supporting Sc-Y-La seems to be totally comfortable with a split d-block.

Basically: arguments that don't grapple with the fact that this is a periodic table, covering properties of actual elements, are doomed to be totally unconvincing. That goes both for these "pure symmetry" arguments that would work regardless of the elements' properties (atomic number triads would seem to support H-F-Cl and He-Ne-Ar to create more triads even if, hypothetically, H and He were perfectly normal alkali and alkaline earth metals), and for "convention" arguments that don't analyse whether the properties of the elements involved are actually fine with that convention.

(2) The asymmetry of the split d-block option does not imply that it is false.

Correct. So let us analyse the situation. What statement is the split d-block making? It is making a statement that the ideal sequence is for one d electron to fill first, then the f electrons, then the remaining nine d electrons. I trust this is uncontroversial, although I am beginning to doubt here that anything here is going to be uncontroversial.

The sequence of ideal configurations should have relation to chemistry and physics, like ideal crystals and the ideal gas law. Therefore, if the statement the split d-block of the La table is true, we would expect La to behave normally for the first d metal of the sixth period (false), and not use f electrons (false); we would expect Lu to behave like a normal lanthanide (true) and use its f electrons (false).

Oops. I guess this might not be true after all. But, crucially, symmetry (and the allied regularity) have not been and have never been enough to prove that. Without looking at the data, you will get nowhere.

(3) "It is well-known (cites Jensen's paper) that Sc/Y/Lu gives trends that are similar to those in the early transition metal groups, while Sc/Y/La gives trends that are similar to those in the s-block groups. To decide which trend is more relevant, we should look at the chemistry of group 3 and the lanthanides. We then find that they are all electropositive metals that reduce water and have only one important, mostly ionic oxidation state (and even for the few exceptions, Ce, Sm, Eu, and Yb, the +3 state is still by far the most important one in aqueous solution). This behaviour is much more like that of their s-block neighbours in groups 1 and 2, and is quite different from that of group 4 (and Th), for which the +4 state is too high to be ionic. This would suggest that La is a more appropriate candidate for the third member of group 3, giving an s-block-like trend that fits their chemistry."

Unfortunately, this turns out to be absolutely false. (No, this is not an attack on anyone but myself, because this absolutely false argument is my own creation from 2016.) Actually, for cations as large as Zr⁴⁺ and Hf⁴⁺, +4 can totally have strong ionic character, and those are pretty electropositive too (just look at the Pauling scale). This all depends on what the counter-anion is anyway: even the +1 state of sodium might not be ionic if your counter-anion is arsenic or something like that. And actually, Sc and Y in group 3 also show totally normal transition metal properties: their organometallic and coordination chemistry is close to that of group 4, it shows normal lower oxidation states there. Well, Lu is like that indeed, La has even worse coordination ability and is more like the s elements. The old traditional categorisation of group 3 as not really transition has mostly died for exactly that reason: now that these branches of chemistry have developed so much, the categorisation cannot stand against the facts!

Therefore: the chemistry of Sc and Y is more or less intermediate; 'but so is that of Zr, Hf, and Rf; and while the chemistry of La is more like a main-group element, and the chemistry of Lu is more like a transition element. That's the same situation of Th vs Rf. Therefore, on balance, since group 4 is still a transition group with main-group-like properties that everyone agrees must follow a d-block trend, group 3 should do so as well.

So, when I say Sandbh lacks understanding of basic first-year chemistry: well, so did I, back then. In order to make a blanket statement like "mostly ionic" you need to already be implicitly focusing on counter-anions of the right electronegativity. The difference is that I figured it out later, thanks to Droog Andrey.

The funny thing is that Sandbh got this right then:

“

In terms of basicity it seems to me that Lu is more like Sc and Y, whereas La is more like Cs, Ba etc. So perhaps argument 4 doesn't hold up that well. In other words, Sc-Y-Lu fits nicely between Ca-Sr-Ba and Ti-Zr-Hf as a progression from groups 2 to 4, whereas La is a bit of a misfit in that it's closer to group 2 than it is to group 4.

”

— Sandbh

(4) "It is not clear how much the concept of a block actually means for the chemistry of an element. Helium is in the s-block, and yet its closest chemical cousins are the noble gases in the p-block. Be and Mg are in the s-block, but are more similar to Al in the p-block and Zn in the d-block respectively than they are to the heavier members of group 2. And it is well-known that Zn, Cd, and Hg, despite being in the d-block, do not show many of the characteristic properties of transition metals. Finally all these chemical similarities almost break down completely in the p-block: for example, B is not very similar to F at all. Since there is already a precedent for breaking the s-block to treat helium better chemically, I do not think there is any real problem with breaking the d-block if that results in treating La better. It may upset Platonic symmetry, but we are not drawing a table to reflect Platonic symmetry. We are drawing a table to reflect chemical properties."

Actually, the idea that the s-block is broken is absolutely false. (Yes, this is still my past self whose arguments I am attacking.) Well, just look at hydrogen and helium: everyone knows that helium is an s block element from its configuration, people put it above the p-block only for chemistry. There's no breaking of the s block at all. Whereas, the La table basically makes an actual statement that La is a d block element, and that the next d-block element is hafnium, with Ce through Lu breaking the d-block in the middle.

Also, the idea that elements in the same block should show chemical similarities is too simple to really work. There are, as correctly pointed out, many examples in which the most obviously similar element (e.g. Al-Sc, Mg-Zn) is universally placed in what looks like the wrong block. In actuality, the reason is that the road from the aufbau to chemistry is a winding one. And yet we are totally sure that electrons control chemistry simply because they are exactly what is used for chemistry. That's why the blocks are there, to focus on the orbitals being used for chemistry. That's why we have Al over Ga and not the chemically more similar Sc, for instance.

Oh, except that La uses 4f orbitals, Lu doesn't. So, Sc-Y-Lu is correct again!

And now, some Lu arguments from 2016 Sandbh! Yes, really!

(5) "In nature, Y is usually found with the heavy REE, including Lu."

I pointed out that by itself this was not conclusive, seeing as Be usually does not occur with Mg through Ba, and he agreed. I still agree with that: this is basically the "pure chemistry" argument. It is more convincing if you compare it with the other early d groups; Zr-Hf, Nb-Ta, Mo-W are generally similar and indeed occur together, whereas the first element in each group is more distinct. So, Y-Lu is recommended, but this argument is incomplete without this buttressing it.

(6) "The (developing chemistry) of scandium is that of a slightly smaller version of lutetium. (according to Cotton)"

Correct as far as it goes. But, as R8R correctly pointed out when I mentioned that Th is similar to Hf but in a different group, and Ti is not so similar but is in the same group, "if such dissimilarities are within the normal range, then how can you even expect this argument to ever result in a conclusive outcome, as it must work both ways?" (And just look at Sn-Pb, which is not a very good resemblance at all!)

So this argument is better phrased from the POV of homogenising the d block.

(7) "Scandium organometallic chemistry is generally similar to that of the later lanthanides. (ditto)"

It is more intermediate between Ti-Co and the late lanthanides, as I noted before. But the late lanthanides are the more d-like of the bunch, so this does indeed support Sc-Y-Lu to homogenise group 3.

(8) "Early period 5 and 6 transition metals show close similarities in properties, in contrast to their period 4 congeners"

Correct, and conclusive.

I pointed out before that this was a result of the Ln contraction, and then operated under the erroneous assumption that 4f collapsed only after lanthanum. Since we now know that this is false, and that 4f has collapsed enough in energy at La to be used for chemistry, my old objection is withdrawn.

(9) "The periodic law applies to physical properties as well as chemical properties. On the basis of 18 mainly physical properties, Lu is a better fit with Sc-Y- than is the case for La. See: Horowitz O & Sârbu C 2005, "Characterisation and Classification of Lanthanides by Multivariate-Analysis Methods", Journal of Chemical Education, vol. 82 no. 3, pp. 473--483"

Correct. Which is funny as Sandbh criticised me this year for tabulating physical properties, which all show La as being a worse fit in the d-block trend.

The point is: while Lu fits well continuing the group 3 trend from Y and continuing the lanthanide trend from Yb, La only fits well continuing the lanthanide trend from Ce backwards. It simply sticks out like a sore thumb in group 3.

In case Sandbh is about to quote Pettifor to point out that condensed-phase La has 2.5 d electrons and is on that basis more of a d metal than Lu with 1.5, note that (a) on that basis, condensed-phase La has 0.17 f electrons and is on that basis more of an f metal than Lu with 0 as well; and (b) Lu still is more sensible in the d block, because yttrium has about 1.5 d electrons, which matches Lu and not La.

(10) "Sc, Y, and Lu have d-like conduction bands whereas La doesn't"

Absolutely correct and decisive. While it is true that the late lanthanides generally also have d-like conduction bands, the point is: while Lu fits well continuing the group 3 trend from Y and continuing the lanthanide trend from Yb, La only fits well continuing the lanthanide trend from Ce backwards. It simply sticks out like a sore thumb in group 3 because of its significantly greater f involvement.

(11) "Nelson (2012) argues that the number of outer electrons possessed by an atom, and the number required for it to achieve an inert gas configuration exhibit an almost exact periodicity. Further, these two numbers correlate almost exactly with the highest conventional valency and the highest carbonyl valency exhibited by an element. For example in iron carbonyl, Fe(CO)5, the carbonyl valency is taken to be 10 whereas Fe has a highest conventional valency of 6. Now, while Y, La and Lu all have a highest conventional valency of 3, Y and Lu require only 15 electrons to achieve an inert gas configuration whereas La would need 29. On this basis Nelson prefers Y-Lu rather than Y-La. I need to read Nelson's paper again but so far, it gets better each time I do. See: Nelson PG 2012, 'Periodicity in the formulae of carbonyls and the electronic basis of the Periodic Table,' Foundations of Chemistry, vol. 15, no. 2, pp. 199–208."

I think this is not terribly lame anymore because I've since realised that the s block is a normal exception. While the carbonyl species are not terribly normal chemistry, the periodicity seems to be exact, it fits the generalisation of the 2-, 8-, 18- and 32-electron rules, and Sandbh has in focusing on Pr⁵⁺ already forced us to throw the "not terribly normal" argument out the window by consistency.

(12) "The Russian authors, Landau and Lifshitz (1977, p. 273–274) wrote: "The filling up of the 3d, 4d, and 5d shells…[has] a characteristic feature of [of] "competition" between the s and d states…The filling up of the 4 fshell also occurs in a slightly irregular manner characterized by the competition between 4f, 5d, and 6s states…In books of chemistry, lutetium is usually placed in the rare-earth elements. This, however, is incorrect, since the 4f shell is complete in lutetium; it must therefore be placed in the platinum group…"[They refer to Sc–Ni as the Iron group; Y–Pd as the Palladium group; and Lu–Pt as the Platinum group]. They first wrote these words in 1956, which Scerri refers to as "one of the oldest categorical statements in favor of Sc Y Lu Lr" (pers. comm). I like the 'competition' metaphor and the simplicity of their assertion. See: Landau LD & Lifshitz EM 1977, Quantum Mechanics (Non-relativistic Theory), 3rd ed., Pergamon Press, Oxford"

Correct and decisive. 4f is a core subshell by Lu.

(13) Condensed-phase configurations...

Absolutely false. My own absolutely false statements from before, admittedly, but still absolutely false and since repented of. With my bold:

“

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

“

What do you mean saying that in condensed phase ds² is normal? I'd say in condensed phase we have mostly Ln³⁺ with f^n-1s² where LUMO has more contribution from f-subshell than from d-subshell in the vast majority of cases.

”

The sensible lesson to learn is not to use condensed-phase configurations willy-nilly; the point is that gas-phase configurations differ often from configurations in compounds, which may differ among themselves! So the only important thing is what orbitals can be used. Then 4f starts to be used at La: the Lu table is vindicated. Very good!

Oh, and a nice highlight, with my bold:

“

If chemical properties trump physical then Lu has more in common with Sc and Y than is the case with La, does it not? This is not a trick question, I want to ensure our arguments are consistent, There are the two Cotton arguments, however weak, Nelson's carbonyl argument, the yttrium group argument, and the old separation group argument. Does La have better chemistry-based arguments for fitting under Sc-Y- than Lu?

”

— Sandbh

No, it doesn't indeed, I've fully repented on that idea. R. Bruce King is really being strange when he calls the Ln and An main-group elements. I have never heard of anyone else who does it. And it doesn't even work thanks to advances in organometallic chemistry of group 3.

But now the significant question. I am sure that if I actually knew this then, I would have concluded that whereas those initial arguments are not very good, Lu is borne out by the chemistry and physics involved. And probably Sandbh would have stayed at Lu, and we would not be having this discussion. Indeed, we may ask him: what would he have thought, if I had said this then?

So, why is it so much more difficult for Sandbh to change his mind back again? Why is it that Sandbh could consider Lu a falsifiable theory but cannot consider La as one?

And that's why I find the situation utterly strange. Double sharp (talk) 04:52, 16 May 2020 (UTC)

@Double sharp: Your multiple use of the BS epithet, even to criticise your self, is unacceptable. Use it in your own company if you want to but leave it out of our talk page. Leave it out of your edit summaries too i.e. on the periodic table edit history page. Sandbh (talk) 12:15, 16 May 2020 (UTC)

@Sandbh: Very well, replaced with "absolutely false". Double sharp (talk) 12:41, 16 May 2020 (UTC)

Coordination numbers

"As indicated earlier in this section, the di-f lanthanide dihalides show close structural analogies with the alkaline earth metal dihalides, rather than with the dihalides of the transition elements. This is reflected in the range of coordination numbers (9, 8, 7, and 6) contrasting with the confinement of dihalides of the first-transition series to a coordination number of 6 (571) at normal temperatures and pressures. This absence of strong stereochemical preferences in the lanthanide series is also apparent from a survey of the structures of the trihalides (86)" (Johnson 1977, doi:10.1016/S0065-2792(08)60038-2, p. 6)

So, if the lanthanides show a smooth transition from s-like high coordination numbers to d-like lower ones, it stands to reason that they should go between the s and d blocks, rather than be sandwiched in the middle of the d block. Double sharp (talk) 04:00, 18 May 2020 (UTC)

How long has this gone on for?!

My poor, slow internet is starting to have issues loading this entire page. Even when it does load, the wall of text is starting to give me a heart attack. It's so long that it might as well be in Earth orbit by now. ― Дрейгорич / Dreigorich Talk 06:59, 15 May 2020 (UTC)

@Дрейгорич: I've moved most of it to Archive 44. Sandbh (talk) 07:36, 15 May 2020 (UTC)

@Дрейгорич: (edit conflict × 1) It's a space elevator by now. XD Seriously, this round has been going on since Archive 42. Which started last Christmas. It's coming close to the five-month mark.

I do think it will be resolved soon, though. Out of the five active participants (including us, of course), we have 3 who favour switching WP to the Lu table, 1 who favours keeping the La table (Sandbh), and one who has not yet decided (R8R). Well, what R8R said above was:

“

I do not understand what the question of the straw poll is very well, and it makes a big difference to me. I would be opposed to a change in English Wikipedia right now, since Wikipedia is a tertary source, and it needs a good precedent for a change that could not qualify as original synthesis (or, as the local terminology goes, original research). I do think that a decision from IUPAC could be authoritative enough to overrule that if editors agreed on that; importantly, because the decision was made by somebody else, someone we could consider authoritative. I will also note that the current version was fixed in a RfC, which has a wider scope than a vote in our relevant but small project, and we'd need an RfC to override that decision. There are house rules here in English Wikipedia, and we have to respect them. At the same time, if I were writing my own self-authored book and were not subject to any house rules, I'd be very fine using a -Lu-Lr table.

Also, generally, it goes that there should be a consensus for a change in Wikipedia, not for retention of an existing policy, which is the status quo, after all.

”

— R8R

But he hasn't yet decided. So, it seems that the reason he has not voted yet for Lu is simply policy-based; I have provided a policy-based argument above for why policy is not against the switch (i.e. that the relevant sources who focus on the issue largely favour Sc-Y-Lu, and that they are surely more reliable than sources which only incidentally cover the problem in the sense of what their flyleaf periodic table says, which probably is allied with a Madelung rule graphic that contradicts it by supporting Lu), so we'll see what he says. And I see he is probably not convinced by Sandbh's arguments. ^_^ (I really do not want to go through another RFC, because the first one was mostly another Project discussion again with a few extra voices making smaller comments, and it will mean re-rebutting Sandbh's unfalsifiable arguments yet again in exactly the same way as before.)

Well, we will wait for him, of course. ^_^ But then it will finish. I note that Sc-Y-Lu has an ironclad majority already in the straw poll; what remains to be seen is if Sc-Y-La will really be a minority of one. We may very well really get a consensus for change! Double sharp (talk) 07:40, 15 May 2020 (UTC)

Since Sandbh has helpfully quoted a source that itself gives strong Lu arguments, I have tried one more time as a "last chance". Along with quoting him from 2016 when he wasn't yet convinced by La below Y. Since it appears that getting through to him currently is impossible except in the case that he finds his own source refuting his own statements. Admittedly the last time that worked when he was the one rereading his source, not me telling him to do it, but at least this seems to have a nonzero chance of success.

I am increasingly tempted by the WP:BRD option of changing everything to Lu if that doesn't work, pointing to the straw poll, pointing to me being one of the major drivers of the old consensus for a reason why it must be considered superseded. That will surely bring more outsiders into it if it is then reverted and discussed. Because I doubt anyone is going to wade through the whole of Archive 42 and 44 and get up to speed with all the argumentation lines, so adding an RFC header here or adding it to Wikipedia:Administrators' noticeboard/Requests for closure is unlikely to produce results soon. Double sharp (talk) 07:34, 16 May 2020 (UTC)

I wanted to write a message discouraging such a unilateral move, and I'm somewhat relieved to see that more people have been called into the discussion instead. However, the question still remains: why would people who could participate in a talk not be given an opportunity to do so? If you want a change from what's been fixed in an RfC, it only makes sense to call an RfC to override that.

Ideally, you shouldn't just care about what's right and what isn't; you should also care that an action you undertake is legitimate. Wikipedia gives a lot of room for action: in its pillars, it is said that anyone can edit it and that there are no firm rules. However, there are still limitations to this openness, something that only came naturally because we wouldn't go through this whole encyclopedia wouldn't work if there were no way to handle a conflict and differing opinions, and so if something's been decided upon, we have to learn to respect that decision. If the new proposal wins, then good, but it has won in a right manner then. If it doesn't, there has to be a reason why it hasn't. Whether the change happens or not, this discussion will be over soon enough; let's say, a couple of months. Let's even say in half a year. In two years already, the decision will have taken place and the feelings born in this discussion will have cooled off. And whether the decision was positive or negative, it will still be there to stay. Or is it not, and we can have this debate every now and then, when one more editor finds the existing arguments wrong. And what if they lose their cool, too?

There's the principle called the golden rule, and I suggest having it in mind, picturing an editor who would argue differently but display a similar sense in actions. How far would we get? If that hypothetical editor mirrors me, what do I do to get to a better place in our disagreements with them? Could it even in principle be that I'm not right? I try to have this in mind in my conflicts. I realize sometimes action might need to be taken, but then again, it's good to remember to ask yourself if that's the case. Is it really that big of a problem if you don't? Will it matter after the hot feelings have died down?

My recommendation is to ask yourself not how you feel in impatience but rather what way is right to solve a problem, for which I suggest imagining a time when it's long over. Think from that perspective what way would be better. In the end, this will also make you a happier person because you've done the right thing. (This would be more difficult to embrace if we were talking about something super important to your being, like housing, but the scale of our little problem is nowhere that big.)

The English language has this beautiful concept that I really like, something that doesn't have a proper equivalent in my mother tongue. It's "integrity." I suggest embracing that powerful concept.--R8R (talk) 13:03, 17 May 2020 (UTC)

@R8R: Yes, I agree with what you say (now that I've cooled down somewhat), and that's exactly why I have called in more editors. I read WP:1AM this morning, BTW. ;) I still fully intend to fight this one out through logical reasoning and appealing to sources, but I want to fight it properly in such a way that regardless of whether the Lu side wins or not, no one can say it was unfair.

To that end, I have greatly expanded the summary of the sources who fought it out at Periodic table#Group 3 and its elements in periods 6 and 7 and at Group 3 element. (I get the argument that the "periodic table" article should only have a summary, but I think it will be easier to start by listing everything out first and then contracting it later.) Now everyone can see the fruits of these almost five months and judge for themselves. Double sharp (talk) 13:33, 17 May 2020 (UTC)

Old ideas wrong. cont.

See archive 44, here.

@R8R: I'd be grateful for your view in this matter, thank you.

The context is Double sharp's comment, "…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."

If my request places you in a too awkward position that's fine; could you please let me know if that is the case. Sandbh (talk) 07:54, 15 May 2020 (UTC)

Courtesy ping @Double sharp: FYI --- Sandbh (talk) 07:54, 15 May 2020 (UTC)

@Sandbh: Noted, thanks. I will also remove it if R8R thinks the request puts him in a too awkward position, out of courtesy. (Though I'll note that the titles recapitulate comments that already have been made here.) Double sharp (talk) 07:58, 15 May 2020 (UTC)

I'm sorry for not being able to respond earlier. It's not even lack of time, but rather lack of strength in the evening on my part. I wanted to leave a few words earlier; now that I both have the time and the strength, I'll try to leave responses where they are most needed in chronological order (including here).--R8R (talk) 09:47, 15 May 2020 (UTC)

Naturally enough, I don't think that this kind of titles facilitate any discussion, or good feelings, or anything positive. The discussion went off the rails I think with the first lol, and at least four participants in total have done something along these lines since then. "LOL" stands for "lots of laughs," and, of course, purposely laughing at somebody else's words is plain arrogant, I hardly need to explain that.

I do, however, take it as a good sign that Double sharp said above that he didn't hold a grudge against you personally, and I hope that will facilitate a return to normal civilized discussion.--R8R (talk) 19:06, 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. And that the problem I point out in them, misunderstandings of utterly basic material that should precede arguing about such a matter, has not gone away. Double sharp (talk) 03:30, 16 May 2020 (UTC)

The consensus

Droog Andrey (talk) 15:42, 16 May 2020 (UTC)

@Droog Andrey: Yes, there are lots of secondary relationships. However, I think the primary ones are the important ones to show for general situations. And I see we agree what they are. Well, except that I think we will have more chances pushing for group 3 first on WP with lots and lots of sources backing us, rather than pushing for helium in group 2 where AFAIK there are not yet quite so many. ^_^ Double sharp (talk) 17:18, 16 May 2020 (UTC)

(ec; lost my edit) @Droog Andrey: What does ( ) mean? And: what are the group numbers/column headers? -- This is not a 'consensus'. -DePiep (talk) 17:26, 16 May 2020 (UTC)

@DePiep: I am not sure if Droog Andrey meant "consensus" seriously; at least I assumed he didn't, as discussion is ongoing (although I am not sure it is getting anywhere at the moment). I presume the group numbers are as usual (1 to 2 at the left, then fourteen unnumbered columns, then 3 to 18), and that the parentheses mean "secondary relationship; there are chemical resemblances, but they are not in the same group". He may correct me if my interpretation is wrong. Double sharp (talk) 17:53, 16 May 2020 (UTC)

Let's not go interpretating. I'm sure DrAn is a grown up person that can speak for themselves. You [DS] saying 'I assumed he didn't', 'I presume' is not clarifying in here. -DePiep (talk) 19:06, 16 May 2020 (UTC)

@Droog Andrey: Honestly, my questions are: (1) What doe the ( ) brackets mean, and (2) where are the group numbers? -DePiep (talk) 19:06, 16 May 2020 (UTC)

@DePiep: Brackets mean secondary relationships, group numbers are the same as in usual 32-column PT. Have fun :) Droog Andrey (talk) 21:13, 16 May 2020 (UTC)

Well, I guess I was right. ^_^ Double sharp (talk) 03:51, 17 May 2020 (UTC)

I like this table - and this section:

This table shows secondary relationships not typically visible in a PT - though not all such relationships, eg, that between the 1st few La/Ac pairs and the 1st few transition metal groups.
This section gives me a place to add a comment to this HUGE thread.

Looking at this discussion from the 30,000 foot level, it seems more akin to discussions in these areas:

130 million chemical substances listed in the Chemical Abstracts Service § Registry
8-9 million biological species classified by taxonomy (biology)
7-8 thousand human languages classified by comparative linguistics
118 chemical elements classified by the periodic table

There are huge discussions and disagreements about the best way to classify languages and species - and I suspect substances also - so why should we expect it to be any different with elements? Because we have such a small set, we tend to think the problem would be simple, but it is not. YBG (talk) 13:22, 10 July 2020 (UTC)

@YBG: It's just a question of consistency. If you want to say, "look, Sc-Y-La ought to be put in there over Sc-Y-Lu", then you're making a standard for "how much change is worth breaking a block" that actually supports everything else, given that actually Lu is more like Y than La is. Pretty much all arguments for Sc-Y-La also give unintended consequences like Ti-Zr-Hf-Th or Ti-Zr-Ce-Th or H-F-Cl or V-Nb-Ta-Pa or Cr-Mo-W-U or Be-Mg-Zn or B-Al-Sc or C-Si-Ti.

Maybe some are okay with a periodic table of mal so, mal so. Sometimes this way, sometimes that way. I think that the icon of chemistry deserves better than that. And I strongly suspect most chemists would agree on the need for logic. Sandbh doesn't seem to, judging from his posts that haven't been archived yet.

The prevalence of the La form is nothing so big as anyone might think (just do a Google Images search, * below Y dominates). And the fact that it is a little bit more common than Lu mostly has to do with chemists taking the periodic table as a given. Surely, it is no coincidence that the majority of those who don't take it as a given and proceed to investigate the issue conclude that Lu is better. All the arguments ever advanced for La are trivially refutable: the argument "but La has no 4f electron" has the obvious rebuttal "but Th has no 5f electron", the argument "but basicity and atomic radius should increase down the table" has the obvious rebuttal "it doesn't for Zr to Hf either", and so on, and so on.

Generally speaking, this is widely considered a case of proof by contradiction by any scientific enterprise based on logic. Not for Sandbh, apparently. He seems to think it is a fallacious extending of his arguments past their contexts. Never mind that those contexts are totally artificial. By those standards we may easily "prove" anything by declaring our context to exclude all counterexamples.

And that's precisely why over six months of arguing this has led me to the conclusion: actually, the answer is simple. The simple test of consistency means that if you insist on "one element, one place", everything points to lutetium under yttrium. Not a single valid argument supports the La option. That's reflected in how lopsided the consensus here has become already: 5-2. And even R8R's opposition to the change now has to do with his opinion that a good precedent is needed; considering that he's said "if I were writing my own self-authored book and were not subject to any house rules, I'd be very fine using a -Lu-Lr table", I think we may reasonably infer that he is not convinced by Sandbh's argumentation.

I was planning to abandon this megathread shortly; almost everyone is convinced away from La under Y anyway, and Sandbh is apparently unconvincable (so far it seems his ideas are not falsifiable by anything other than IUPAC saying "Lu should go under Y"; that's of course totally precedented in this talk, in which he refused to accept my totally standard statements about the idea of an element's chemistry being "mostly ionic" or "mostly covalent" being nonsensical until he found his own source parroting them back to him; apparently even directly quoting Greenwood and Earnshaw wasn't enough, even though he refers to it too). But if you have more questions, then I will certainly answer them.

I have already started drafting the RFC and my explanation of the situation in my sandbox. Sandbh seems convinced that it'd be a waste of time. Judging by the amazing consensus that has developed here so far, I suspect not. Double sharp (talk) 14:35, 10 July 2020 (UTC)

PT article victimised?

@Sandbh and Double sharp: TBH, these 41 edits/today in a live article are not helpful. I prefer all those issues be resolved at this WT:ELEM page. IOW: let's not expand the discussion into article ~editwarring. I recall WP:ELEM is one of the the best science discussion WProjects I met. -DePiep (talk) 17:16, 16 May 2020 (UTC)

@DePiep: Actually, there is no edit war; 39 of the 41 are my edits, 2 are Sandbh's. So, this is more or less just how it looks like when I work on an article and add stuff with sources. I haven't done any edits installing Sc-Y-Lu, just edits adding lots of sourced material into the section discussing the controversy. Double sharp (talk) 17:17, 16 May 2020 (UTC)

Double sharp OK, thanks for clarifying. I hope you don't blame me for not checking each edit in the issue ;-). Have a nice edit. -DePiep (talk) 17:30, 16 May 2020 (UTC)

@Double sharp and DePiep: The coverage of the two options La-Ac and Lu-Lr has become unbalanced. The word count for the two used to be 314: 287 i.e. 52% and 48%. Each option had two paragraphs. The spread is now 39% and 61%, with three paragraphs for La-Ac, and five plus a block quote for Lu-Lr.

I further note the explanatory tone of the two options was formerly impartial in its presentation, as it should be. The latest version introduces weasel words such as "superficially", "very", and "minuscule". It adds content to discredit La-Ac and make Lu-Lr look better.

It is one thing to argue within our project; it is quite another to carry one's bias over into the article space. Double sharp, I view this as another example of unacceptable behaviour on your part including excessive use of bolding; removing some of my citation supported content; laughing at me; slandering me; swearing; and effectively demanding I provide a falsifiable hypothesis when I'm under no obligation to do so.

You can act in a civil manner (with a due allowance for occasional episodes of tetchiness) or you can carry on the way you are, in which case I'll consider involving an Admin. Sandbh (talk) 03:58, 17 May 2020 (UTC)

Go ahead and invite one. The coverage in reliable sources focusing on the matter is indeed favouring Sc-Y-Lu; I simply made sure this was reflected by our article, citing reliable sources copiously. The only citation-supported content I have removed has been statements that are either supported by very old citations (hence not really understanding the issues that were discovered much later) or statements that are plain wrong and are easily refuted by more reliable sources focusing on the matter. Double sharp (talk) 04:03, 17 May 2020 (UTC)

P.S. Guess who started the laughing first: not me.

“

@Double sharp: Noting you like to discount the relevance of gas phase configurations I have to laugh at your continuing focus on Th, and it's indisputable f character. LOL! An La-Yb f-block is more congruent with chemistry. Woe is poor Lu, and its status as a lanthanide, banished to the d-block. 06:55, 16 February 2020 (UTC)

”

That's way before I started including "LOL" in my statements only in May. For a discussion beginning last Christmas, and that has gone round and round in circles with you continuing to repeat the same falsehoods after careful correction from reliable sources. (Case in point: the supposed group divide between groups 3 and 4, which, as I have been saying and backing up with reliable sources since January, does not exist.) I agree that I went somewhat overboard, and apologise for it: I should not have done that. But I note that my laughing was directed at your arguments, not at you personally. And that I backed up each and every one of my accusations with copious quotes from you demonstrating them. And that the only swearing, while indeed overboard on my part, was me referring to arguments as BS (which Droog Andrey also did) when they were obviously against the facts, not directed personally against you. And that my "demand" for providing a falsifiable hypothesis is something recognised by authorities on the philosophy of science as necessary to tell if an approach is scientific or not.

Again, I agree that I should not have gone even this far, and apologise to you; but I think that having to go round this for nearly five months at least explains my actions even if it does not excuse them. Double sharp (talk) 04:09, 17 May 2020 (UTC)

P.P.S. Let me just add that everything I added was sourced. (Except for that point about Th having 6d² incumbency over Rf, which is admittedly not sourced but also uncontroversial looking at an electron configuration table.) It's not me discrediting the La-Ac table; the reliable sources do it all already. Double sharp (talk) 13:40, 17 May 2020 (UTC)

Copied the new section to group 3 element as well. Double sharp (talk) 06:00, 17 May 2020 (UTC)

@Droog Andrey: As a subject-matter expert, what do you think of the current version of the section Periodic table#Group 3 and its elements in periods 6 and 7 as edited by me? Do you consider it biased, or is it an accurate reflexion of the reliable sources that focus on this issue? Double sharp (talk) 05:45, 17 May 2020 (UTC)

@Double sharp: Looks fine for me. Droog Andrey (talk) 20:06, 23 May 2020 (UTC)

Calling an admin and chemist, as well as the previous closer, after myself

@DMacks: Since you are an admin and a chemist, and have contributed on this talk page above (but not in this discussion, like Droog Andrey has), I would like your opinion as well. If you know a chemist on WP who specialises in the rare earths and/or actinides, then please by all means extend an invitation as well, as this is the precise subject under dispute. The twin issues that are currently ongoing are:

(1) Is the text at Periodic table#Group 3 and its elements in periods 6 and 7 a neutral reflexion of the relevant reliable sources?

(2) Should the periodic table on English Wikipedia be presented with Sc-Y-Lu-Lr in group 3 as the default form, as it was before the 2016 RFC; or should it carry on as Sc-Y-La-Ac? Based on the arguments presented on this talk page and archives 42 and 44, with lots of sources backing the statements up.

@Tazerdadog:}} Although you are not an admin, and have not been so active over the past months, I would like your opinion as well if possible as you closed the previous RFC on this at Template talk:Periodic table. My argument is that this needs to now be revisited as new information has come in suggesting that the arguments we used to support Sc-Y-La before were false, and that the relevant sources (being the ones that focus on the group 3 issue) generally support the Lu option; and that since I contributed so much to that previous discussion (being then on the La side) and now disagree with most of what I said then, this indicates that it must be relooked at.

The previous discussion (unfortunately very long) can be found at Archive 42 and Archive 44, segueing into the last sections still on this main talk page. Note that my understanding and knowledge of the literature grew during this discussion, and that indeed hardened my stance against the La table as this went on as more and more papers contradicted the arguments for La. My current source-based arguments against La are basically what is already present at Periodic table#Group 3 and its elements in periods 6 and 7, plus the fact that most authors who focus on the issue end up supporting Lu.

I call the two of you for outside opinions, if it is not too much trouble for the two of you to navigate through this wall of text, because at present the discussion seems to be deadlocked, even though it has a majority being persuaded by the sourced arguments supporting a switch to Lu. Again, I am deeply sorry for asking you to take on such a large undertaking, but if not I fear this may not be resolved as our two sides are apparently deadlocked. If you have other commitments and cannot do it, then I understand and ask if you know anyone else on WP who may be willing to do it. Double sharp (talk) 07:44, 17 May 2020 (UTC)

Metrics

Our periodic table article runs to some 11,600 words. Of these words, the counts for the La-Ac and Lu-Lr sub-sections are 1,035 and 1,655 words or 23% of the entire article, in sum. The Lu-Lr subsection alone exceeds the word count of all other sections of the article bar the periodic trends and patterns section. It is longer than the next sub-section (La-Ac) by 60%. In turn, the La-Ac sub-section beats the next longest sub-section (kainosymmetry) by 47%. If we add in the new kainosymmetry 700-word sub-section (hands up how many people have heard of that concept?) the proportion of the article goes up to just short of 30%.

I believe the article would now fail the FA criteria on grounds 1a. "It is: well-written: its prose is engaging and of a professional standard;" 1d. "neutral: it presents views fairly and without bias;" and 4. "It stays focused on the main topic without going into unnecessary detail and uses summary style.".

I propose to redraft these sections, in my sandbox, so they do meet the FA criteria. Much of this content is better located in our article on Group_3_element. I intend to start by redrafting the two group 3 sub-sections into (a) observations in support of and (b) observations not in support of, and seeing how they then look. My aim will be to achieve a balanced presentation of each option, in summary form for our periodic table article, and in more detail, as appropriate, for our group 3 article.

I've pinged active project members, participants, and others. Sandbh (talk) 07:37, 24 May 2020 (UTC)

A first cut of separating out our periodic table article arguments in support of/or not, for the two group 3 options, shows the following attribution of word count:

Option	Support	Not
La-Ac	30%	70%
Lu-Lr	98%	2%

Sandbh (talk) 08:13, 24 May 2020 (UTC)

That's exactly reflecting the distribution of sources. Most sources studying the question support Lu-Lr. And even most sources who are not commenting on the question directly, but are weighing in on related material (i.e. ground-state electron configurations, or similarities in the periodic table), expose the problems fundamentally inherent in the La-Ac arguments. It's not "support" and "oppose"; what you put under "oppose" is an ironclad refutation, impeccably cited to reliable sources, of the premises the La arguments use. La-Ac arguments are presented based on (a) ground-state electron configurations, which authorities agree are irrelevant; (b) supposed similarities in chemistry of group 3 to the s elements and the principle of increasing basicity, which authorities agree are not all that matters and that are not telling the full story anyway. (Ah, I see I forgot to point out, based on reliable sources, that Lu being smaller and less basic than Y is nothing new since it is not clear that Hf is actually bigger than Zr either, see Jørgensen. Not to mention that Ga is less basic than Al.) Sc-Y-La has nothing to stand on and the reliable sources agree on that.

As for kainosymmetry, I bet you many more have heard of it under its also common names "primogenic repulsion" or "lack of radial nodes in the first orbital of each l value". I am not opposed to either of those names (maybe "orbitals without radial nodes" is the best name). I also wonder how many have heard of "linking or bridging groups" (which in reality should include everybody, as everything is a continuum here). Double sharp (talk) 10:03, 24 May 2020 (UTC)

Officer781

@Officer781: Pinging you, since I have discussed this with you on your talk page. Double sharp (talk) 10:24, 24 May 2020 (UTC)

Well, I would like to state that:

Firstly, having a split d-block is highly unusual and awkward. If someone were to be asked to build a long (32 column) periodic table from scratch he would not split it and upon getting to know how we currently do it would find it highly unintuitive.
Secondly, that Lanthanum and Actinium having a d1 configuration is part of the "d1 exceptions" which also includes Cerium, Gadolinium, Thorium (d2 but ok), Protactinium, Uranium, Neptunium and Curium (see Electron configuration). Notably, there is a cluster of 2 Lanthanides and 5 Actinides at the start of the f-block that exhibit this, because at the start of the f-block the d-orbitals are more energetically accessible. So it is "coincidentally" d1. Why we don't argue about why Cerium, Gadolinium, Protactinium, Uranium, Neptunium, and Curium should be Group 3, or why Thorium should be Group 4, but yet do so for Lanthanum and Actinium, is beyond me.
Thirdly, having Lutetium and Lawrencium in the d-block by no means discounts their status as Lanthanides and Actinides respectively. Elements are not so clear-cut and we can still consider them to be part of the d-block and yet have other characteristics. I would like to point out that this is the same treatment for the zinc group. They can be d-block AND be Lanthanides, Actinides and Post-transition metals respectively. I'd suggest that we keep the Lanthanide and Actinide colours for Lutetium and Lawrencium but put them in Group 3.

Eric Scerri and William Jensen have made good arguments in favour of Lutetium and Lawrencium. I defer to them but these are my main points in favour of Lu and Lr as part of Group 3. I don't know about Kainosymmetry so I have no comment as of now.--Officer781 (talk) 12:02, 24 May 2020 (UTC)

@Officer781: Hello Officer781. It's nice to hear from you, here.

1. The split d-block table has been around for many years, and has not raised any concerns aside from those raised by Scerri. It may look awkward, but we are here to draw Nature as it is, not how we think it should look. I'm not saying the split- d-block form is right, mind you, only that it could be. Just as Lu in group 3 could be.

2. The group 3 argument most recently started in 2008 when Lavelle said having La and Ac start the f-block would represent the only case of the first two rows of a block starting with elements having no electrons in common with that back. Such a precedent, in his view, was not warranted.

3. The group 3 argument is not about lanthanoid status, so much, other than the Ln being originally defined in the 1920s as La and Ce-Lu.

Scerri has put forward some arguments in favour of Lu. In Scerri's view, Jensen was too selective in his arguments. Sandbh (talk) 07:08, 26 May 2020 (UTC)

Re 1: Scerri's point, as I read it, is that the splitting is ad hoc and requires independent justification. What I would say is that since the splitting is a statement that the expected pattern doesn't continue, to defend it you must marshal some justification for a split between d¹ and d² from real properties.

Re 2: Lavelle did not mention starting the block. He wrote "However placing lanthanum (La) and actinium (Ac) in the f-block is the only case where a pair of elements that belong in the same group are systematically placed in a group that results in their being part of a block with no outer electrons in common with that block." And while that is true if you restrict yourself to ground-state gas-phase configurations (which is itself a deep rabbit hole), the same thing is true of Lu and Lr if you place them in the f-block. Double sharp (talk) 08:54, 26 May 2020 (UTC)

R8R

@Sandbh: I have not been watching the recent changes in periodic table; I merely saw that some changes had been made. If you're interested in my help, I could join you next weekend to see if there's anything worth correcting and sketching out a new structure of the subsection if that happens to turn out to be necessary. Ideally, I'd prefer that there was a way to talk through inclusion of each contentious statement available for everyone involved, including yourself and Double sharp. Can we do that on the talk page of your sandbox?--R8R (talk) 12:08, 24 May 2020 (UTC)

I am, by the way, not opposed to having the detailed text only in the group 3 element article (where I have already placed something similar), and having a brief summary at periodic table only. Double sharp (talk) 16:39, 24 May 2020 (UTC)

Дрейгорич

Definitely summarize the issue in the main article, and redirect users to Group 3 for further reading. Similarly for the hydrogen/helium placement controversy. ― Дрейгорич / Dreigorich Talk 18:59, 24 May 2020 (UTC)

@Дрейгорич: +1 Sandbh (talk) 06:48, 26 May 2020 (UTC)

Sandbox update

The write up of the two options now has the following top-level structure:

Supporting content

Introduction
Origin
Chemistry (inc. periodic trends)

Opposing content

Arguments 1,2, 3 etc

One can get a relatively quick appreciation of each camp on this basis.

The rough word counts, excluding collapsed green boxes for commentary and notes, are currently La-Ac 800 (300 pro; 500 con) and Lu-Lr 800 (675 pro; 125 con). The next step will be to blend in relevant commentary, including any overlooked arguments. --- Sandbh (talk) 00:30, 27 May 2020 (UTC)

In fact, Sc-Y-Lu is probably older (1895!) than Sc-Y-La

The first appearance in fact comes from 1895, with Hans Peter Jørgen Julius Thomsen (the same visionary who predicted a seventh noble gas at A = 292 that can only be what we now call oganesson). See Jørgensen's paper doi:10.1016/S0168-1273(88)11007-6:

“

At the end of last century, the most urgent question to answer about the Periodic Table was how many lanthanides there are. An interesting attempt to answer this question was made by Julius Thomsen (1895a) describing a set of vertical series containing 1, 7, 7, 17, 17 and 31 elements, each series starting with an alkali-metal and ending with a halogen. The relations between the second 7-series and the first 17-series admitted a 'double allegiance', all the elements Na to Cl being connected by diagonal lines both to the element with the same Mendeleev column number. K to Mn, and Cu to Br. The only connection between one 17- and two members of the 31-series was between zirconium with cerium on one hand, and the unknown element just before tantalum on the other. Julius Thomsen allotted the same number, 14, of places to the elements including lanthanum to ytterbium (and two empty places between Yb and Ta) as we do, but mentioned only 10 lanthanides, and not all the atomic weights in the order accepted today. It was speculated that the series 1 + 2 x 3 + 2 x 5 + 2 x 7 involving the three first odd prime numbers may produce the numbers 1, 7, 17 and 31 by being broken off.

Having heard about argon (discovered 1894), Thomsen (1895b) wrote a second paper about a conceivable group of chemically inert elements with A = 4, 20, 36, 84, 132, 212 and 292 without mentioning helium explicitly. This element has an emission" line close to the two Fraunhofer lines of sodium. This line was detected first during a solar eclipse in the outermost layers of the surface, by Janssen on August 18, 1868, and afterwards by Lockyer, who was observing the solar edge in October 1868, naming the element helium. In view of the simple line spectrum, it was considered likely to be a metallic element, and it was a great surprise when Ramsay (1895a) found that a gas extracted from uranium minerals gives this emission spectrum. This observation was presented to the Royal Society in London on April 25, 1895, and it is not too likely that Thomsen knew of it, though a telegram from Ramsay had been read in the Academy of Sciences in Paris March 25 (Ramsay 1895b) and the second paper by Thomsen arrived at the Editor on May 1, 1895. When the other noble gases (having complicated line spectra, rather similar to argon) neon, krypton and xenon were discovered in the.atmosphere by Ramsay and Travers in 1898, no doubt was left that the vertical series of Thomsen had 2, 8, 18 and 32 elements. Niels Bohr published the vertical version (with two sets of inner boxes) repeatedly, beginning 1922, and because of the novel theoretical background, it became known as the Thomsen-Bohr Periodic Table.

”

As for why he mentioned only ten lanthanides, perhaps it is because not all of them were yet discovered: in 1894, europium, lutetium, and promethium were not known. The point is: Thomsen placed La at the start of a 14-element series La-Yb that perfectly fits our idea of an f-block. So not only is Thomsen a bit of an "unsung hero" of the modern periodic table, but also this proves that Sc-Y-La has never been the undisputed version. In fact, this may mean that Sc-Y-Lu is actually the older form! Double sharp (talk) 10:21, 17 May 2020 (UTC)

Thomsen's 1895 table is here. Group 3 is B-Al bifurcating into a -Sc-Y-La tranche, and a -Ga-In tranche. The latter tranche bifurcates into an (-Lu) tranche, and a -Tl tranche.

Group 4 is C-Si bifurcating into -Ti-Zr and -Ge-Sn tranches. At Zr there is another bifurcation into -Ce and -Hf.

In the article Thomsen refers to "a larger number of the less common Earth corresponding elements all of which are closely related show" between Ce and Hf (which was not then known). So his thirteen rare earths ran from Pr to Lu (which was then not known). He shows eight rare earths with placeholders for another five. None of these 13 RE have hard line connections to the metals in the previous period. The atomic weights are listed in ascending order.

Jørgensen's interpretation i.e. 14 Ln, ten mentioned, and not all the atomic weights in the order accepted today, doesn't accord with what Thomson actually wrote. As well, the number of Ln was not known before 1913, and the Ln were not named as such until 1925.

Bohr's follow on table of 1922, which gave rise to the expression "Thomsen-Bohr Periodic Table" showed only 13 Ln, Ce-Yb. Sandbh (talk) 01:43, 26 May 2020 (UTC)

Well, we may read his paper here (in French):

“

On voit par le tableau comment les lignes pleines partent du zirconium dans deux directions opposées menant, l'une au cérium, qui a pour poids atomique 140, l'autre à un corps simple encore indéterminé, dont le poids atomique sera 180. Entre ces deux extrêmes s'insère alors la majeure partie des éléments qui ont des relations réciproques et répondent aux corps terreux rares.

”

— Julius Thomsen

"We can see from the table how the solid lines leave zirconium in two opposing directions, one leading to cerium, which has an atomic weight of 140, the other to a so far unknown element, which will have an atomic weight of 180. Between these two extremes are inserted the major part [my italics] of the elements which have reciprocal relations and respond to the name of rare earths."

I interpret this to mean that not all the rare earths are between Ce and eka-Zr [= Hf]. Just most of them. Lanthanum and cerium were definitely considered rare earths in his time, so probably was yttrium.

So I think Jørgensen's assertion is not incorrect, if looking at it from a somewhat anachronistic perspective, as Thomsen did indeed leave fourteen places going from La to Yb, with four blanks there (and then another two blanks where we would have Lu and Hf). However, now that I have seen it, I think Thomsen's table is not really classifiable as either Sc-Y-La or Sc-Y-Lu (it is neither, looking at the kinship lines), and thus I have deleted the interpretation of it as a Sc-Y-Lu table. Double sharp (talk) 03:51, 26 May 2020 (UTC)

The first pro-Lu table is probably Bassett's one: Henry Bassett, “A Tabular Expression of the Periodic Relations of the Elements”. Chemical News 65 (1892): 3-4, 19.
The first real Lu table is probably Werner's one: Alfred Werner, “Beitrag zum Ausbau des periodischen Systems”. Berichte der deutschen chemischen Gesellschaft 38 (1905), 916. doi:10.1002/cber.190503801163
Droog Andrey (talk) 17:50, 27 May 2020 (UTC)

@Droog Andrey: Thank you! Neither is quite the modern form (both being Be-Mg-Zn among other things), but both definitely make the claim that La is not in the same group as Y, and that there is an unknown element two spaces before Ta that should go there. Double sharp (talk) 04:32, 28 May 2020 (UTC)

Solid-state electron configurations

I complied this table after some discussion with Double sharp about the relevance of gas-phase electron configurations compared to solid-state configurations.

(a) The table includes two versions of the f-block, the first starting with Ce-Th; the second with La-Ac. The table with the first f-block version has 17 anomalies; the table with the second f-block version has 45 anomalies.

(b) In the case of the Sc-Y-La-Ac form, I wonder if such a solid-state table is more relevant these days than a table based on gas phase configurations, which has about 20 anomalous configurations. Partly we use gas phase configurations since electron configurations were first obtained (~100 years ago?) from spectroscopy, and this field primarily deals with gas phase atoms. That said, are gas phase configurations still so relevant these days—for this purpose—given solid-state physics? As well, most elements (85%) are solids, rather than gases (or liquids).

(c) It provides a first order explanation as to why the Ln like the +3 oxidation state. You can also see the later An metals (Es-No) like to be +2.

I’ve never been able to find a periodic table of solid-state electron configurations. Perhaps that has something to do with it? Then again, surely I’m not the first person to have drawn one of these?

This table is similar to Double sharp's table of idealised configurations, here. One difference is that the solid-state table shows group 12 as (sp)² whereas DS shows group 12 as (dsp)¹². --- Sandbh (talk) 11:56, 28 May 2020 (UTC)

Above post updated, and rearranged to provide better structure. Sandbh (talk) 02:05, 7 June 2020 (UTC)

Update June 6th:

The heavy alkaline earths now show as anomalous on account of d sub-shell hybridisation, which gives rise to their crystalline structures i.e. Ca-Sr are fcc (unlike the hcp of Be and Mg) and Ba-Ra are bcc.
Pa-Pu now show as anomalous given f-electron hybridization, which gives rise to their low symmetry crystalline structures
The two f-block options have been swapped so that the option with the lowest number of anomalies (17 v 45) appears first. In both cases, excluding the f-block, there are just six anomalies.
The heavy alkaline earths are shown as incipient d-block metals; La-Ac as incipient f-block metals; and group 12 as incipient p-block metals.

Still to address: reluctant pair for e.g. Pb (seems more likely to to be (sp)² rather than (sp)4); ec of e.g. F₂ etc; also H₂. Sandbh (talk) 06:36, 6 June 2020 (UTC)

@Sandbh: Seeing as your counting of anomalies would seem to suggest Be-Mg-Zn as giving fewer anomalies then Be-Mg-Ca (then you could label Ca-Sr-Ba-Ra as one separate thing), I am inclined to say that the supposed fewer anomalies with La-Ac vs Lu-Lr (even if it is true, which I doubt following Gschneidner) as it stands is not a conclusive metric at all for saying if the La or the Lu table is superior. Which is not even getting into the problem that your exclusion of the f electrons from the solid-state electron configurations appears to stem from them not having a very big presence in the conduction band (responsible for the metallic bonding), which is (1) an oversimplification, as Gschneidner and others have pointed out, and (2) rather questionable in the first place because in metals conduction takes place in partially filled bands that have properties of both the valence and conduction bands as they exist for nonmetallic elements, so there should not be a significant distinction at all between the valence and conduction bands. A brief guide. I just remind that for the lanthanides (except lutetium) 4f is very close to the Fermi level, as noted by Gschneidner and corroborated by the source you sent me, and that in all of them (except lutetium) 4f may readily participate in chemistry. They're surely a part of the valence band.

I still wonder where this is going to go with the nonmetals with conduction bands out of reach of the valence electrons' energies. That includes copernicium, by the way. Maybe in that case it is just going to be bonding, in which case we either say hello to all the core electrons in the nonmetals contributing London dispersion forces if we include intermolecular forces, or have to axe fluorine 2s because it contributes a net zero to the bond order if we only include intramolecular forces. Either way, it seems likely that there will not be so much regularity left after all these corrections are incorporated. Never mind that the way the electrons are used in the pure elements may not necessarily be what is done in compounds, as can be seen comparing the use of the 5p electrons in Xe vs XeF₄. Double sharp (talk) 07:13, 6 June 2020 (UTC)

@Double sharp: The solid-state ec table is a contribution to the debate. It's a first order approximation of the same ilk as the gas phase table. Nature is clever in complicating our task by precluding full consistency and simplicity in any periodic table. In this vein, and as a model, there is no need for undue concern about hard cases as long as these comprise a minority. F: I presume it's reasonable to include s²p⁵ as contributing to the London dispersion forces between F₂ molecules. Xe: I treat the solid-state configurations as a starting point, to compare configurations in compounds. The s-s ec seem more relevant, as I understand it, for the transitions metals, and at least the Ln. Sandbh (talk) 02:05, 7 June 2020 (UTC)

@Sandbh: With fluorine, if you want to include London dispersion forces, the 1s² core must also be included. So, that's already causing a problem for all the nonmetals forming covalent molecular structures. The f elements are in fact almost all anomalous from your perspective because of the dual nature of the f bands, so not a single one of them is right. (They are not near the Fermi level for nothing, and when the f bands don't contribute much it is for a divalent f element that is already "anomalous".) And we have the cases of the alkali metals, already discussed. If we add all those to your anomaly list it will go above 59. Why, every f element is anomalous (28), plus Ca-Sr-Ba-Ra (32), plus Na-K-Rb-Cs-Fr which lack much p involvement (37), all the molecular nonmetals but the first-row ones plus carbon (C-N-O-F-Ne-P-S-Cl-Ar-Se-Br-Kr-I-Xe-Rn-Cn, 53), and then all the "inert pair" elements (for which already the seventh row Nh through Og will be enough to hit 59, even if I can't remember how much of the 6p row should count here). Since half of 118 is 59, the hard cases are certainly not a minority!

The lanthanides are in fact an excellent demonstration of how the solid-state configurations do not tell the full story and have questionable relevance. 4f is not fully delocalised, yet it impacts the melting points, and participates in chemical reactions because it is in the valence band. That's even true for europium for which 4f delocalisation is at its minimum and lanthanum for which the 4f collapse is still underway. (But, revealingly, not for lutetium.) Much better to look at all configurations that appear across all chemical environments. More complicated, sure, but much more relevant than what we have with either gas-phase or solid-phase configurations. Not to mention that "solid phase" immediately means the gaseous elements are being considered in very far from normal conditions. And also because once you do that the number of hard cases suddenly drops to become a real minority: just the s elements, except with Ne replacing H. Double sharp (talk) 04:16, 7 June 2020 (UTC)

@Double sharp: That's interesting.

As a first order approximation, I may as well leave out London forces. Same applies to your other concerns about the anomaly list going above 59. Yes, "solid phase" immediately means the ~10% of gaseous elements are being considered in very far from normal conditions. That is much better than gas phase configurations, where > 80% of the elements are being considered in stupendously far from normal conditions.

I have thought about adding a reluctant pair dashed dividing line which looks like the opposite of the metal-nonmetal dividing line. Then again, it isn't so relevant. While Bi e.g. has a reluctant pair, Bi(V) is nevertheless still known. Indeed all of the elements impacted by the reluctant pair are still known in their group oxidation state. Sandbh (talk) 06:19, 9 June 2020 (UTC)

@Sandbh: Not true, there is radon (no VIII state) and the seventh row. I also remark that BiPh₄⁺ is also Bi(V) formally but has very little actual 6s involvement. ^_^

Well, if you leave out London dispersion forces, the entire noble gas column has no bonding whatsoever. So the approach then becomes very focused on metals and only the nonmetals that form giant covalent structures get something that fits them reasonably. That's precisely why I prefer considering the elements in their most normal condition of all: not in the pure elements, but in a large variety of compounds. And you seem to be agreeing with that by noticing that Bi(V) is still well-known even if Bi metal probably has the reluctant pair effect around. In that case we are back to my table with 4f on La and 3d on Zn, and the Lu table is a shoo-in. ^_^ Double sharp (talk) 06:26, 9 June 2020 (UTC)

@Double sharp: Given Xe (VIII) exists there is no reason to expect Rn (VIII) wouldn't. The OS are shown as "highest known" rather than group OS. I don't follow what the concern is about period 7. Recall the table is an idealisation. You raise some good points about the reluctant pair effect. It's not a big deal to add that; I'll see what it looks like. You're right, I need to give some more thought about the pesky NG. Sandbh (talk) 08:15, 9 June 2020 (UTC)

@Sandbh: Xenon has no big 5s and 5p_1/2 contraction, radon has it for 6s and 6p_1/2. Already RnF₆ is expected to be quite unstable, it's quite possible that radon(VIII) might not exist. The jury is of course out there as long as no one seems to have tried it. In period 7, probably flerovium has no +4, moscovium has no +5, and on to oganesson having no +8.

As I've been saying, there is a very simple solution that indeed brings the situation closer to real chemistry: don't just focus on the situation of no other atoms around (gas-phase) or only other atoms of the same type around (solid-phase). Go generally to the situation where any other atoms may be around, i.e. look at all compounds. It's more complicated for sure, just as solid-phase is more complicated than gas-phase. But it's worth it to make the basis actually what happens in the whole of real chemistry: you need it to get sufficient complexity. And it instantly means that aside from helium, neon, and argon, no one can complain about unusual conditions. Double sharp (talk) 08:32, 9 June 2020 (UTC)

@Droog Andrey: I'm aware that in those organometallics with stabilised group oxidation states like PbEt₄ and BiPh₄⁺ the 6s orbital is mostly nonbonding. But is it participating in the inorganics like PbF₄, BiF₅, PoF₆, AtO₄⁻? Double sharp (talk) 06:34, 9 June 2020 (UTC)

Observations

Double sharp

@Sandbh: What do the f's outside the brackets mean? If they mean to claim that the f electrons are not part of the valence band, that's wrong. Maybe this is most obvious for the early 5f elements: just Google the band structure of uranium or plutonium, they obviously have strong 5f-6d hybridisation.

As Gschneider and Wittig will tell you: the f electrons are not only corelike in the lanthanides, they make a small contribution to the valence band. And as is plainly obvious from the extreme properties of plutonium, they make a large contribution for the early actinides. That means there's a charge-transfer motif between 4fⁿ and 4fⁿ⁺¹ as usual, and what changes is which one makes up more of the average (it mostly just goes down from La to Yb, although Ce has more than La). A Lu table correctly tells us that this happens between La and Yb only, not Lu which acts as a normal transition metal. And of course we have more extreme situations in the early 5f elements.

You have never been able to find a periodic table of solid-state electron configurations probably because there are only average occupancies there. The counts of electrons in each orbital are always going to be nonintegers once you get past H and He. Nonetheless you can still see 4f starting to be part of the valence bands at La quite clearly. Double sharp (talk) 13:38, 28 May 2020 (UTC)

@Double sharp: The f's outside the brackets mean that, as an idealisation, the f electrons are not involved in bonding within the solid-state of the element concerned. In real life there looks to be one significant exception. I now have two sources, one explicit, and one suggestive, indicating that Ce metal might be better shown as f^½5d^1½6s². In this case, by "significant", I mean where the electron concerned has a contribution of 1 or ½. So I should show Ce as an anomaly with 4f^½(fds)^3½. I don't discount "small" contributions to the valence band but for the purpose of a solid-state table, don't count these as significant unless they get to at least close to a ½. Less than that makes me think that other "hand-waving" factors are likely to be more significant.

I have no knowledge of comparably "significant" f contributions to U or Pu. I've seen mention (twice) of 5.2 f electrons in real α-Pu metal, which is close enough to f⁵, as currently shown in the table. Sandbh (talk) 05:52, 29 May 2020 (UTC)

@Sandbh: This is certainly not true. Straight from Los Alamos: "the most-important new result from modern electronic-structure calculations is that, in its α-phase, all eight valence electrons are in the conduction band, which means that the 5f electrons in α-plutonium behave like the 5d electrons of the transition metals: participating in bonding and holding the metal together". Double sharp (talk) 06:07, 29 May 2020 (UTC)

@Double sharp: Yes, I've seen that. So, should Pu metal be shown as (fsd)⁸? Sandbh (talk) 06:21, 29 May 2020 (UTC)

@Sandbh: In general all the early actinides should be considered fdsp metals. Remember that for Ac through Np 5f is higher up and hybridising readily, being found amidst the obviously contributing bands. At the very least from Pa onwards it is completely undeniable. As for the trivalent lanthanides (not Lu though), and generally the trivalent later actinides (not Lr though), they may usefully be considered f^{n − ε} (fsdp)^~3 with both localised and delocalised f electrons. Asking for 1/2 to be "significance" is going to overlook too many obviously valence orbitals: I just remind that the 4f orbitals are obviously ready for chemical action at least in every lanthanide which has a +4 state or a "classical" +2 ion, in which redox processes change 4f electron count. That's already over half of them, interpolation (based on steadily increasing nuclear charge) makes it hard to argue with for all of Ce through Yb at least. For the actinides it is even more even without the interpolation. Double sharp (talk) 06:26, 29 May 2020 (UTC)

Officer781

Two things I would like to point out, with more focus on point 2 as I am more well-read in that area (I am more of a chemist than a physicist so my knowledge is much more heavily weighted towards chemical compounds than atoms):

I feel that having three electrons in the sd orbitals is not automatically the "default configuration". One can also consider the default to be two electrons in s and the rest in f. See electron configuration. The +3 configuration if I am not wrong is also quite popular in transition metals. The number of electrons having this configuration is less than your table looks I think, but I am not an expert.
The elements in the s-block (groups 1 and 2) are not sp. They may be for Beryllium and Magnesium, but everything below has more available sd orbitals than sp orbitals. Either it is sd or sdp for the heavier members. You can go look at what Gernot Frenking says about bonding in alkaline earth carbonyls. Since the ground state of the s-block only has the s-orbitals occupied, there is no special affinity of the s-orbitals for the p-orbitals. The only reason why Beryllium and Magnesium hybridize with the p-orbitals is because they are next in sequence. The orbitals next in sequence for Calcium and Strontium are d-orbitals and the next in sequence for Barium is the f-orbitals (it does seem that Barium has less contribution from f-orbitals mainly because of the highly contracted nature of the 4f orbitals, ie first row anomaly). Pekka Pyykkö did not call these elements "honorary transition metals" for nothing if the s and p orbitals have special affinity here. Our page on VSEPR also notes the hybridization of the s-orbitals with the d-orbitals is what gives heavier alkaline earth halides their bent shape, while they are linear for beryllium and magnesium because of hybridization of the s-orbitals with the p-orbitals.

Yeap, that's about all for now.--Officer781 (talk) 03:25, 29 May 2020 (UTC)

@Officer781: Where did Pyykkö refer to Ca-S-Ba as honorary transition metals?

You can see the metallic valencies of some actinides (+ pre-actinide Ra) from some authors here: it's clear that quite a few of the ones in the middle have valencies greater than 3. Double sharp (talk) 03:44, 29 May 2020 (UTC)

@Double sharp: Since I got to this I have a question. Why do we consider s-block elements as "main group"? They have not much in common with main group and although Beryllium and Magnesium can be considered main group, I'd argue that Calcium and Strontium are transition metals instead. Gernot Frenking and Pekka Pyykkö have also pointed this out especially in light of the synthesized alkaline earth octacarbonyls.--Officer781 (talk) 03:47, 29 May 2020 (UTC)

@Officer781: I would say this is a continuum. Ca, Sr, Ba indeed show "pre-transition" properties, but:

Even Cs does that. These come in gradually, K << Ca < Sc < Ti < V which no one can deny is transition (for Ti you may still argue that +3 is easily oxidised; for V the most stable state is +4 already, +5 is common but already somewhat oxidising).
Ca, Sr, Ba are rather extreme in properties for the d-block, which can only hold 10 columns and not 11: even though Ba and Hg both have some sort of d involvement, Zn-Cd-Hg makes a reasonable continuation past Cu-Ag-Au, they have real d-band contributions, and Ca-Sr-Ba are rather too alkaline for the d block! Not only do they show up as outliers in the range of variation, but in many cases they act like honest-to-goodness divalent versions of the alkali metals (Be and Mg, not so much).

And that's why I consider the more chemically useful classification to be Be-Mg-Ca-Sr-Ba-Ra, stressing instead the greater similarities of Ca, Sr, Ba, Ra with the group 1 metals than with the following d transition elements. Yes, Ca and Sr are intermediate, but Ba strongly skews to group 1 and not group 3; you cannot put Yb there, it makes no sense with the +3 oxidation state present. (Well, I guess this is not really controversial.) That way we get a table which reflects the symmetry-breaking preemptive s-orbital filling. Double sharp (talk) 03:55, 29 May 2020 (UTC)

s-block metals

@Sandbh: Other than our usual Lanthanide Actinide debate, I am okay with the zinc group being considered main group. My particular gripe is labelling the s-block elements (sp) as that implies p-orbitals have a special place with s-block elements which is only true for Beryllium and Magnesium. As can be seen I have a bigger issue with this than the Lanthanide/Actinide debate. Either we consider all of them just s, or split them according to rows, where first row is s, second and third rows (sp), fourth and fifth rows (sd), sixth row (sdf or sd or sf depending on your stance), and so on.--Officer781 (talk) 03:58, 29 May 2020 (UTC)

@Officer781: I think this table is about solid-state configurations in particular. OTOH, the Ca 3d band in the metal is already partially occupied and contributing to conductivity too, so your criticism is on point. Group 2 metals don't have full s bands in the solid phase because then the antibonding half would be occupied too! In actuality already both lithium and beryllium metals have 2s and 2p band occupation. Double sharp (talk) 04:10, 29 May 2020 (UTC)

Okay, I did not realize we are restricting our conversation to solid-state configurations. I am not particularly well versed in this so I will let the rest chip in. I've always wondered why they considered sp band together instead of split into s band and p band. I am not a solid-state guy as you can tell but rather a chemist. My actual degree is in Materials Science (with more focus on the chemistry side of things).--Officer781 (talk) 04:25, 29 May 2020 (UTC)

@Officer781: Yes, in solid state element terms there's no controversy (as I understand it) about treating Group 1 and Be-Mg as (sp). I've read about d hybridization for the heavy Group 2 metals. I don't yet know how extensive this is and whether it's significant, in my terms or if it's a smaller contribution. My impression is that it's incipient or small, rather then significant. Sandbh (talk) 06:12, 29 May 2020 (UTC)

OTOH, this paper doi:10.1103/PhysRevLett.49.1768 suggests at least 0.5 d occupancy. So perhaps I need to show Sr, Ba, Rn as (dsp)². Sandbh (talk) 06:31, 29 May 2020 (UTC)

This paper doi:10.1103/PhysRevLett.49.1768 says that, "From this experimental point of view, d-electrons are already responsible for the stability of the fcc structures in Ca I and Sr I at ambient conditions.", which is a big deal, on par with FCC Th.Sandbh (talk) 06:39, 29 May 2020 (UTC)

I cannot help but notice that Yb and No are fcc like Ca and Sr, but Ba and Ra are bcc. Not to mention that Zn and Cd are hcp like Be and Mg, but Ca and Sr are fcc. Just an interesting observation at this point, which I do not yet know how to explain. ^_^ Double sharp (talk) 06:46, 29 May 2020 (UTC)

hcp is just before IIIA; fcc is just before IIIB; bcc is just before "IIIf" :) Droog Andrey (talk) 17:30, 29 May 2020 (UTC)

Do the p bands actually have your desired 0.5 occupancy in the group 1 metals? Not that I think 0.5 is a good cutoff in the first place, but just asking as the s-p gap gets bigger down the table. Not to mention that if they do have more than that, then by simple mathematics the s bands would not... Double sharp (talk) 06:34, 29 May 2020 (UTC)

@Double sharp: This paper doi:10.1088/0953-8984/5/44/011 says:

Li 0.53s 0.47p
Na 0.75  0.25
K  0.67  0.33

So, Li, for sure. I'm not sure I want to show the rest of the series as anomalous. Sandbh (talk) 06:49, 29 May 2020 (UTC)

@Sandbh: Lithium indeed I expected to be the most likely. But the s-p gap gets bigger down the table. So it would seem to me that by the time you deal with Rb, Cs, and Fr we may be in a difficult position. Especially for caesium I have to wonder about the relative sizes of the 5d and 6p occupations. Double sharp (talk) 06:52, 29 May 2020 (UTC)

@Double sharp: I did think about making group 1 = s¹, and just showing Li as anomalous, being (sp)¹.

@Sandbh: This seems more or less like the exact sort of thing where I would want to forgo hard boundaries and instead call it (s++)^{1 or 2}, say that there is just a continuum with lessening p involvement down groups 1 and 2, and especially for group 2 greatening d involvement with Ca < Sr < Ba (also probably happens to a small extent for group 1). Double sharp (talk) 07:45, 29 May 2020 (UTC)

@Double sharp: I thought about something like that. My inclination is that since hybridization occurs over most of the periodic table to just focus on the more egregious, stand-out or significant cases. And add a disclaimer or note to that end. To pick out some remark-worthy boundaries among the fuzziness. Sandbh (talk) 08:14, 29 May 2020 (UTC)

@Sandbh: It nonetheless seems to me that if you consider the hybridisations generally you actually get more regularity throughout, such as for the s elements. And also for the f elements, which if considered as just (fsdp) with partial f contribution to the valence band throughout instead of trying to find a positive cutoff beyond with f involvement is ignored, end up with total regularity following the Lu table. Double sharp (talk) 09:14, 29 May 2020 (UTC)

@Double sharp: That thesis I linked to in the Incipient metals sub-section gives the Ln metals as fⁿ(spd)³. Sandbh (talk) 07:27, 30 May 2020 (UTC)

@Sandbh: To a rough approximation, maybe. However chemically the 4f electrons can certainly participate in a majority of these metals: remember that even in ytterbium they can be ionised (Yb²⁺ is [Xe]4f¹⁴, but Yb³⁺ is [Xe]4f¹³. Therefore I am not convinced that the f contribution to the valence band is totally negligible if they are still ready and willing to be used for chemical reactions. And, from below, it seems that calculations support that my scepticism of this idea is well-founded. And, especially, for the actinides this idea is just not going to work. Double sharp (talk) 09:46, 30 May 2020 (UTC)

p-block elements

Are those s-electrons really always bonding? Probably often, but I find that terribly hard to believe for the heaviest ones with the inert pair effect going at full blast. (I admit this is kind of a problem with my table as well for flerovium, but at least you might argue that compounds of Pb through At in their group oxidation states exist even if they are oxidising.) And also the chart's claims seem quite odd to me for the strongest nonmetals. Exactly what is the bonding involvement of 2s and 2p in solid neon? That is surely bound almost solely by London dispersion forces. But then 1s by the same token should also be considered: the core electrons count here, that's why Xe has a higher melting point than Ne! Double sharp (talk) 06:43, 29 May 2020 (UTC)

Lead has a close-packed structure but an abnormally large inter-atomic distance that has been attributed to partial ionisation of the lead atoms. OTOH, the group 4 elements like to hybridise to provide 4 bonding electrons. So, I don't know for sure about what's going on in lead metal.

In the case of the noble gases, I don't know. Certainly the bonding is just van der Waals. I'm guessing that since atoms "like" to hybridise their orbitals and that 2s and 2p are in the same shell, that there will be such hybridisation.

1s in Ne sounds like a rabbit hole; just like the 14f electrons in Lu shorten some its bond lengths. Sandbh (talk) 07:32, 29 May 2020 (UTC)

@Sandbh: It's hardly a rabbit hole, being high-school chemistry:

“

The reason that the boiling points increase as you go down the [noble gas] group is that the number of electrons increases, and so also does the radius of the atom. The more electrons you have, and the more distance over which they can move, the bigger the possible temporary dipoles and therefore the bigger the dispersion forces.

Because of the greater temporary dipoles, xenon atoms are "stickier" than neon atoms. Neon atoms will break away from each other at much lower temperatures than xenon atoms - hence neon has the lower boiling point.

This is the reason that (all other things being equal) bigger molecules have higher boiling points than small ones. Bigger molecules have more electrons and more distance over which temporary dipoles can develop - and so the bigger molecules are "stickier".

”

— Chemguide

Double sharp (talk) 07:34, 29 May 2020 (UTC)

Mass matters more than size. Just check the boiling points of H₂ and D₂. Droog Andrey (talk) 17:53, 29 May 2020 (UTC)

@Droog Andrey: Hmm, that is true (T₂ is even higher). So, is the increased melting point of Xe vs Ne primarily due to having over five times as many electrons, or due to having over six times as much atomic mass? Double sharp (talk) 05:32, 30 May 2020 (UTC)

And it's not just noble gases, let's talk for example about fluorine as F₂. Well, fluorine is 1s²2s²2p⁵. Note that the MOs derived from 2s give no net bond order (both bonding and antibonding orbitals are filled), as do the (much lower in energy) ones from 1s. Between molecules we only have London dispersion forces again. But if we go that far then we have the same situations where core orbitals must count, just comparing F₂ vs Cl₂ vs Br₂ vs I₂. Double sharp (talk) 07:50, 29 May 2020 (UTC)

@Double sharp: That wasn't what I was talking about which was the 14f electrons in Lu. I intend to ignore electrons other than valence or semi-valence electrons. On F₂ I have no answer. I don't know enough about what goes on in e.g. solid F. I did read an article discussing sp hybridisation in solid H crystals, which sounded unbelievable. What do you make of that one? Sandbh (talk) 08:07, 29 May 2020 (UTC)

@Sandbh: My problem with this comparison is with regard to how much of the contribution the electrons are making. Sure, Lu 4f never contributes anything to the valence band of the metal, it just sits in there as a core orbital causing incomplete shielding effects. That is fine, there is a clear difference between the 4f contribution and the 5d6s6p contribution, the second clearly dominates for interatomic forces. Then I look at solid or liquid Xe. The interatomic forces are simply London dispersion forces, the electrons are just travelling around in the electron cloud. It seems to me that whatever extra perks the outermost 5s and 5p electrons are getting in terms of distance from the nucleus are mitigated by the fact that those are 8 electrons out of the 54 whose movement can create London dispersion forces. And it seems quite plausible that the net effect of the 46 core electrons is actually greater than that of the 8 valence ones here, because the important thing is also the magnitude of the dipole that you are creating. It is not clear at all to me that you can single out the (sp)⁸ outer electrons as the bonding ones in such a situation. And for radon, it will be worse: 8 out of 86.

This is why I think the condensed phase is still not helping enough: you cannot put solid Cs and solid Ne in the same boat, the bonding type is too different and the conditions at which both can be seen are rather far from normal. That's why my approach tries to include all valence orbitals in all chemically normal compounds (i.e. stuff you can actually work with, or at least you could if not for short half-lives), with some common sense applied for He, Ne, and Ar.

Isn't this article about exciton states in solid H₂? So not quite the same kind of thing.

P.S. 14f in Lu are not valence or semi-valence (assuming that means "can be moved to valence" like 4f in your average lanthanide like Dy, say) electrons, neither are 14f in Lr. They are core electrons like 14f in Hf or Rf. So why are they still included on your table? ^_^ Double sharp (talk) 09:11, 29 May 2020 (UTC)

@Double sharp: The part of the article that caught my eye was, “The point is that the lowest conduction band is highly s-p hybridized; for instance, at /~ the eigenstateis s-like, while at X, L, W it is p-like, and in a generical k point a strong mixing occurs.” I don’t know enough about excitons to work out if this does or does not have any significance. Sandbh (talk) 11:00, 29 May 2020 (UTC)

@Sandbh: Neither do I, but since excitons seem to be related to excitation I suspect it might not be. Especially because that 1s-2p gap is quite big. Double sharp (talk) 12:26, 29 May 2020 (UTC)

BTW, the first excited state of hydrogen atom is 2p_1/2. Droog Andrey (talk) 17:59, 29 May 2020 (UTC)

Incipient metals

Given d sub-shell involvement in the heavier alkaline earths, and p hybridisation in Be-Mg and group 12, this looks to be what's going on. Sandbh (talk) 04:16, 30 May 2020 (UTC)

@Sandbh: If La is an "incipient" f-metal, then so are almost all the lanthanides, which have smaller 4f valence contributions. Remember, in order to fit the melting-point data we have to include a surprisingly high (about 0.7) 4f occupancy for La, per Gschneidner's paper (10.1016/0022-5088(71)90184-6); only from samarium onwards does it fall to about 0.1. However, I think that by any reasonable definition we have to call Ho for example an f-metal. And also that by this measure thorium would also be an "incipient" f-metal: the melting point drop is already visible, even if it is likely to be less dramatic than what happens next.

Also notice that the dhcp lanthanides are precisely the ones with the significant 4f involvements, looking at Gschneidner's Fig. 8. Double sharp (talk) 05:24, 30 May 2020 (UTC)

Melting point depression. For comparison, Gschneidner notes that pseudo-La if it were 5d^1.56s^1.5 like Lu really is should have a melting point of 1450 °C, vs Lu 1652 °C. So we may assume that if no f involvement was involved, the drop would be about 200 °C, and any further drop points to more f involvement.

Only for La-Lu and Ce-Hf is the 4f-5d comparison sort of fair: the delocalisation of the fourth electron on Ce is ambiguous. (Nonetheless, the melting point drop is immense and I cannot believe that full delocalisation of the fourth electron would save it.) I give Pr-Sm for completeness only, it is clearly unfair and hence in brackets. However, Ac-Pu vs Lr-Hs should be fair. Now note that the melting points of the first two 6d metals seem to be similar to and a bit less than those of the first two 5d metals from predictions, so in a pinch you can still see there must be a big drop that looks like the trough at Ce-Hf.

La	Ce	(Pr)	(Nd)	(Pm)	(Sm)
920	795	(935)	(1024)	(1042)	(1072)
Lu	Hf	Ta	W	Re	Os
1652	2233	3017	3422	3186	3033
Ac	Th	Pa	U	Np	Pu
1050?	1842	1568	1132	644	639
Lr	Rf	Db	Sg	Bh	Hs
1600?	2100?	?	?	?	?

I trust the f-involvement drops are clear even from this incomplete data. The likely melting point difference from Pa-Pu to Db-Hs should be huge, as the melting points drop for Th-Pu but should rise for Rf-Hs. Double sharp (talk) 05:42, 30 May 2020 (UTC)

@Double sharp: Yes, thanks for that contribution. As you say, 0.7 is a surprisingly high figure. I dunno; if it was that big I'd expect it would've been commonly known by now. That figure beats even Th metal's "puny" ~0.5 f. I'm in two minds about whether to include Th metal as an incipient f-block metal, as opposed to Th as a single atom.

I recall the chat about La metal having the most d occupancy of any of La-Lu. And we know Lu is metallurgically more like a late Ln than an early 5d metal. Which makes me think La is a good light 5d metal, there being no other light 5d metals. It's BP is the highest of the group 3 metals, > 3d metals, > and all Ln including Lu. That said, we still have the MP anomaly.

More work required on getting a better read on the extent of La metal f occupancy. Sandbh (talk) 06:39, 30 May 2020 (UTC)

@Sandbh: That is not true. Metallurgically speaking, Lu is both a perfectly normal early 5d metal and a normal late lanthanide. (Probably because for Gd-Yb 4f is more deeply buried than for La-Eu.) As Pettifor who you like to refer to points out, lutetium is like yttrium in that both have about 1.5 5d occupancy. Lanthanum is, on the other hand, not a normal early 5d metal: as Merz and Ulmer pointed out, its conduction band structure is not like the early 5d metals, and as Pettifor pointed out, lanthanum has 2.5 d-occupancy on average, unlike yttrium with 1.5. On the other hand, lanthanum is a pretty normal early lanthanide: it is not too different from praseodymium or neodymium. So, paradoxically, La metal having the most d occupancy of any of La-Lu is precisely what makes it a bad light 5d metal, because a d metal in this column (looking at 4d for comparison) should not have quite this much d occupancy: Y has 1.5, only Zr has 2.5.

If you want to know what the lightest 5d metal should be, it seems to me most useful to compare with what the second- and third-lightest of them are, i.e. hafnium and tantalum. It's obvious that lutetium is far closer to them in most ways than lanthanum.

As for how well-known the f contribution in La is: I just remind that the pretty big d involvements in Ca, Sr, and Ba are somehow not commonly known either. Remember that thorium 5f involvement was not well-known before that paper either, despite it being an obvious extension of Wittig's argument that thorium without 5f should be hcp like Ti, Zr, and Hf. Same argument works for La dhcp vs Sc-Y-Lu hcp.

I also remind that metallurgically speaking, Lr is a perfectly normal 6d metal (probably), but not at all a normal late actinide, because it's trivalent and not divalent. ^_^ Double sharp (talk) 09:32, 30 May 2020 (UTC)

@Double sharp: As we wrote, "the abnormal conduction band structure of La 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." And we noted conduction band anomalies elsewhere in the PT.

La, with 2.5 d electrons strikes me as a better candidate for d-block membership. Lu is certainly closer to Hf and Ta, as I'd expect given its Z-proximity. And we noted, "…metallic lutetium resembles closely erbium and holmium, except that it melts at a slightly higher temperature and is essentially non-magnetic, the details of producing, purifying and fabricating it are almost identical with those described under Holmium. Leal, Restrepo and Bernal (2012) compared 4,700 binary compounds of 94 elements. Sc and Y ended up in their own cluster; Lu ended up in a cluster with Er, Ho and Gd (La landed in its own cluster, as did Ce)." According to Restrepo, La is not a pretty normal early lanthanide. Sandbh (talk) 07:01, 31 May 2020 (UTC)

@Sandbh: What we wrote is not enough. First of all, if a nonhydrogenic f orbital is the cause of the weird conduction band structure, that is in itself already strong evidence that La is not a simple d metal and that it should be considered as an f metal. What are the band structures of Pr and Nd? I bet they will show a significant phenomenon of this type. The early actinides also probably behave like transition metals here because their 5f electrons are indisputably delocalised, where are we then?

And I think I have already explained many, many times what the problem with Restrepo's study is. I do not take his clusters terribly seriously: anyone well-versed in rare earth chemistry will tell you that La is a perfectly normal early lanthanide. Double sharp (talk) 08:13, 31 May 2020 (UTC)

Here's an open access thesis which notes "The standard model of the rare earths identifies the 4f shell as atomic-like, with vanishingly small wave-function overlap between neighboring atoms of the crystal lattice (the only exception here is Ce which sometimes forms a narrow band". Earlier, it refers to the standard model as being "extremely successful in describing the properties of the rare-earth elements and their compounds." This sort of confirms my understanding that 4f hybridisation is a level beyond simplest sufficient complexity. That said, the author does refer to 0.1 f presence in La, which seems a much more reasonable figure (p. 58). Sandbh (talk) 07:22, 30 May 2020 (UTC)

@Sandbh: But if we take that line there seem to be no 4f metals at all apart from cerium. And the only 5f metals are going to be the early actinides, already by americium or at most curium we return to more 4f-like behaviour. I think this is not a very useful way to explain the involvement of this subshell. Particularly since it is obviously chemically involved for every lanthanide which either has a +4 oxidation state or a "classical" +2 oxidation state, because then redox processes Ln³⁺ to Ln⁴⁺ or Ln²⁺ will change f-electron count. That is already Ce, Pr, Nd, Sm, Eu, Tb, Dy, Tm, Yb, which is a majority. With 5f it is already including at least all of Pa-Cf and Fm-No. I prefer to say: 4f is always involved at least a little, it is an indirect valent subshell. That also shows the significant difference we have between Yb and Lu, since at Lu it is no longer even that.

0.1 of an f electron on La (probably dhcp) accords quite well with Glotzel's figure of 0.17 for metastable fcc La. I am inclined to consider this significant. Remember, that means that on average one in six or at least one in ten La atoms in a metallic rod are going to have f occupancy!

Question: how much is the contribution of Pr or Nd 4f to the valence band? Those are the next trivalent lanthanides, so we may compare them with La. I suspect they might be comparable or maybe even a bit less due to the 4f collapse. Double sharp (talk) 09:32, 30 May 2020 (UTC)

f-block metals

For the 4f metals, I recommend The Dual Localised or Band-like, Character of the 4f States by Temmerman et al. It has a nice quote that backs up what Gschneidner was saying about two kinds of f electrons in the Ln:

“

...some properties of the lanthanides could be explained by a '4f-band' framework and some by a '4f-core' framework. This obviously implied a dual character of the 4f electron in lanthanides: some of the 4f-electrons are inert and are part of the core, some of the 4f-electrons are part of the valence and contribute to the Fermi surface.

The correct treatment of the 4f electrons in lanthanides is a great challenge of any modern theory. On the one hand, when considering the spatial extent of their atomic orbitals, the 4f electrons are confined to the region close to the nuclei, that is, they are very core-like. On the other hand, with respect to their position in energy, which is often in the vicinity of the Fermi level, they should rather be classified as valence electrons. ...

”

— (source)

And that's why I strongly believe that 4f hybridisation must be included to obtain simplest sufficient complexity. Because excluding it gives a theory that is insufficient to explain significant properties of the Ln. Double sharp (talk) 09:56, 30 May 2020 (UTC)

@Double sharp: I had a look at Rare-earths and actinides in high energy spectroscopy (Bonnelle and Spector 2015) doi:10.1007/978-90-481-2879-2.

They write that 4f electrons hardly participate in bond formation (pp. xiv, 29, 52, 81, 100, 191, 249) except in in particular cases, as when the valence of the rare-earth changes from trivalent to tetravalent (p. 246).

Re the "dual" model, they write, "Concerning the 4f electrons, two different situations can coexist in solids and, consequently, two initially opposite points of view can be unified: the one treats the 4f electrons as core electrons, the other considers the 4f electrons as weakly hybridized with the valence electrons in narrow energy bands. In the latter case, however, the on-site f–f interactions are considered to be strong, pushing the 4f electrons back toward localization. The hybridization of the 4f orbitals with the s–d valence band generally remains very weak, except in some particular cases as α-cerium (pp. 52).

The presence of the d electrons is considered as governing the crystalline structures of the trivalent rare-earths, which can, therefore, be considered as independent on the 4f electrons (p. 52).

The presence of localized f electrons stabilizes high-symmetry phases associated with large atomic volumes as well in the rare-earths as in the actinides (p. 73).

Changes in the 4f localization associated with effects of temperature, pressure or alloying are observed in the light rare-earths (p. 316).

I think this confirms Locht's assertion that the standard model, which treats 4f involvement in the Ln as negligible (except as noted) is "extremely successful in describing the properties of the rare-earth elements and their compounds." Sandbh (talk) 07:09, 31 May 2020 (UTC)

@Sandbh: So we agree that 4f electrons are participating when the valence of the rare earth changes. For example, Pr³⁺ [Xe]4f² to Pr⁴⁺ [Xe]4f¹; Sm³⁺ [Xe]4f⁵ to Sm²⁺ [Xe]4f⁶. Well, the little problem is that almost all the lanthanides have a "classical" +2 or +4 state. Straight from our lanthanide article:

Approximate colors of lanthanide ions in aqueous solution^[1]^[2]^[3]
Oxidation state	57	58	59	60	61	62	63	64	65	66	67	68	69	70	71
+2						Sm²⁺	Eu²⁺						Tm²⁺	Yb²⁺
+3	La³⁺	Ce³⁺	Pr³⁺	Nd³⁺	Pm³⁺	Sm³⁺	Eu³⁺	Gd³⁺	Tb³⁺	Dy³⁺	Ho³⁺	Er³⁺	Tm³⁺	Yb³⁺	Lu³⁺
+4		Ce⁴⁺	Pr⁴⁺	Nd⁴⁺					Tb⁴⁺	Dy⁴⁺

Ergo, it seems almost all the lanthanides have to be considered to have significant 4f participation in bond formation. Yes, 4f prevails in non-bonding MO's mostly, but:

this situation is in fact farthest from the truth in the earliest lanthanides, cerium and lanthanum (just look at those cubic complexes of La that cannot otherwise be explained):
even so, electrons are coming out of the 4f orbitals and being exchanged into the directly valent 5d and 6s orbitals, that's already chemical involvement of the 4f subshell. We obviously have to count electrons that are ionised away as part of the valence orbitals. Otherwise Na can't be a 3s metal either.

I also remind that structure of transition metals varies completely regularly with valence as long as magnetism or strong relativistic effects are not involved. This is completely not true for the trivalent early lanthanides which do not have the "right" crystal structures for group 3 transition metals. Which is in itself a symptom of f involvement, which was pointed out by Wittig, and was already instrumental in confirming that 5f in Th should have been looked for and was found.

“

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.

”

— Jörg Wittig (10.1007/BFb0108579)

“

Very little, if any, attention has been paid to the fact that Th, when compared to Ti, Zr, and Hf, actually should be expected to be a hexagonal close packed (hcp) metal like all other group IVA elements. Since this is not the case, the next step is to investigate whether Zr or Hf transform to the fcc structure when subject to high pressure. The reason why one should look for such a possibility is that pressure induced crystallographic transitions establishing connections between elements in the same row of the periodic table are well known for other groups of elements [5,11]. Indeed, the high pressure behavior of the elements Ti, Zr, and Hf shows that there is such a relationship between these three metals. However, neither Zr nor Hf undergo a transition to the fcc phase under pressure, but instead they are observed to transform into the body centered cubic (bcc) structure at 300 and 710 kbar, respectively [12]. Thus, among these tetravalent elements, Th is the only one showing an fcc atomic arrangement. Therefore we have to conclude that the fcc crystal structure for Th is indeed anomalous, and it becomes a challenge to investigate the fundamental reason for this.

”

— Johansson et al. (10.1103/PhysRevLett.75.280)

Now, yttrium does show the hcp→Sm-type→dhcp→fcc sequence when you increase the pressure (10.1016/0304-8853(82)90251-7), and that has been used as an argument to deny that 4f is the reason for it. However, as you go further in yttrium and the rare earths you get low-symmetry structures that must be explained with 4f involvement (10.1088/0953-8984/24/36/362201; presumably here 5s and 4d are charge-transferring to 4f, which due to pressure has probably been brought low enough). Wait, I said "rare earths": there is one exception among the heavy ones. I cannot help but notice that this is completely absent from Lu. Which tends to support my stand that the really significant difference in the rare earths is from Yb to Lu when the possibility of 4f involvement vanishes, not La to Ce.

Since this last argument admittedly is rather inconclusive, I propose a test: compare the band structures of La with those of Pr and Nd. I bet you La will be very similar to theirs. Combined with the chemically and physically obvious ways in which Lr fails completely to fit with the late 5f metals it strikes me that this would make a strong argument for Lu in group 3. Double sharp (talk) 08:38, 31 May 2020 (UTC)

@Double sharp: Thank you. Re "Which is in itself a symptom of f involvement," that is not necessarily the case for La, per Pettifor's conjecture about the d-electrons being responsible for dhcp in La. And as per Bonnelle and Spector, "The presence of the d electrons is considered as governing the crystalline structures of the trivalent rare-earths, which can, therefore, be considered as independent on the 4f electrons (p. 52).

Given La-Pm dhcp is close packed, I struggle to see how this could due to f-involvement, which we know is responsible for the low symmetry structures of the middle An (Pa-Pu). Which is followed by dhcp in Am-Es, where the f electrons are localized. f-involvement is however suggested to be responsible for Th fcc, so that is still a problem. Maybe it has something to do with Th being on the low-symmetry precipice. I don't know. Sandbh (talk) 05:56, 1 June 2020 (UTC)

@Sandbh: Just read the paper about thorium 5f involvement (10.1103/PhysRevLett.75.280). f electron involvement does not always result in low symmetry, as evidenced by thorium. I rather find it quite revealing that it is the earliest f elements with the most chances for slight f delocalisation that show this dhcp structure. That applies to La-Pm (early lanthanide series) as well as Am-Cf (the actinides that can still reach +4 even though f electron usage has become indirect). If it were merely a matter of d electron count, then although I am not an expert in solid-state physics, it seems to me a most remarkable coincidence that no d elements show this structure. I just see that this structure only appears for f elements and think it's suggestive, just like Hamilton did. Also, I see you agree that for cerium 4f electrons must be considered as partly delocalised: well, that one also has stable dhcp and fcc states around standard conditions. That's similar to lanthanum for which dhcp is stable and fcc is metastable, and praseodymium and neodymium which transition to fcc at high temperatures, which generally corroborates my stand that La is in fact close to Ce, Pr, and Nd with the strongest f involvements in the Ln series.

Once again I wonder about the band structures of Pr and Nd and how they compare to that of La. Double sharp (talk) 06:24, 1 June 2020 (UTC)

@Double sharp: Johansson et al. (2014): "The very fact that such a diagram can be designed can also be seen as an independent confirmation of the insignificant role the 4f electrons play for the crystal structure in the trivalent lanthanide metals." Sandbh (talk) 11:21, 4 June 2020 (UTC)

@Sandbh: Then:

How do they propose to explain the melting-point anomaly that Gschneidner pointed out, and:
even if that's true, that means that low 4f involvement in La metal actually is not a strong argument against putting it in the f-block in the first place, since Pr through Yb have the same thing going on, and:
it also doesn't really matter, because we can see that even if the 4f electrons are localised in the solid metals, they are for sure chemically active in most of the lanthanides already, including all of La-Yb. And we know that already from LaF₃ with donation into the 4f orbitals that is not different from what happens in Ce(IV) complexes.

I continue to much prefer "pre-f" La, Ac, and Th in the f-block to "non-f" Lu and Lr. And while I don't dispute that the 4f electrons are mostly core electrons in the solid metals, chemistry proves that they cannot be treated only as such, and some physical properties also continue to suggest a minor but nonnegligible 4f contribution to understand the full picture (i.e. low melting points associated with 4f-5d hybridisation; otherwise, the low melting point of La is difficult to explain). Double sharp (talk) 11:49, 4 June 2020 (UTC)

References

^ Cite error: The named reference Greenwood&Earnshaw was invoked but never defined (see the help page).
^ Holleman, p. 1937.
^ dtv-Atlas zur Chemie 1981, Vol. 1, p. 220.

Band structures

Going by structural similarity, the sequence looks like this:

Y: similar to Sc
Ba---effectively no resemblance to La
A. La, with a congested line (CL) running significantly above the central horizon (CH) [can't see much similarity to Y]
B. Ce-Pr, with the CL running along the CH
A. Nd-Pm-Sm, with the Cl running along the CH
C. Eu: like an earthquake, with the top half going right, and the lower half going left
A. Gd-Tb-Dy
D. Ho-Er-Tm-Yb*: For Yb the CL drops significantly; 
D1. Lu similar to D except the CL drops again; also the top line increases in energy so that only a third of it remains on the chart
Hf---effectively no resemblance to Lu

I can't see much in this:

[Ce-Pr] [Nd-Pm-Sm] [Eu] [Gd]
   B        A       C    A
[Tb-Dy] [Ho-Er-Tm] [Yb] [Lu]
   A        D       D*   D1

[La] [Ce-Pr] [Nd-Pm-Sm] [Eu]
 A      B        A       C
[Gd-Tb-Dy]   [Ho-Er-Tm] [Yb]
    A            D       D*

In a double periodicity sense, there is a modicum of better regularity in La-Ac (on the L) compared to Lu-Lr:

2-3-1-1      1-2-3-1
2-3-1-1      3-3-1

Over to you. Sandbh (talk) 08:29, 1 June 2020 (UTC)

@Sandbh: Do you have the original pictures? It seems at least from this that La and Lu are tentatively not terribly different from the surrounding lanthanides, but a bit more extreme as they come at the ends of the trends. What does the congested line represent? And what represents the 4f contribution to the band (which surely must be lowest at Lu)?

The crashes at Eu and Yb mean that Lu-Lr gives better double periodicity, as it fits well with a half-filled subshell being harder to delocalise (compare Mn and Zn). So I would tentatively consider this "inconclusive but suggestive towards the Lu table". Double periodicity is not just about making both lines look like each other (just compare Sc-Mn to Fe-Zn, or Ac-Am to Cm-No or even Th-Cm to Bk-Lr). It's about seeing the special position of the halfway and ending elements, which is already visible as early as B-N vs O-Ne. Which is why I keep insisting that the special positions of Eu and Yb are a strong sign that La-Yb is the right f block, because they match Mn and Zn.

How does Lu compare with the TMs from Ta onwards? And does La or Lu look more like Sc and Y? Double sharp (talk) 09:49, 1 June 2020 (UTC)

P.S. I suppose there is no chance of having data for the 7th row. But there I am very sure that due to the valency sequence Lr will not look much like Es through No and will obviously fit better with Rf onwards, so I suspect the argument if we had complete data would favour the Lu table. Double sharp (talk) 09:56, 1 June 2020 (UTC)

@Double sharp: I had a look at this 2000 paper by Johansson doi:10.1023/A:1012667128586 re d-occupancy in the Ln. A few extracts:

"It is a well known fact that for practically all the lanthanide elements the 4f electrons are localized, or nonbonding."

"On the right in figure 1, Yb is clearly a divalent lanthanide metal. Similarly, lutetium is a trivalent lanthanide and has three valence electrons. On the left in the same figure, these two elements are seem to be also [my italics] the first two members of the 5d transition series and the third, hafnium, will accordingly have four valence electrons."

"This difference may be understood in terms of the greater radial extent of the 5f orbitals relative to the 4f orbitals."

"Early in the series, Fr–Th, we observe a decrease in radius, which is caused by an increase in the amount of d character."

"A more complete treatment for the transition metals, due to Pettifor [46,47], related the hcp-bcc-hcp-fcc sequence through a d transition series to the change in d occupation number across the transition metal series.

"For the [trivalent] lanthanides the structure sequence hcp-Sm-type-dhcp-fcc was shown by Duthie and Pettifor [20] to depend upon the 5d occupation number, which itself is related to the Johansson–Rosengren f-parameter [5,15,19], which was used to rationalize the structure sequence."

"Finally, we would also like to mention that most recently Ahuja et al. [107] have shown that even the zero pressure fcc crystal structure of thorium is anomalous. If thorium were a normal tetravalent d transition metal its crystal structure should be expected to be hcp as for Ti, Zr and Hf. Ahuja et al. [107] showed that it is the presence of itinerant 5f electrons that makes the fcc structure stable in thorium. Thus, for all the early actinide metals, Th–Pu, it is the 5f electrons which determine the crystal structure behaviour."

From this 1983 paper cited by Johansson:

"The divalent alkaline earth metals have a crystal structure sequence of their own, i.e. hcp~fcc~bcc~hcp, as a function of d-occupation number, and…the divalent lanthanides, Eu and Yb, are part of that sequence."

But check the Q&A session, afterwards.

@Sandbh: Interesting. Will read when I have time. ;) Double sharp (talk) 09:24, 2 June 2020 (UTC)

Actinium

I don't yet know why Ac adopts fcc. Sandbh (talk) 08:12, 2 June 2020 (UTC)

This 2015 article doi:10.1002/pssb.201451569 doesn’t help with the question but provides some insight as to the nature of Ac. Effects of spin–orbit coupling on actinium under pressure:

”From the calculated density of states, we can see that the contribution of 5f states at the EF are almost negligible. These results are important, because from our study we concluded that Ac is a d-type system, similar to the transition metals.” Sandbh (talk) 11:02, 2 June 2020 (UTC)

@Sandbh: But, as you can see from the article, there are f states above the Fermi level that hybridise with the d states in the conduction bands there. And that implies that the conduction electron distribution has significant f character. Which rather supports my point about Ac as a 5f metal. ^_^ Double sharp (talk) 12:03, 2 June 2020 (UTC)

@Double sharp: Yes. They seem to place more importance on hybridization at the Fermi level. Earlier, they say, "it was found that the d–f hybridization at EF is almost negligible, i.e., the bands at EF are mainly of d-character. Then we conclude that, like the transition metals, Ac can be classified as a d-type system." So they say this at a page 4, and repeat this finding in their conclusion on page 6 (never mind f states above the Fermi level). Sandbh (talk) 06:53, 3 June 2020 (UTC)

@Sandbh: According to Wittig, it does not much matter whether the band is above or at the Fermi level. Let's see what he has to say about thorium in 10.1007/BFb0108579: "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." I do not see any difference between what he is describing and what we see in actinium. Double sharp (talk) 07:27, 3 June 2020 (UTC)

doi:10.1016/0022-3697(76)90167-0 (1976): "More likely, the f.c.c. structure of cerium, actinium and thorium is due to some d-s hybridization…". Sandbh (talk) 06:44, 3 June 2020 (UTC)

Which fcc structure for cerium? For the gamma phase 4f is mostly localised, for the low-temperature alpha phase it is not. And we know that if 5f were not involved for thorium it would be hcp like Ti, Zr, Hf, and Rf. So I think this source has likely been overtaken by later results.

As I have been saying many times, the structures of the transition metals vary completely regularly with valence as long as relativistic effects or magnetism are not involved. If you want to put La and Ac in the d-block, and use the d-orbitals only explanation, then the burden of proof is shifted to what mechanism is driving an increased d occupation for La and Ac that does not hold for Sc, Y, Lu, and Lr. So we are faced with two choices:

Either the 4f shell does not drive this. In which case, all things being equal, Lu in group 3 creates less anomalies in crystal structure, and less anomalies in d-band occupancy. Lu has the right number of d electrons for a group 3 metal (1.5 like yttrium), La (2.5) does not.
Or some sort of 4f resonance mechanism is somehow favouring occupation of 5d rather than 6s. I obviously do not know enough to correctly describe this, but Wittig's article (10.1007/BFb0108579) seems to suggest that something similar is quite possible: "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." And if this is correct, then Lu in group 3 is clearly favoured because this would prove 4f involvement in lanthanum metal. (We have, of course, already proved it for lanthanum compounds.)

Judging from the fact that the dhcp structure is only seen for f-block elements and La, I personally suspect the second alternative is more likely. But, the question is a bit moot because it seems to me that regardless of which one is right, the Lu table comes out looking better.

Not to mention that all things being equal, I would much rather have the "pre-f" elements La, Ac, and Th in the f-block than the completely "non-f" elements Lu and Lr. For which the f band must surely be deeply buried and doing nothing, looking at how it is for the compounds of Lu we've previously looked at here. And it also gets rid of the thorium double standard the La table still has a problem dealing with. Double sharp (talk) 07:24, 3 June 2020 (UTC)

@Double sharp: Well, there you go: "Actinium (which has no 5f electrons in the metal, free atom, or in any of its ions)…".

@Sandbh: Not totally conclusive as we know actinium 5f may be populated by ligand-to-metal charge transfer. What do they say about Th, which has no 5f electrons in the atom, and for which compounds with Th³⁺ and Th²⁺ centres seem to be 6d¹ and 6d² in the ground state? And what's the cite for this information about Ac metal, seeing as its short half-life should make it difficult to investigate thoroughly? Double sharp (talk) 08:09, 3 June 2020 (UTC)

...and I also see your source is from 2008 and therefore cannot have taken into account the 2015 results above about Ac 5f6d hybridisation above the Fermi level. And it also says "In metallic materials and in some other compounds with elements lighter than plutonium, the 5f orbitals are sufﬁciently diffuse that the electrons in these orbitals are ‘‘itinerant” (delocalized, chemically bonding, often with unique magnetic moments and electrical conductivity). In metallic materials and in most compounds with elements heavier than plutonium the 5f electrons are ‘‘localized” (not contributing signiﬁcantly to electrical conductivity or to chemical bonds)" (Pu can go both ways), and since Ac is lighter than Pu it seems to literally imply that Ac 5f is itinerant. Which is in accordance with the sources I previously gave here (doi:10.1103/PhysRevB.30.6943). Double sharp (talk) 11:40, 3 June 2020 (UTC)

@Double sharp: Haire (2007) gives a table of ec of the An in the solid state:

Ac    no f hybridization
Th    as above with potential for some 5f character being present
Pa-Pu f hybridization
Am-Lr no f hybridization

--- Sandbh (talk) 06:28, 4 June 2020 (UTC)

@Sandbh: Your source is not really focusing on Ac (searching for "actinium" only gives occurrences of "protactinium"), which is what I would prefer to see before ruling out f hybridisation for it. For one thing, the source you sent me yesterday (figures below) attributes a similar f occupancy at the Fermi level to Ac and Th. For another, I bet a lot of sources neglected f hybridisation for Th without focusing on it, maybe because of the ground state with no 5f in the gas phase, before it was pointed out that that model didn't make sense. Which seems even more likely to happen for Ac with the shape of the PT as commonly drawn influencing people to predict that searching for 5f in it won't be fruitful and therefore not try, and it being harder to study than thorium. And for yet another, the 2015 source you quoted right above affirms 5f-6d hybridisation above the Fermi level of actinium, which immediately implies that its conduction electron distribution has significant 5f character. For these reasons I think your source may not be right. Double sharp (talk) 07:59, 4 June 2020 (UTC)

@Double sharp: In this 1998 article, Simple model for complex structures, the authors offer a model that shows the light An prefer distorted structures whereas TM prefer cubic or HCP structures, with the exception of Mn (which they account for). They focus on U, Np, and Pu showing how the stability of their structures varies according to the number of f electrons.

Their model suggests the fcc structure should be stable for an f occupation of ~0.5, which is consistent with the observed structure in Th (Figure 2).

The same figure shows FCC as the most stable structure for Ac (~0 f occupancy).

They conclude the high-pressure structure in Am at ~110 kbar (11 Gpa) is either not α-U as suggested, or alternatively that the 5f configuration at this pressure is not delocalized and spin degenerate. They add that many other possibilities are of course possible, such as itinerant magnetism, partial delocalization, and so on.

Per Tonkov & Ponyatovsky (2005), Am at ~10 Gpa has a monoclinic structure; at 15 Gpa it has the α-U structure. --- Sandbh (talk) 07:39, 5 June 2020 (UTC)

@Sandbh: Actinium is not mentioned once in your article. Judging from Fig. 2 the model would be consistent even if actinium had a positive 5f occupation that was equal to or smaller than that of thorium: it would correctly predict an fcc structure. The latter of which, given results from the other articles we have raised here, I find quite plausible as we can see the same melting-point lowering for Ac vs prediction of Lr.

I also point out that the bar for chemical activity is lower than the bar for complete delocalisation in the metal. 4f does not meet the second bar in any lanthanide but cerium (it usually is mostly a core orbital with some valence behaviour), but it meets the first one in all but lutetium. Double sharp (talk) 07:45, 5 June 2020 (UTC)

P.S. The crystal structure trend in the f-block is pleasingly more consistent if it runs La-Yb, Ac-No. That way, the 4f row starts with a bunch of dhcp elements (La-Pm), an intermediate Sm, and then the hcp elements Gd-Tm, with Eu and Yb as divalent exceptions that sensibly recall how Mn and Zn have exceptional structures in the 3d row. And the 5f row starts with some elements where f involvement probably changes the crystal structure to fcc (we agree on this for Th, it is suggestive for Ac given its similar band structure to Th plus the same melting point anomaly), before the elements with stronger f-involvements have full-on distorted structures (Pa through Pu): then a return to the level of involvement of early 4f (Am-Cf) and then divalence as f sinks into the core. This is extremely consistent with the level of chemical involvement of the f subshell in both the 4f and 5f rows: higher in energy for Ac and Th, hybridising readily with 6d for Pa through Pu, something like a reserve orbital of the 4f type for Am through Cf, and then reluctant for Es through No. Lr is clearly something else where 5f is never breached chemically. And it is in part this consistency that leads me to consider Gschneidner's argumentation that f cannot be totally ignored here convincing.

Putting Lu and Lr in the f-block, as usual, means that they jut out weirdly from the trend and match neither neighbour element. La and Ce are both dhcp, Ac and Th are both fcc. Yb and No are fcc, Lu and Lr are hcp. And as usual Lr fits very badly indeed after Es-No all fcc. Double sharp (talk) 07:53, 5 June 2020 (UTC)

Why states above the Fermi level (e.g. Ac 5f) matter, courtesy of {{Band structure filling diagram}}:

Double sharp (talk) 04:39, 6 June 2020 (UTC)

Phase changes of some rare earths at standard pressure

From here: Sc and Y show no phase changes (i.e. change to a different crystal structure) till the melting point. This is the same as Lu, as well as the last trivalent lanthanides Er and Tm. Ta-Au also are like that, but Hf and Hg show phase changes. Zr seems to be the only 4d metal for which there was evidence of a phase change before the melting point.

La is not like that. In fact, La, Pr, and Nd act the same way: they start at dhcp, then as the temperature rises go through fcc and then bcc phases until they melt. Ce is almost the same, but has an extra low-temperature fcc structure (this is the phase with the delocalised f electron). Gd-Ho start at hcp but change to bcc near the melting point; Sm goes from its special structure to bcc before melting. Eu acts like Ba (bcc till melting); Yb starts at fcc, then moves to bcc, then melts.

Th through Am all undergo phase changes; Cm and Bk are at least known in multiple phases at STP. The absence of known phase transitions for Ac may be a matter of absence of evidence rather than evidence of absence due to its short half-life.

On the face of it this seems like a strong Lu argument, as La acts like a normal early rare earth with the biggest chemical 4f involvements (Pr reaches a mixed-valence +3, +4 oxide when burnt in air), and Lu acts much more like Sc and Y than La does. Double sharp (talk) 10:09, 1 June 2020 (UTC)

4f in Ln complexes

Interesting 2016 paper: doi:10.1021/acs.jctc.6b00238. As I am pressed for time today, here are just some quotes without much commentary.

“

The widespread application of complexes of lanthanide (Ln) elements begs a better understanding of their electronic structure.1,2 In this context, the question of whether the 4f orbitals of Ln participate in any bonding with its ligands, or to which degree this may occur, has been the subject of theoretical as well as experimental research. The spatial extent of 4f orbitals is small, limiting the possibility of overlap with ligand orbitals.3 For paramagnetic species, the spin density is likewise considered to be localized at the 4f center.4–6 However, recent computational and experimental research has indicated that for early lanthanides the 4f shell may act as an acceptor for ligand → metal (L → M) dative (donation) bonding.7–9 The 4f shell radially contracts with increasing atomic number within the lanthanide series. But even for late lanthanides, the assumption of the 4f shell not participating in bonding has been challenged. For instance, a significant covalency of the Yb 4f shell was attributed to YbCp3, based on experimental magnetic and optical data.10

...

The case for 4f orbital covalency loses traction when discarding orbital mixing without overlap as a measure of covalency and given the small spatial extent of Ln 4f orbitals. However, experimental evidence for both 5d and 4f covalency in octahedral lanthanide hexachlorides was recently obtained by Löble et al. using X-ray absorption spectroscopy (XAS),8 with the observed trends being supported by the results from KS calculations.

...

Questions surrounding 4f covalency in lanthanide complexes remain, and they warrant further study. For instance, would a degeneracy-driven L → M dative bonding lead to a partial electron transfer to the metal and thereby significantly alter the electron density distribution? Or would the DE [delocalisation error] be able to give rise to a functional-dependent variation of Ln 4f density via overlap-driven L → M dative bonding? For late lanthanides, and for Lu(III) (4f14) in particular, how may the DE or degeneracy impact any mixing between metal 4f and ligand orbitals in KS calculations? Are the 4f populations assigned to complexes of early lanthanides based on KS calculations physically and chemically meaningful, or mainly an artifact of the DE? Are sizable excess 4f populations from L → M dative bonding obtained in KS calculations for which the DE is minimized as best as possible?

...

To summarize thusfar: The Lu systems show no evidence of mixing of the 4f shell with ligand orbitals such that it would cause 4f delocalization. For the La(III) and especially the Ce(IV) systems, all calculations, including CCSD and TLC, produce sizable 4f populations. For highspin Gd(III), donation into 4f β-spin orbitals still amounts to on the order of 5% of an electron, with some calculations also producing a degree of delocalization of the α-spin 4f orbitals. The KS calculations for the Yb(III)complex 4 andYbX3 model systems give surprisingly large excess 4f populations. ...

Of the five NBOs calculated for LaF3 with dominant 5d character and assigned as ‘low occupancy lone pairs’, i.e. 5d acceptor orbitals of dative bonding (occupations between 0.025 and 0.04), two have only 5% f character. This may qualify as predominantly a polarization of the 5d orbitals. The other three NBOs have between 18 to 31% f character, which may be more appropriately interpreted as a d-f hybridization where a significant portion of electron density that may initially be donated to 5d ends up in the 4f shell. Finally, the sum of 4f NAO populations corresponding to symmetries other than those of the d orbitals, i.e. a′ 2 and a′′ 2, constitute between 30 and 40% of the total f populations given in Figure6. The situation is similar for the otherLaX3 complexes studied herein and therefore we forego further discussion of these results. Additional relevant NBO data on select complexes can be found in Figure S2. Based on these calculations and the data shown for LaF3, it would seem appropriate to assign at least some of the 4f populations determined by the NPA to ligand → 4f donation rather than mere polarization of a partially occupied 5d shell.

”

I am inclined to say that this supports what I have been saying about 4f involvement in La being similar to that in Ce, about 4f-5d hybridisation in La-Yb being significant, and about 4f having no significant contribution for Lu, and about going from Yb to Lu being the moment where the 4f involvement disappears. All this seems to support the Lu table, as Lu's lack of usage of 4f matches precisely Hf through Hg, whereas La is more similar to Ce than any of them. Double sharp (talk) 09:48, 2 June 2020 (UTC)

Spectra of singly ionised La and Ac (1957)

The spectra of singly ionised La⁺ and Ac⁺ have extra odd-parity terms that Sc⁺ and Y⁺ lack. These are due to 4f and 5f occupation respectively. It seems that [Rn]7s5f is a low-lying excited state for Ac⁺ at only about 3.50 eV. The main difference is that La⁺ 4f is more tightly bound that Ac⁺ 5f. Doubly ionised Ac²⁺ has [Rn]5f at about 2.91 eV, which bodes quite well for its possibility of occupation in chemical environments from ligand-metal charge transfer to Ac³⁺ (although of course La²⁺ has it significantly lower).

No 5f terms were found for neutral Ac, but the authors note that full observations were not done. For lanthanum they were, and 4f terms were indeed found. At the time this was written no 5f terms were known for neutral Th either, though.

Note that 5f Ac seems to be more firmly bound than 7p, but that 7p is in fact a bonding orbital for it (Ac₂ dimer has 0.49 7p occupation). I note that Ac₂ dimer has a little bit more 5f occupation than Th₂, Pa₂, and U₂ have 7p. ^_^

This difference seems to be another fairly good Lu argument. Double sharp (talk) 11:54, 3 June 2020 (UTC)

Band structures of period 6 and 7 elements

Sandbh has recommended to me Dimitris A. Papaconstantopoulos' Handbook of the Band Structure of Elemental Solids. So, here are Fermi-level state densities (States/Ry/atom). I apologise if there are errors, as seems inevitable with this many figures:

	s	p	d, e_g	d, t_2g	f		s	p	d, e_g	d, t_2g	f
Cs	14.05	1.93	1.87	2.59		Fr	7.19800	1.89658	3.90929		0.09406
Ba	2.34	1.33	7.68	4.16		Ra	1.289	0.978	4.268	1.909	0.238
La	0.99	2.898	5.673	11.717	3.809	Ac	1.259	2.872	5.405	10.092	2.052
Ce	1.646	1.764	2.351	7.192	44.412	Th	0.727	1.053	2.019	4.673	4.894
Pr	1.411	1.816	0.888	6.449	129.894	Pa	0.842	0.815	0.593	3.002	16.978
Nd	0.556	1.646	1.207	3.879	314.386	U	0.366	0.662	1.572	1.466	44.126
Pm	0.572	2.596	2.179	4.632	602.730	Np	0.303	0.762	2.071	1.923	82.779
Sm	0.654	3.307	2.100	2.601	588.530	Pu	0.281	0.560	0.852	1.087	42.570
Eu	0.554	5.261	1.906	9.271	0.422	Am	0.634	3.101	1.703	2.778	203.384
Gd	1.039	8.119	3.094	5.338	869.284	Cm	1.283	3.838	1.857	2.413	223.695
Tb	0.463	3.227	1.991	4.430	533.679	Bk	1.129	3.497	2.278	3.780	303.489
Dy	0.278	1.215	1.240	2.596	541.986	Cf	0.882	1.417	1.262	2.394	234.130
Ho	0.386	0.735	1.167	1.791	848.050	Es	1.130	1.049	0.989	1.465	325.858
Er	0.545	0.641	1.161	1.203	475.896	Fm	1.476	1.089	1.011	1.136	230.741
Tm	1.168	1.740	2.231	2.196	387.232	Md	1.187	0.609	1.256	1.128	80.238
Yb	0.578	4.452	3.271	2.319	4.546	No	0.168	0.411	1.099	1.215	0.161
Lu	0.291	2.462	2.242	7.297	0.393	Lr	0.197	1.410	2.363	5.021	0.374
Hf	0.14	0.93	1.97	3.62		Rf	0.41	2.49	2.38	8.61	0.56
Ta	0.54	2.46	2.83	11.25		Db	0.343	2.320	2.360	10.081	0.459
W	0.18	0.68	1.18	3.68		Sg	0.226	0.407	0.891	3.185	0.233
Re	0.23	1.28	3.52	6.01		Bh	0.316	0.656	6.142	2.673	0.367
Os	0.10	0.49	4.36	4.54		Hs	0.130	0.425	3.469	2.978	0.249
Ir	0.12	0.33	4.91	7.35		Mt	0.111	0.274	3.828	5.429	0.230
Pt	0.23	0.36	6.91	22.41		Ds	0.352	0.246	6.154	14.604	0.186
Au	0.98	0.58	0.67	1.75		Rg	1.960	0.238	0.215	6.061	0.097
Hg	1.761	1.182	0.140	0.329	0.106	Cn	Not a metal!

I think this strongly suggests that:

La is more of an f metal than Lu is;
Lu fits better with Hf-Hg than La does (Lu has the f bands fully occupied and below the valence band, for La they are just above the Fermi level):
Eu and Yb are the half-filled and full-filled elements for the 4f subshell, as those are the ones for which 4f is noticeably harder to delocalise (easier for Eu than Yb); for No 5f is almost unusable;
The thorium double standard I repeatedly accuse the La table of is well-founded, as Th 5f seems about equal to La 4f or Ac 5f.
The f-involvements of Lu and Lr are similar to those of the next 5d and 6d metals respectively, where the f bands are deeply buried.

So, there's another Lu argument, which is even more impressive when you consider that he had to push the f electrons into the core even for Ce-Sm. Double sharp (talk) 04:28, 4 June 2020 (UTC)

Of course, I note that states not too far past the Fermi level that hybridise with those around there can surely matter as part of the conduction band distribution. That's exactly why actinium 5f bands matter, just like thorium 5f and lanthanum 4f. Double sharp (talk) 04:41, 6 June 2020 (UTC)

@Double sharp: Do you know what is meant by d, e_g and d, t_2g? I don't. Sandbh (talk) 02:33, 8 June 2020 (UTC)

@Sandbh: See Crystal field theory. Which is, incidentally, touched on briefly (if only qualitatively) in the UK high school syllabus, albeit without the terminology. This terminology of course appears in Greenwood and Earnshaw (see p. 922). Double sharp (talk) 03:47, 8 June 2020 (UTC)

@Sandbh: There are symmetries of d-subshell orbitals. Droog Andrey (talk) 05:22, 8 June 2020 (UTC)

A challenge, based on Gschneidner

From his paper:

“

This dual 4f electron model enables one to explain at least qualitatively, the crystal structure sequence⁷, the melting points and heats of sublimation of the lanthanides. Heretofore, one model has never been able to explain all three of these properties, although plausible models which do not involve 4f electrons, can be used to explain each of these properties alone.

”

So, based on this, I raise the challenge: can you explain all of these, along with the coordination numbers of the Ln dropping from La to Lu, and the superconductivity issues raised by Wittig, without invoking 4f involvement, and have it all form one coherent picture as the 4f theory does? Not to mention that the dual 4f electron model is actually supported by calculations showing that the 4f states are always near the Fermi level for the trivalent lanthanides but not lutetium?

That's why I consider the 4f theory more plausible by Occam's razor. Not only does it fit exactly with what we know from the rest of the table, it also explains a lot of things and is supported by the facts. Double sharp (talk) 04:50, 6 June 2020 (UTC)

@Double sharp: I haven't yet responded to this challenge, given how much research it will require. Consistent with Friar Occam, and as far as I currently know:

the fall in CN from Ce to Lu is caused by the f-electron induced Ln contraction. Note, and this is important, there is no such contraction in La.
f involvement is not required to explain the crystal structure sequence of the f-block metals, aside from Pa-Pu; ditto mp and heats of sublimation
as discussed, f involvement is not necessarily required to explain the superconductivity issues raised by Wittig
as Gschneidner noted, "plausible models which do not involve 4f electrons, can be used to explain each of these properties"
there is no first principles requirement for expecting there to be one coherent picture; as we know, Nature is clever in complicating our task by precluding full consistency and simplicity in e.g. any periodic chart.
the 2006 paper you quoted from has zero citations
it refers to a 1971 paper, with 116 citations. That's nice, but over ~50 years is no show stopper.
in this 1990 ASM article doi:10.31399/asm.hb.v02.a0001089 in which Gschneidner, as the lead author, discusses the rare earths, he mentions 4f hybdridization just once, in passing. He discusses the physical and chemical properties without barely any mention of the 4f electrons, aside from one non-specific chemistry mention, and in the context of magnetic and optical properties: "For properties that depend upon the number of 4f electrons (that is, magnetic and optical properties), separated, and sometimes quite pure, individual rare earth elements are generally required…The 4f electrons are energetically and radially buried in an atom, do not enter into the bonding, and are only slightly influenced by the external environment around the lanthanide atom." He gives ec for gaseous, solid state, and ionic forms of the rare earths, using whole numbers (good enough for him). In his discussion of MP, BP, and heat of sublimation, nothing is said about 4f electrons etc.

I did find a paper doi:10.1016/0022-3697(76)90167-0 giving the ss ec for Ac as s^1.5 p^0.4 d^1.1…and writing that the f.c.c. structure can only be explained by ds hybridization. This accords with Bonnell and Spector (2015) who observed that Ac was not an actinide. Th was given as s^1.8 d^0.2 f^1.8 f^0.2. Further, "There is an almost filled s band, a small p character which according to the Engel correlation would give a b.c.c. structure effectively found at high temperature; thus the f.c.c. structure seems related to d-s hybdization, and the lack of a h.c.p. structure is explained by the small p character (I have seen a reference to this p character in a Russian text). Further, "…there exists also a small f character and this result can be compared with recent X-ray spectroscopy experiments on thorium metal [18] showing the presence of a localized excited 5f state about 1.7 eV above the Fermi level. This 5f state can be treated as a virtual bound state to explain the temperature dependence of the electronic density of states which has been found in most properties (resistivity, thermal conductivity, specific heat, magnetic susceptibility)[19]." Sandbh (talk) 07:51, 9 June 2020 (UTC)

@Sandbh: So, you cannot explain all of it as simply as the 4f explanation can. (BTW, 4f involvement is absolutely necessary to explain the superconductivity properties, as I already explained. And I see we're still hearing about how La supposedly is not impacted by the 4f contraction, never mind its 4f occupancy in its compounds.) You can only explain each one individually through different reasons, which usually when applied to other parts of the table start arguing for Be-Mg-Zn or B-Al-Sc instead, or trip over the thorium double standard. Shades of epicycles, indeed.

I see that "simplest sufficient complexity" only applies when you think it supports the La table. When it supports the Lu table you instead say "Nature is clever in complicating our task". Double sharp (talk) 08:00, 9 June 2020 (UTC)

Molar magnetic susceptibilities

The La are characterised by, inter alia, their magnetic properties but I'd never fully appreciated what that meant.

To this end, here’s a table of MMS values (χ) for the elements.

MMS is a measure of how much a material will become magnetised in an applied magnetic field. It is the ratio of magnetisation M (magnetic moment per unit volume) to the applied magnetising field of intensity H. This allows a simple classification into two categories of most materials' responses to an applied magnetic field: an alignment with the magnetic field, χ > 0, called paramagnetism, or an alignment against the field, χ < 0, called diamagnetism.

Observations
1. The average value for each block is:

2. Ln having unpaired 4f metals (Ce to Tm) have magnetic susceptibilities two to four orders of magnitude larger than those of normal metals.

3. Mn (511), Pd (540), O (3415) and Bi (-280) also stand out. A magnetic cross would be good for repelling a bismuth vampire.

4. I'm not seeing any support here for f presence in La or Ac, nor in Lu. Th is no better.

5. MMS reduces going down all groups of the d-block. The average reduction going from 4d to 5d is 50%.

6. In group 3 there is a reduction of 48% on going from Y to La. If Lu is instead placed under Y the reduction is 2%. --- Sandbh (talk) 02:51, 8 June 2020 (UTC)

@Sandbh: In other words, the thorium double standard strikes again.

The funny thing is that the reason why 4f causes this much is easily understood. 4f is not strongly delocalised, ergo it stays on the atom providing a strong magnetic moment. And this remains mostly in the lanthanide ions because 4f is buried enough to not be deeply affected by the ligands once the first electron(s) have been taken out of it. You don't see this so much for 5f which is more like 3d because the early 5f elements can use their 5f electrons even more readily. And notice that lanthanum is almost the same as thorium here. This is almost certainly a consequence of the fact that the f collapse has not finished by the time you are at La, Ac, or Th, therefore this effect doesn't happen. As we can see from all the examples previously shown here of f involvement in lanthanum and thorium, it is not because there is no f involvement but because their f orbitals remain above their d orbitals rather than being deeply buried the other way round.

Before saying that a category is characterised by something, you have to ask if that is the fundamental thing that makes them what they are, or if it is a consequence of something else. Here we see that this is actually a consequence of the singular situation of having a deeply buried f shell that is chemically active but at the same time buried enough to not be strongly affected by the ligand field. Double sharp (talk) 03:51, 8 June 2020 (UTC)

P.S. Exactly where did you find a source claiming Cm, Bk, and Cf to be ferromagnetic? Double sharp (talk) 04:32, 8 June 2020 (UTC)

doi:10.1103/PhysRevB.99.224419 Sandbh (talk) 01:02, 24 June 2020 (UTC)

@Sandbh: Interesting. But that is at ~205 K for fcc curium, which is neither at standard conditions nor the most stable allotrope at standard conditions. That would rather be dhcp curium, which is claimed to be antiferromagnetic at ~65 K. In the absence of a Curie temperature stated I would be cautious: at ~205 K, Gd and Tb are also ferromagnetic. Double sharp (talk) 06:51, 24 June 2020 (UTC)

@Double sharp: In doi:10.1016/0038-1098(75)90392-0, Fig. 1 shows the magnetic susceptibility of Cm as being about 0.03 (emu) at 300 K for an average sample size of 39.2 micrograms. This appears to suggest a MMS for Cm of (0.03 x 247 (atomic weight))/(39.2 x 10^–6) = 182,250 cf Gd 185,000. Does that look about right? For what it's worth, doi:10.1016/0038-1098(77)90239-3 notes the room temperature resistivity of Cm and some other physical and chemical properties show it's very similar to Gd (Table 1). I've seen mentions that the MMS of the trifluorides are similar. Sandbh (talk) 03:15, 3 July 2020 (UTC)

@Sandbh: That does seem reasonable. Curium has more localised f orbitals like the lanthanides in general, so the magnetic moment will be more like the 4f elements than the d elements. (Although that, of course, does not stop Cm from using its f electrons for chemistry anyway, just like the lanthanides.) Double sharp (talk) 03:23, 3 July 2020 (UTC)

@Double sharp: Values for Cm-Cf are graphed here: doi:10.1088/0034-4885/41/10/001. Chart updated; no surprises. Sandbh (talk) 06:41, 3 July 2020 (UTC)

I like these analogies:

Group	Metal	Sub-shell	Group	Metal	Sub-shell
7	Mn, Tc, Re	½-full d	7'	Gd-Cm	½-full f
11	Cu, Ag, Au	full d, accessible	13′	Yb-No	full 4f, accessible
12	Zn, Cd, Hg	full d, inaccessible	14′	Lu-Lr	full 4f, inaccessible

--- Sandbh (talk) 04:59, 8 June 2020 (UTC)

I dislike them strongly as Gd-Cm in fact are one electron above a half-full 4f subshell. Eu-Yb have 4f^{7 or 14}6s² and are really analogous to Mn-Zn 3d^{5 or 10}4s²: for both, the half- or fully-filled subshell is harder to get electrons out of, resulting in asymmetric structures for Mn and Zn and structures not fitting the trend (divalency collapse) for Eu and Yb, along with stabilisation of the +2 oxidation state. Meanwhile, the full d of Zn-Cd-Hg is really accessible for chemical bonding, so Lu-Lr is really analogous to the Ga group instead. That perfectly fits the trend: as you approach the full subshell, 3d or 5f is collapsing, ergo going Fe-Co-Ni-Cu-Zn the +2 state is more stable in each element than in the one before it just as it does going Cf-Es-Fm-Md-No. Adding Ga and Lr, with their returns to trivalency, to the trend, is not comparing like with like as the third electron no longer comes from the previously collapsing orbital but from somewhere else: 4p and 6d respectively. (No, I don't care about the anomalous configuration of Lr, the 6d configuration is a low-lying excited state anyway.)

Any look at oxidation states or physical properties will show you that. As we have gone over many, many times here. Just try finding any physical property at all in which Gd-Cm show a position on the trend more similar to Mn-Tc-Re than Fe-Ru-Os. Double sharp (talk) 05:57, 8 June 2020 (UTC)

@Double sharp: We're in the solid-state ec thread, wherein Gd is f⁷, as is Cm. As recognised by Schwarz, and by Scerri, solid-state ec's are more relevant to the chemistry of the elements. Eu is f⁷; Am lets the Lu camp down, being f⁶. That's my impression of the Lu option; there is always at least one element that lets the side down. The asymmetric structures of Mn and Zn are not due to it being harder to get the electrons out. Cu, for example, up to the 6th IE has uniformly higher IE's than Mn, yet is quite content to adopt plain old fcc. The full d sub-shell of Zn-Cd-Hg is not readily accessible for bonding; show me some of their compounds in an oxidation state higher than +2. Sandbh (talk) 07:39, 8 June 2020 (UTC)

@Sandbh: Neither are. In the solid state gadolinium and curium are both approximately f^7-ε (localised f orbitals) + (fdsp)^3+ε (contribution of three electrons in dsp on average plus a minute amount of 4f/5f delocalisation that explains why their melting points are lower than those of lutetium and lawrencium with no such f contribution). As recognised by anyone using common sense, including Schwarz, what is most relevant to the chemistry of the elements is the configurations in compounds in general. Not just in the gas phase, and not just in the solid phase either. What he wrote in 10.1021/ed8001286 was: "The qualitative behavior of chemical elements can be rationalized with the help of the dominant electronic valence configurations of the atoms embedded in a molecular or crystal environment." He never said "with only other atoms of the same type around in that molecule or crystal". The Lu option is consistent, the La option is always let down by thorium or by Be-Mg-Zn or by B-Al-Sc.

Then, please, by all means, explain why the asymmetric structures in the d block happen precisely at (1) the half-filled element Mn and (2) the closed-shell elements Zn, Cd, and Hg. Copper has no problem because it's perfectly happy to delocalise the d electrons normally, the same cannot be said of manganese and zinc. Technetium and rhenium are not anomalies just because the double periodicity weakens after the kainosymmetric first row, ergo only the stability of the fully-filled shell remain significant whereas that of the half-filled shell no longer is. Just compare group 15 to group 18, or Eu-Yb vs Am-No.

Asking for Zn, Cd, Hg compounds in oxidation states above +2 is missing the point, as usual. The transition metals have lots of carbonyl complexes in the 0 oxidation state like W(CO)₆, that doesn't mean that the tungsten atom isn't using any electrons for bonding. The bonding in ZnF₂ contains 4s and 3d valence contributions overlapping significantly with the fluorine 2p orbital, ergo 3d is a chemically active subshell for zinc. Same thing for LaF₃ containing 5d and 4f overlaps with fluorine 2p and with ligand-metal donation into the 4f orbitals that, while still mostly indirectly valent, are acting more or less like those in GdF₃, say (10.1021/acs.jctc.6b00238). You will never find anything of that order coming from lutetium 4f. But you will even find it from ytterbium 4f in YbCp₃. Double sharp (talk) 07:49, 8 June 2020 (UTC)

@Double sharp: While atomic orbitals and electron configurations such as Eu f⁷ and Am f⁶ are approximations, they are useful, and indispensable in practice. What Schwarz said applies as well to the elements in their condensed forms. I have no particular interest, at this time, in revisiting what is going in Mn and Zn. Since Russel & Lee are at hand, they suggest the half-filled 3d sub-shell of Mn gives each atom a large magnetic moment. The α-Mn and β-Mn structures align the atoms' magnetic moments anti-ferromagnetically. Below 727 °C the minimum energy arrangement to do this is the complex α-Mn structure.

Yes, given the success and extensive use of the oxidation state model—exemplified in our fine table of oxidation states of the elements—asking for Zn, Cd, Hg compounds in oxidation states above +2 is right on the mark. The level of detail you enter into is not needed here. Friedrich, a physicist, has written on this:

"Exact sciences cherish approximations. More often than not, resorting to approximations is a matter of necessity…that is the case when a problem cannot in principle be solved exactly. For instance, many-body problems fall all in this category, whether they are classical or quantum…We note that here many means more than two; hence there are very many manybody problems. Approximations are also introduced when seeking a qualitative understanding of a problem: approximations (called in this context models or treatments) reveal the structure of problems and aid in identifying analogies with other problems, thus adding to the sense that we can make of them…

* * *

"Approximations to the solution of a certain problem form a hierarchy, according to the degree of their accuracy; for many problems, an arbitrary accuracy can be achieved in principle and often in practice. A good example is the N-electron atom problem."

--- Sandbh (talk) 02:44, 9 June 2020 (UTC)

@Sandbh: All the oxidation-state consideration in the world will not tell you exactly which orbitals are bonding. Oh, look, praseodymium can make +4. If your dogma is that 4f must be a core orbital for everyone but cerium you'll suspect it came from promotion into 5d, and if your dogma is that 4f must be a valence orbital for everyone you'll say that there must be some 4f contribution to the bond. You have to do the calculation and see which it is. And, guess what, there is 4f involvement, just look at PrO₂. But you have to do some calculations, or more likely for us look up papers where someone else has done the calculations, to tell that there is. Care to tell me how oxidation states alone tell me whether it is the 3d or 4s electrons that are being used for the +2 state in Zn? Your approach doesn't have enough complexity to explain this.

A far more useful explanation is the dual f-electron model. Well, let's see how much positing f involvement explains at one go:

Melting point trend in Ln and An;
Molecular geometries of coordination complexes;
Trend in coordination numbers (decreases as f involvement goes down);
Trend in crystal structure of pure metals;
Heat of sublimation trend in Ln and An;
Superconductivity transition temperature trend.

Can you, denying f involvement, explain all of this in one go with one simple idea? If not, I posit that it is denying f involvement that leads to going beyond "simplest sufficient complexity".

And you miss the point that elements in their condensed forms are still not getting much closer to real chemistry than elements in their gaseous forms. We've simply graduated from "no other atoms around" to "only other atoms of the same kind around". Neither seems to happen much in real chemistry for obvious reasons.

Meanwhile, this table is still a fine exhibition of the thorium double standard inherent in the La table. Double sharp (talk) 02:57, 9 June 2020 (UTC)

A funny case where class-A-ness matters more than forming aqueous cations

Consider the distribution of the fission products in irradiated nuclear fuel. The noble metals (Ru, Rh, Pd) tend to appear as alloy pellets, but Zr and Nb follow the alkaline earths and lanthanides in appearing in complex oxide phases (Greenwood and Earnshaw, p. 1260). Heavy groups 4 and 5 surely do have something more in common with the preceding groups than the succeeding transition ones, after all!

In this context the relevant thing is fluoride volatility, in which the important change of behaviour happens between oxidation states 4 and 5. So much for the 3 vs 4 group divide. Ah, except that in the bad cases like Zr, chloride volatility is used again. Another perfect confirmation of how the boundaries shift and there aren't any sharp ones, and how you will get so much more understanding from really understanding electronegativity differences instead of trying to draw arbitrary lines. Double sharp (talk) 04:26, 8 June 2020 (UTC)

@Double sharp: The G&E example does not add much value in the specific context of this thread. That is to say, > 80% of the periodic table up to Lr are class A acceptor atoms, like Zr, Nb, and the alkaline earths and lanthanides. The class a; class b; and borderline, "acceptor ion" classification scheme (p. 909) is too broad, in this case. Sandbh (talk) 07:10, 8 June 2020 (UTC)

G&E are problematic for the Lu camp given they show Sc-Y-La-Ac and say +4 (aq) for Ti, Zr, Hf is too high to be ionic. E-pH diagrams of group 3 and 4 are sharply contrasted. The trivalent cations Sc³⁺, Y³⁺, Ln³⁺ are prominent, taking up ~17, 28 or 39% of the area of their respective plots (Ac 48%; Lu 30%). In contrast, Ti^{2+, 3+} takes up just ~5%, while the tetravalent cations Zr⁴⁺ and Hf⁴⁺ are not on the radar in sight (ph –1 to 15; –4 to 3 volts).

As we noted in 2017, "Sc-Y-La-Ac further shows simple trends of increasing basicity and in this respect are much more like their leftward neighbours Ca-Sr-Ba than their rightward neighbours Ti-Zr-Hf. The +4 state is too high to be ionic in group 4, even for Th and what little we know of Rf. While KCl, CaCl₂, and ScCl₃ are ionic compounds, the group 4 tetrahalides (Cl, Br, I) are volatile covalent liquids or solids. While one can obtain aquated La³⁺ (or Lu³⁺), hydrolysis proceeds so far for Hf that HfO²⁺ is obtained instead. La in particular is such a hard base that it is taken up by the body as if it were Ca." Sandbh (talk) 07:10, 8 June 2020 (UTC)

False. In acidic solutions Zr⁴⁺ and Hf⁴⁺ are obtainable, there is still cationic chemistry (hydrolysed for sure, just like what happens for actinide +4 cations), ZrO₂ and HfO₂ are high-melting, mostly ionic solids. There's not any sense in comparing just chlorides and nobody else, we can easily compare oxides or fluorides to see the line move past Zr and Hf, or compare arsenides to see only group 1 showing anything that can vaguely be considered ionicity at all. By similar "logic" we can equally well "prove" that Ga-In-Tl are much more like their leftward neighbours Zn-Cd-Hg then their rightward ones Ge-Sn-Pb by considering aqueous chemistry in the group oxidation state (for which Ge⁴⁺, Sn⁴⁺, Pb⁴⁺ really are too acidic for water, unlike Zr⁴⁺ and Hf⁴⁺), and off to B-Al-Sc this argument goes just like so many others purporting to support Sc-Y-La and no other seismic changes. But I see that false statements are still being repeated no matter how many times I refute them. It really does seem like the Lu side of this argument can by now be conducted by simply saying "this was refuted in Archive X, section Y, subsection Z, paragraph W, and also in section Y', subsection Z', paragraph W', etc. etc. etc." in almost all cases. Double sharp (talk) 07:15, 8 June 2020 (UTC)

P.S. The argument as you quote it is also circular. Sc-Y-Lu-Lr shows a typical transition trend that is much more similar to that of Ti-Zr-Hf-Rf. +4 state is not too high to be ionic and the rest is irrelevant or false as explained above. The hard basicity of lanthanum and actinium in fact makes them terrible outliers in the d-block which otherwise has no bases that hard, but are totally normal for the f-block. Double sharp (talk) 08:28, 15 June 2020 (UTC)

@Double sharp: Zr⁴⁺ and Hf⁴⁺ aren't seen within the normal pH range of –1 to 15, –4 to 3 volts, soluble species concentrations = 10^−1.0 M. There's nothing false about that. Likewise NO⁺ and NO²⁺ can form in highly acidic media. Likewise they don't appear in the elemental E-pH diagrams I was looking at. Likewise, no doubt, G&E had the same paradigm in mind. C&W (p. 882) write that the aq. chemistry of Zr is not very extensive as a +4 ion, even a large one, tends to be extensively hydrolysed (as you noted). Only at very low concentration (~10^−4.0 M) and pH 1 to 2 does the Zr⁴⁺ (aq) ion "appear to exist."

Looking briefly at the e-pH plots for Zn-Cd-Hg, the cationic forms for the first two take up 25% of their plots whereas poor Hg is down to 5%. Cationic Ga-Tl are 10–13%. Cationic Ge is 0%; Sn 1½; and Pb 8½%. So, yes, in terms of aqueous chemistry, Ga-Tl are more like Zn-Cd-Hg. Nothing surprising there.

The relevant premise, per classification science, is that while the line moves, it spends more of its time in one camp than other camps. That's how we characterise the four seasons for example, not by extrema but by the spread of normal boundaries. That's why we regard Na as a metal rather than a nonmetal, never mind it becomes nonmetallic at ~1.5 Mbar. Per G&E, groups 1–3 spend more of their time in the ionic part of the year, so to speak. Groups 4–5 significantly enough less so. As Hinrichs (1869) observed:

"…elements of like properties or their compounds of like properties, form groups bounded by simple lines. Thus a line drawn through C, As, Te, separates the elements, having metallic lustre from those not having such lustre. The gaseous elements form a small group by themselves, the condensible [sic] chlorine forming the boundary…So also the boundary lines for other properties may be drawn."

As Hinrichs did, so Goldsmith did, so G&E did (p. 909), so Schweitzer and Porterfield did with their e-pH plots, so I did (on my way to 1,500 accesses), as do you. Sandbh (talk) 01:14, 9 June 2020 (UTC)

@Sandbh: I only did it for simplicity's sake. That's why the definition I used is literally a one-category "a metal has a Fermi surface". (And it needs an update, now that I remember that copernicium is a radon-like insulator.) And if you read what I wrote later:

“

Some sanity has been used here, recognising that the trends are continuous: for example, Sb and Bi are not true metals, but they are much more like metals than nonmetals. (Antimony is about as weak as you can get as a metal and still skew more towards metallishness, I suppose.) For comparative purposes, it can be useful to broaden the scope of "nonmetals" to pretty much include the whole of groups IVp through VIIIp (yes, even lead!), and at the other extreme broaden the scope of "metals" to include even B, Si, Ge, As, Se, and Te (yes, even selenium!). So I have coloured to the right all the elements that may be treated both ways without raising too many eyebrows. Although I somehow doubt much will be able to nonmetallise Mc through Ts. XD Obviously 7p and 8p are my guesses.

”

In other words, I recognise that there isn't a sharp boundary, and it may well in some situations be worth calling even Pb a nonmetal and calling even Se a metal. Not the slightest problem with that. Therefore just to draw something I used the one-category definition "has a Fermi surface" with some sanity for antimony and bismuth. But in order to avoid misconceptions and to deal with copernicium being a problem I am tempted to forgo the whole thing and simply colour in blocks. It will certainly be more helpful for understanding.

I just remind that every +4 cation is heavily hydrolysed, that doesn't mean they should be neglected. Just read Wulfsberg, page 30. Even for most +3 cations, like Al³⁺ and its group or the d-block ones, metal hydroxides already start precipitating below pH 7, the solutions get cloudy. The d-block +4 cations already form lots and lots of hydroxide/oxide, but (1) so do the f-block +4 cations, and (2) the reaction is reversible (the precipitate dissolves again in concentrated hydrochloric acid). It's only past that that the reaction becomes irreversible, so you are in this case taking a real sharp-ish boundary and moving it to the wrong place. Let's also see what Greenwood and Earnshaw has to say about the largest +4 cation of thorium (pp. 1275–6):

“

The aquated, dimeric ion [Th₂(OH)₂]⁶⁺, which probably involves two OH bridges, seems to predominate even in quite acidic solutions, but in solutions more alkaline than pH 3 polymerization increases considerably and eventually yields an amorphous precipitate of the hydroxide. Just before precipitation it is noticeable that the polymerization process slows down and equilibrium may take weeks to attain. The same effect is found with Pu^IV where the persistence of polymers, even at acidities which would prevent their formation, can cause serious problems in the reprocessing of nuclear fuel.

The isolation of An^IV salts with oxoanions is limited by hydrolysis and redox compatibility. ...

”

— Greenwood and Earnshaw

Ergo, if you want to complain about Zr⁴⁺ and Hf⁴⁺, then there are no +4 cations left, and thorium has no simple cation either. I simply recognise that this is the same phenomenon as afflicts +3 cations, just at a lower pH. And that it is different from what happens for "cations" like As³⁺ or Ge⁴⁺ which simply do not exist in water.

Why is it that Ga-In-Tl supposedly being closer to Zn-Cd-Hg than Ge-Sn-Pb under this metric (which I've already explained doesn't work very well) apparently has no bearing on whether we should split the p-block, but the group 3 issue apparently has some on splitting the d-block? Even if it were true that groups 1-3 fitted together better, that's not an immediate excuse for splitting the d-block anymore than group 12-13 fitting better than group 13-14 is an excuse for drawing the table like this:

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 Ce-Lu Hf Ta W  Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
Fr Ra Ac Th-Lr Rf Db Sg Bh Hs Mt Ds Rg Cn Nh Fl Mc Lv Ts Og

In fact, in some sense this is more consistent about making its mistakes than Sc-Y-La. The d-block trend Zr-In is consistent with the f-block trend Th-Lr: both have an element that does not fit the trend dangling off the end. Well, Mn²⁺ and Zn²⁺ are "imitating" the electron configurations of Fe³⁺ and Ga³⁺, we can draw "analogies" to Eu²⁺ and Yb²⁺ before supposedly "half" and "full" Gd³⁺ and Lu³⁺. And it also puts aluminium with the pre-transition metals and boron as an honorary metal atom. Why don't you support this table as your argument logically demands by consistency? Seaborg also has a dual placement of Al both over Sc and over Ga, you know. Double sharp (talk) 02:49, 9 June 2020 (UTC)

@Double sharp: Given Sb has a predominately nonmetallic chemistry I don't agree it's much more like a metal than a nonmetal. Bi is about as weak as you can get as a metal and still skew more towards metallicity.

The use of some pragmatic sanity is goodness, as is simplicity's sake.

Cationic Al takes up 18% of its E-pH plot, which is respectable. While Zr⁴⁺ and Hf⁴⁺ are not on the radar, Th⁴⁺ is 15%, which is impressive. Pa^3&4+ are 1½%; U^3&4+ are 2½%; Np³⁺ is 10%; Np ⁴⁺ is 1%; Pu is about the same.

The PT you show above is similar to Pauling's (1960). I guess it did not get up due to the tyranny of Platonic symmetry, as Jensen complained about. Pauling subsequently dropped it.

I can support it in some aspects, but not as a general chemistry table. Ditto an Lu table.

If you treat metals as elements having Fermi surfaces, you'll have to count carbon (graphite) and arsenic as metals.

Sandbh (talk) 05:44, 9 June 2020 (UTC)

@Sandbh: When amorphized, C and As don't have Fermi surfaces anymore. But they are still stable in those forms. Ergo they are excluded. Amorphous antimony, however, lacks stability. Being less stable than white phosphorus is no mean feat.

Sb does not have a predominantly nonmetallic chemistry, it has a real Sb³⁺ cation (heavily hydrolysed as usual, but still cationic – reminds Zr⁴⁺) in water. Nothing new here, it's the same story as Fe³⁺ being played out at a lower pH. Sb is about at the limit of +3 cations just as Sn is at the limit of +2 cations and At at the limit of +1 cations. If you want to exclude that level, then Bi³⁺ is gone also, it needs strong acid. And it even manages to form antimony sulfate when dissolved in sulfuric acid. That's pretty intermediate between metals and nonmetals chemically, and physically Sb is not a bad p-block metal (these metalloids have much stronger physical metallicity than chemical metallicity). Just look at alloys: Sn and Sb alloys with other elements are usually metallic, for Ge and As they are usually not. If you want to focus on chemistry, then I guess rhenium stops being a metal at all. You do know Re dissolves in nitric and sulfuric acids to form perrhenic acid, not any rhenium nitrate or sulfate, yes? And that Sb³⁺ is way more stable than Re³⁺ as a simple aquated cation because the latter will happily start forming clusters?

You cannot compare different oxidation states equally, the +4 cations must be given more slack than the +3 ones for heavy hydrolysis just because of their charge. Well, like Droog Andrey suggested in archive 35 (many of these points I'm using in this comment are from him in that archive), compare Al³⁺ with Pu⁴⁺. Plutonium is hydrolysed more, yet aluminium is the weaker metal. (He originally used thorium, but plutonium makes the point starker.)

Just look at Marcel Pourbaix's Atlas of Electrochemical Equilibria in Aqueous Solutions, you will see small slivers for Zr⁴⁺ and Hf⁴⁺. Besides, the important difference is between whether you can get cationic species at all or if the hydrolysis is immediate, total, and irreversible. So, in this one case where there might be said to be a sharp boundary based on what species are not too acidic to persist in water, you shift the boundary artificially inward. ^_^

So, exactly what is the problem with the above table for general chemistry? In general chemistry it is generally better: Rayner-Canham notes that Al is often more like Sc than like Ga, and the Zintl line is between groups 13 and 14. The trend down B-Al-Sc-Y-La-Ac is a perfect match to Be-Mg-Ca-Sr-Ba-Ra, as befitting pre-transition elements with the noble gas core and two or three outer electrons that are readily removed. The heavier elements are mostly pre-transition in all cases, Mg and Al are intermediate, Be and B are the most nonmetallic (ah, but boron is still electron-deficient and acts as an honorary metal atom, and is not more out of place here than hydrogen is above lithium).

It's only when focusing on electronic structure that it looks "wrong". But then the Lu table is more consistent precisely because it makes clear that for Lu and Lr, f is a core orbital. La and Ac can use their f orbitals for chemistry and are correctly placed in the f block. Double sharp (talk) 05:59, 9 June 2020 (UTC)

P.S. Thank you for drawing my attention to the fact that I drew some boundary lines for metallicity on my table. I have removed them for consistency's sake and replaced it with colouring only by blocks. Other boundaries move too much: only electronic structure remains constant enough to serve as a basis! Double sharp (talk) 08:43, 14 June 2020 (UTC)

MP and BP of the Ln

@Droog Andrey: According to Double sharp, you wrote, "Boiling point trend of lanthanides definitely supports Sc-Y-Lu-Lr since it supports natural subfamilies La-Eu and Gd-Yb."

My reference is: Lundin R & Wilson JR 2000, "Rare Earth Metals - Overview of the physical and chemical characteristics of the rare earths includes details on their applications as alloying elements in metals and in zinc alloy coatings", Advanced materials & processes, vol. 158, no. 1, pp. 52—56

They divide the REM into five groups:

those with low MP and high BP - La, Ce, Pr, Nd
low BP - Sm, Eu, Yb, Tm
high MP and high BP - Gd, Tb, Y, Lu
high MP, mid to low BP and a high vapour pressure at the melting point - Dy, Ho, Er and Sc
Pm which really belongs in Group 1 but is highly radioactive and for that reason has no significant commercial use.

For the Ln, that looks like this:

La	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb	Lu

Or in double periodicity form where group 3 = Sc-Y-La-Ac:

Ce	Pr	Nd	Pm	Sm	Eu	Gd
Tb	Dy	Ho	Er	Tm	Yb	Lu

Or in double periodicity form, where group 3 = Sc-Y-Lu-Lr:

La	Ce	Pr	Nd	Pm	Sm	Eu
Gd	Tb	Dy	Ho	Er	Tm	Yb

I conclude MP and BP support Sc-Y-La-Ac since they support natural subfamilies Ce-Gd and Tb-Lu. How do you see this? Sandbh (talk) 04:53, 9 June 2020 (UTC)

It's a copy-pastable strong Lu argument:

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

Half- or fully-filled shell = delocalisation harder = metallic bonds weaker = lower melting and boiling points. Ergo, they come at Eu and Yb. Additionally lower melting point = increased f involvement per Gschneidner for all these approximately trivalent lanthanides. Ergo, it is strongest at the start of the series, La, Ce, Pr.

Remember, double periodicity is not about just creating matches between the two tranches. Otherwise we may start every period in group 2 and end it at group 1. Well, to paraphrase Droog Andrey: the trends are all still there, the extreme properties of the penultimate elements are just an exception because they closed the p⁶ shell early. The halfway and full-way marks have to mean something that is readily explained by getting the half- or fully-filled subshell. Your table shows Sm-Eu and Tm-Yb with low BP, that's exactly fitting what should happen at the end of each tranche. Ending the tranches at Gd and Lu doesn't make any sense if they're supposed to mean anything.

It's less obvious for the actinides because now the f contribution is much higher at the start of the series (it is already important for the Ln, but not as important as for the early An). So other factors are swamping the also already weaker double periodicity. However you can still see Am has a dip in boiling point and has a lower melting point compared to Cm, so Am has a much stronger case to be the halfway element than Cm. This weakness in double periodicity, which nevertheless still makes some appearance, is analogous to the 4d row. Double sharp (talk) 04:12, 9 June 2020 (UTC)

Electronegativity

Supports Sc-Y-Lu: under four different scales, the value of Sc is closer to the value of Ti than the value of Ca. And only in Allen is this not true for Sr-Y-Zr as well, and we should not pay too much attention to that since Allen is not completely well-defined for d and f elements in the first place.

Pauling: Ca-Sc-Ti 1.00, 1.36, 1.54; Sr-Y-Zr 0.95, 1.22, 1.33
Allred-Rochow: Ca-Sc-Ti 1.04, 1.20, 1.32; Sr-Y-Zr 0.99, 1.11, 1.22
Allen: Ca-Sc-Ti 1.03, 1.19, 1.38; Sr-Y-Zr 0.96, 1.12, 1.32
Kulsha-Kolevich: Ca-Sc-Ti 1.10, 1.33, 1.40; Sr-Y-Zr 1.05, 1.28, 1.35

Therefore we can see that group 3 is closer to group 4 than group 2.

Meanwhile we can also see that the low electronegativities of La and Ac are simply outliers in the d-block, but Lu and Lr fit well:

Pauling: La 1.1, lowest in the d-block, even if it is a bit closer to Hf 1.3 than Ba 0.89; of course, Lu 1.27 is perfectly reasonable (higher than otherwise lowest Y 1.22); similarly, Ac 1.1 vs Lr 1.3
Allred-Rochow: likewise La 1.08 lowest in the d-block, otherwise lowest Y 1.11; this is closer to Ba 0.97 than Hf 1.23
Kulsha-Kolevich (the only scale with all 118 elements): compare Ba 0.92, La 1.11, Lu 1.31, Hf 1.38; Ra 0.85, Ac 0.97, Lr 1.29, Rf 1.34. Note that otherwise the most electropositive d-block element is Y 1.28 and see how much La and especially Ac simply fit badly. Actually, here is a chart in colour:

Is	IIs	IIIf	IVf	Vf	VIf	VIIf	VIIIf	IXf	Xf	XIf	XIIf	XIIIf	XIVf	XVf	XVIf	IIId	IVd	Vd	VId	VIId	VIIId	IXd	Xd	XId	XIId	IIIp	IVp	Vp	VIp	VIIp	VIIIp
H 2.20	He 3.20
Li 1.00	Be 1.50																									B 2.00	C 2.50	N 3.00	O 3.50	F 4.00	Ne 4.50
Na 0.90	Mg 1.30																									Al 1.70	Si 1.90	P 2.24	S 2.64	Cl 3.06	Ar 2.94
K 0.80	Ca 1.10															Sc 1.33	Ti 1.40	V 1.48	Cr 1.56	Mn 1.52	Fe 1.60	Co 1.64	Ni 1.69	Cu 1.77	Zn 1.71	Ga 1.80	Ge 1.96	As 2.22	Se 2.52	Br 2.86	Kr 2.70
Rb 0.77	Sr 1.05															Y 1.28	Zr 1.35	Nb 1.44	Mo 1.53	Tc 1.51	Ru 1.62	Rh 1.68	Pd 1.73	Ag 1.79	Cd 1.66	In 1.74	Sn 1.86	Sb 2.04	Te 2.28	I 2.58	Xe 2.39
Cs 0.70	Ba 0.92	La 1.11	Ce 1.13	Pr 1.14	Nd 1.15	Pm 1.16	Sm 1.17	Eu 1.09	Gd 1.20	Tb 1.21	Dy 1.23	Ho 1.24	Er 1.25	Tm 1.26	Yb 1.19	Lu 1.31	Hf 1.38	Ta 1.46	W 1.54	Re 1.55	Os 1.67	Ir 1.75	Pt 1.84	Au 1.93	Hg 1.81	Tl 1.78	Pb 1.82	Bi 1.88	Po 1.98	At 2.09	Rn 1.94
Fr 0.72	Ra 0.85	Ac 0.97	Th 1.01	Pa 1.04	U 1.06	Np 1.08	Pu 1.12	Am 1.07	Cm 1.18	Bk 1.22	Cf 1.27	Es 1.32	Fm 1.36	Md 1.39	No 1.37	Lr 1.29	Rf 1.34	Db 1.41	Sg 1.49	Bh 1.59	Hs 1.72	Mt 1.83	Ds 1.92	Rg 1.99	Cn 1.91	Nh 1.87	Fl 1.85	Mc 1.57	Lv 1.65	Ts 1.76	Og 1.61

Just compare Ac with the values of the true d elements. Also notice that in this chemical electronegativity scale (so not suffering from the Pauling-scale problem in elements like Mo and W), the early d metals have similar electronegativities in each group. Just compare how well that works out if La and Ac are in group 3: very badly.

And just look at the trends from the penultimate group to the ultimate one of each block. Except for the exceptional s block with only two groups, we see electronegativity goes down (except fluorine to neon, exceptional as 2s2p is a complete 2nd shell). Halogens are more electronegative than noble gases, group 11 more electronegative than group 12. That similarly strongly supports Sc-Y-Lu. (Also true in Pauling and Allen for the d block; these however overestimate the electronegativity of the noble gases, which should apart from Ne be less than those of the corresponding halogens.)

Electronegativity strongly supports Sc-Y-Lu independent of the scale you pick. And it is based on the properties of elements in compounds, with atoms of other elements around, and for that reason is obviously much more relevant to real chemistry than either solid-phase or gas-phase electron configurations. To get something this useful from electron configurations you have to consider configurations in compounds, i.e. orbitals used to form MOs with significant bonding contribution. And, guess what, lanthanum 4f and actinium 5f are immediately forced inclusions of the same kind as thorium 5f. Double sharp (talk) 08:23, 15 June 2020 (UTC)

Looking at the trend lines for the three scales, I get a 97% or better fit going down group 3 as Sc-Y-La-Ac. For -Lu-Lr the best fit values I can get are 0.58, 0.7044, and 0.42 --- Sandbh (talk) 07:21, 22 June 2020 (UTC)

@Sandbh: Why are you looking at trend lines when it is abundantly clear from the other d-block groups that we should not expect a linear trend down group 3? Group 3 gives a trend more similar to the other d-block groups, i.e. a nonlinear trend, only if it has Lu in it. Those best-fit values mean about as much as the ones I would get trying to fit a line to a parabola: for them to have meaning, you must have some reason to expect a linear trend.

I ask again: how exactly do elements as electropositive, as hard, as large, as reactive as lanthanum and actinium fit in the d-block? Nobody else in the d-block comes close. But you find such elements in the f-block. Double sharp (talk) 07:24, 22 June 2020 (UTC)

Representativeness

In fact, the 3rd IP chart works well as a double argument. Not only does it clearly show natural La-Eu / Gd-Yb tranches (mimicking Sc-Mn / Fe-Zn), it also clearly shows that La and Ac, if placed in the d-block, become outliers. Nobody else is that reactive, nobody else is that hard, nobody else is that electropositive, nobody else is that large, and nobody else has such a low 3rd IP:

In the f-block, they are no longer lone wolves far away from the pack, but are instead perfectly ordinary early lanthanides and actinides.

La and Ac always significantly expand the range of variation of chemical behaviour if placed in the d-block. In the f-block they do no such thing. Neither do Lu and Lr in the d-block.

As Sandbh said in Archive 38, "a set of items is presumably more representative of its label the more the individual items in it match the label". Quite so. Therefore a category becomes more useful as its members become more homogeneous, and that Lu and Lr in the d-block is strongly supported.

Additionally, the label of the blocks are simply the orbitals: s, p, d, f, and soon g. Therefore, clearly we must expect elements in the x-block (x = s, p, d, f, g) to have some sort of usage of the x-orbitals. A Lu table is consistent with this, as La, Ac, and Th all have the same kind of usage of the f-orbitals. A La table violates this badly, as it puts La and Ac with their f-involvement (not different in kind from that of thorium, note the double standard) in the d-block (where they make the d-block significantly less homogeneous), and put Lu and Lr with no f-involvement at all in the f-block. And all for no chemical gain at all because Lu and Lr are in fact far more like d-block elements than La and Ac.

The standard He over Ne table, unless specifically colour-coded to mark out He as an s-element, incidentally also badly violates this by putting helium with no prospects of p-involvement over neon in the p-block. But at least there is some excuse for this since helium admittedly behaves chemically closer to neon and argon than beryllium and magnesium. Where's the excuse for it in group 3? There isn't any, because Sc-Y-La makes group 3 look not like a d-block group, but like an s-block group. Not to mention that the idea of keeping "s-like" elements together by cleaving group 3 away from group 4 is altogether wrong-headed: not only does it overlook the also rather s-like group 4 elements (which form aqueous cations and are not that different from thorium; just look how hydrolysed Th⁴⁺ really will be in aqueous solution), it also forgets that there exist such things as f-block elements, which unite in themselves the hardness of the s elements with the multiple oxidation states of the d elements, and is thus a further echo of the old erroneous "asteroidal" hypothesis! Double sharp (talk) 09:29, 16 June 2020 (UTC)

The idea that La³⁺ is not part of the f-block contraction because it has no f electrons

Doesn't make sense in the first place.

Suppose, counterfactually, that La did have a 4f electron in the ground state. Then I think this controversy would never have arisen in the first place, everyone would be favouring Sc-Y-Lu. Except that then La³⁺ would still not have any f electrons, so the same argument would still "prove" that La³⁺ is not part of the f-block contraction and that the f-block should run Ce-Lu. Even in that hypothetical that ground-state La was [Xe]4f¹6s².

Of course, there is not even anything like this situation in the first place anywhere else on the table. There's no constant oxidation state there, the only reason it happens for 4f is because we have a singular situation of a deeply buried subshell without radial nodes. Even for 5g that's unlikely to happen exactly that way due to relativistic expansion of the g subshell. Asking for this deeply exceptional situation to become a general rule for periodic table placement is the tail wagging the dog. Especially since it drags 5f kicking and screaming into it when we all know that this situation does not occur for 5f, which is very happy to provide oxidation states above +3. The majority even have a +4 state (thorium through einsteinium).

But, for sure we can equally point to a contraction from Y³⁺ to Ag³⁺ as Greenwood and Earnshaw does: high-school chemistry implies such things always exist in each period. Alas! Y³⁺ has no d electron and cannot go into the d block! And it's the most common oxidation state by far too! Well, Sandbh says below "+4 is the most common oxidation state for the 4d and 5d metals". Even better! Y⁴⁺ has no d electron either and has jumped into ionising the krypton core! Here we go with a d-block spanning columns 5 to 14 if you want to avoid a double standard!

The truth of the matter is that there is no obligation that the ion must still contain the characteristic electron type. They have been ionised, hurray, they're participating in chemistry. Otherwise sodium is suddenly not an s element either because Na⁺ has no 3s electron anymore. Ergo, the fact that La³⁺ has no 4f electron on it does not mean that La is suddenly not an f element, unless you want to claim that Cs⁺ and Ba²⁺ having no 6s electrons bars Cs and Ba from the s block too.

The more important fact is that ligand-to-metal charge transfer can push some electron density into the 4f orbitals on La, which can make a small participation to the bonding orbitals. That idea, electron configurations and bonding MOs in compounds, is the one way of using electron configurations that you can generalise just about everywhere and is actually relevant (not the artificial "solid- or gas-phase configuration" situation where only elements of the same type are allowed nearby). You will never see this for lutetium. And there's no analogy of Lu to zinc because Zn 3d is used as a bonding MO even if its electrons are not ionised. You cannot simply just look at the maximum oxidation state of +2 to rule it out, you have to do the calculation. Unless you want to claim that BiPh₄⁺ has significant 6s bonding involvement just because it is Bi(V). It does not.

Sc-Y-Lu is vindicated again. Double sharp (talk) 12:00, 16 June 2020 (UTC)

The argument that nothing changed in the chemistry of lutetium

Doesn't make sense either.

Since Mendeleev, reality has not changed, the secondary relationships like F-Cl-Mn are still there. That doesn't mean we should stick to his 8-column layout.

When Seaborg advanced the actinide concept, nothing changed in the chemistry of uranium either.

I also add that Sc-Y-Lu tables have been around since 1892 (Bassett) and 1905 (Werner), even before Lu was discovered. The fact of the matter is that Sc-Y-La has never had an uncontested reign: it has always had competition from Sc-Y-* and Sc-Y-Lu. Now that we know what is really going on with the blocks, we can see that actually Bassett and Werner had this one right all along. But it's not because of some supposed "chemistry battleship" rolling on with Sc-Y-La, as there was no such thing in the first place. It cannot even agree where to put hydrogen and helium. Double sharp (talk) 12:02, 16 June 2020 (UTC)

P.S. Just search "periodic table" on Google Images and see how many examples of Sc-Y-* you get. There is no "chemistry battleship" flying the flag of Sc-Y-La. ^_^ Double sharp (talk) 12:21, 23 June 2020 (UTC)

The argument of differentiating electrons

Makes no sense, as they are ill-defined. There is no such thing between vanadium [Ar]3d³4s² and chromium [Ar]3d⁵4s¹.

And in any case, ground-state electron configurations are irrelevant for chemistry. They simply mean "what is the configuration taken when no other atoms are around". So are solid-state electron configurations, which simply mean "what is the configuration taken when only other atoms of the same type are around". Neither is a chemically normal situation!

We must use chemically normal situations, in which we can see lanthanum 4f has a capacity for usage not different from thorium 5f. Putting one in the f-block and forcing one out is a double standard.

For more double standards, simply take any Sc-Y-La argument and see what it arbitrates on the group II issue (Be-Mg-Zn or Be-Mg-Ca?), the group III issue (B-Al-Sc or B-Al-Ga?), or the thorium issue (is thorium a d-block element after all?).

That is what Sc-Y-La is: a double standard. Tearing Lu out of the d-block for no chemical gain (since, as we all know, lanthanum is not within the range of variation of the other d elements but lutetium is), putting it in the f-block with zero usage of f electrons for chemistry. With arguments which really support boron and aluminium over scandium, thorium in the d-block, or beryllium and magnesium over zinc. But not acknowledging any of that. Double sharp (talk) 05:47, 17 June 2020 (UTC)

The argument of keeping pre-transition-like groups 1 to 3 together

So what about aluminium, far away in group 13?

And what about zirconium and hafnium, which do the same thing that those trivalent elements in group 3 do at a lower pH? Double sharp (talk) 13:29, 21 June 2020 (UTC)

There are only so many things you can do in a periodic table. Al being far away in group 13 is one of them unless you place it (and H and B) over Sc ^_^.

Zr and Hf fall off of the "normal" plot, in a manner somewhat analogous to sodium becoming a nonmetal. Many things become possible given sufficiently extreme conditions. Sandbh (talk) 06:30, 22 June 2020 (UTC)

@Sandbh: But you must be consistent. If you claim "keeping pre-transition-like groups 1 to 3" is important, then you must explain why you do not put aluminium over scandium in group 3. Especially when the chemistry of aluminium is more similar to that of scandium than that of gallium in many ways.

“

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.

”

— Periodic patterns: the Group (n) and Group (n + 10) linkage. Geoff Rayner-Canham (2012)

And even when aluminium does not skew more towards scandium, we can still note that gallium breaks a trend because it is less basic than aluminium rather than more. That's the same situation that lutetium under yttrium finds itself in. Of course, if we look globally we realise that both are because of the immediately preceding 3d and 4f contractions.

So: if you argue Sc-Y-La because it makes a pre-transition trend – Al belongs over Sc. If you argue Sc-Y-La to give increasing basicity down the table – Al belongs over Sc. If you argue Sc-Y-La because group 3 is supposedly more like group 2 than group 4 (it's really intermediate, look at organometallic chemistry especially for ways group 3 is more like group 4) – Al belongs over Sc. (Because group 13 is more like group 12 than group 14 by these measures.) And if you argue that Al cannot go over Sc because Al uses only s and p orbitals, whereas Sc also uses d orbitals – Lu belongs in group 3 as La also uses f orbitals. And if you argue that La³⁺ has no f electrons and cannot start the f block – Sc³⁺ has no d electrons and by that logic cannot start the d block, so Al belongs over Sc.

It's simply inconsistent to argue for Sc-Y-La and not also advocate moving aluminium over scandium. A periodic table can easily accommodate that. That's only what these La arguments say, mind you: other La arguments would similarly require moving magnesium over zinc or thorium under hafnium. The Lu table, au contraire, does not suffer this. Except maybe for helium over neon, which can be swallowed because there is nothing else so huge chemically. (If you doubt this, try finding a Lu argument that I have used that if applied to anywhere else on the table argues for a change. With the obvious exception of helium over beryllium, because I support that anyway.)

The only consistent argument so far for Sc-Y-La seems to be "that's the most common form". Which is rather questionable given the large quantities of supposedly Sc-Y-La tables that are really Sc-Y-*. And would also torpedo your current preference of hydrogen over boron, and which incidentally makes hydrogen over lithium questionable too (the variant of floating hydrogen is also quite common).

The conditions required for zirconium and hafnium (pH < −1) are not too extreme for a normal laboratory. (You know that Sigma-Aldrich's concentrated HCl already gives you that, yes?) They appear on the plots in Pourbaix's Atlas of Electrochemical Equilibria in Aqueous Solutions. If they're excluded, we have to say bye-bye to Ce⁴⁺ and Pu⁴⁺ as well. A cation as the starting point of hydrolysis still is important for chemistry even if the predominant species at a slightly less acidic pH is strongly hydrolysed. Al³⁺ is moderately acidic, at normal pH it is already significantly hydrolysed. Th⁴⁺ is more so, Zr⁴⁺ is still more so. But both are still not so acidic that they react irreversibly with water. Here is one significant exceptional situation where you can point to a "hard" border, confined as we are in this discussion to aqueous media, as to what cations are too acidic to persist in water. (Of course it all goes away once you allow other solvating ligands and many nonmetals start forming cations.) Moving it inwards to exclude Zr⁴⁺ and Hf⁴⁺ is simply subjective, ignores the real boundary here, and obscures the trend. Double sharp (talk) 07:22, 22 June 2020 (UTC)

From what I've read, the consistency question seems to come down to the treatment of gas phase configurations. So Al stays in the p-block. And Ce starts the f-block. In the case of He its nobility trumps configuration consistency. In the case of Th its similarities with Ce trumps the configuration requirement, with some organisational tidiness thrown in for good measure.

It's what Jones (2010, pp. 169–171) said:

"Though classification is an essential feature of all branches of science, there are always hard cases at the boundaries. The boundary of a class is rarely sharp…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."

Or as Scerri (2020, in press) writes:

"Needless to say, the characterization of these blocks of the periodic table is only approximate, just as the assignment of electronic configurations to atoms represents an approximation. Moreover, one may readily concede that an element such as thorium does not actually possess any f-orbital electrons and yet it is classified as being among the f-block elements even in all four of the periodic table representations shown in figures 10 to 13."

For Nb and Zr I'm applying the convention that for most practical purposes the pH scale extends from 0 to 14. --- Sandbh (talk) 04:42, 24 June 2020 (UTC)

@Sandbh: Don't you think that's quite inconsistent in the first place? If you believe gas-phase configurations matter, then why are not all the Madelung anomalies treated the same way as lanthanum having no 4f electrons as a single gaseous atom? And why is helium put over neon when it is clearly not a p element? If it's because its chemistry is more similar to neon than beryllium, then why is aluminium not over scandium, since He over Ne is a precedent for similarity in chemistry trumping gas-phase configurations? You can probably come up with reasons parrying each of those objections. But with this many hard cases (B-Al-Sc, Be-Mg-Zn, C-Si-Ti, Ti-Zr-Ce-Th, Ti-Zr-Hf-Th, Ca-Sr-Yb, He-Ne, H-F, etc., some with the most common elements indeed, not for getting every Madelung anomaly in the d or f block) I doubt you have much "economy of description" anymore. Is this supposed to be a table reflecting blocks first, reflecting general chemistry first, reflecting gas-phase configurations first, or something else? You cannot serve two masters. (Not to mention that if we are talking about a general chemistry table, then Sc-Y-Lu is still preferred because La and Ac are quite the outliers as d-block elements but look perfectly normal among the f-block ones.)

Contrast the general approach advocated here by myself and Droog Andrey. Well, we just look at what orbitals the valence electrons can be in in any reasonable compound, i.e. the orbitals contributing to bonding MOs. There's no gap between that and real chemistry like there is for gas-phase configurations. (Even for noble gases it is not a problem, as getting helium and neon bonding in charged systems is easy. HeH⁺ is well-known. Neutral systems are far more problematic.) We get almost total consistency, with the s-block as a consistent exception that has its own regularity. There's not even any "approximation", the blocks fall out with astonishing consistency. And I don't even need to concede anything about thorium, it has 5f contributing to bonding MOs like actinium 5f and lanthanum 4f. No double standard in sight, and all done with exactly one idea of valence subshells that has an obvious and direct relation to chemistry. That's absolutely "economy of description", with no need to say "oh, actually in this case we have our idea trumped by something else" anywhere.

12M HCl is commercial concentrated acid with pH −1.1. As concentrated HCl is needed for the manufacture of many chemicals in industry, it seems to me that a reasonable definition of "most practical purposes" must include that. Double sharp (talk) 06:45, 24 June 2020 (UTC)

It's consistent as long as the "rules" are understood. The only rule is that a block starts upon the first occurence of the applicable electron (with an optional accomodation for He). Scerri talks about pragmatism (conventional form) and philosophy (LST). There are, evidently, not enough hard cases to cause many chemists to lose sleep. The table has its roots in 19th century chemistry with a flavouring of quantum mechanics doi:10.1007/s10698-015-9246-8.

On the pH question I had in mind "most practical" = "domestic" rather than "industrial". --- Sandbh (talk) 07:28, 24 June 2020 (UTC)

@Sandbh: If the table "supposedly has its roots in 19th century chemistry with a flavouring of quantum mechanics", then why is this "rule" based first on orbitals in a situation hardly relevant to chemistry? And what about thorium with no 5f yet in that chemically weird situation (gas-phase atom with nobody else around)? Why does the rule force us to delay 4f (this despite lanthanum having 4f contribution to bonding MOs) but not 5f besides symmetry? The use of thorium 5f for chemistry is about as much as that of lanthanum 4f. Double standard again. Of course if the table really was based on chemistry then it would immediately note that lutetium is chemically far more like a transition metal than lanthanum is and go straight for Sc-Y-Lu. As indeed chemists before WWII sometimes did on the grounds of separation groups! It would also on the other hand result in some awkward things such as uranium and seaborgium both trying to take the space under tungsten. And aluminium over scandium. But my point is: La under Y both doesn't make sense from quantum mechanics and doesn't make sense from chemistry. There should be even less reason to use it than B-Al-Sc.

If our criterion is not making chemists lose too much sleep then there is indeed very little to recommend Sc-Y-Lu over Sc-Y-La. The only problem is that by that logic there is also very little to recommend B-Al-Ga over B-Al-Sc. Or Be-Mg-Ca over Be-Mg-Zn for that matter.

And exactly how "domestic" is the aqueous chemistry of these heavy elements? The table is meant for chemistry, which can go pretty far from "domestic" conditions in a lab. Zr⁴⁺ and Hf⁴⁺ are maybe not too interesting for a home lab because you probably cannot get to them with the sort of reagents you are likely to be able to procure and use safely there, that is true. But then all the radioactives except maybe thorium and uranium are not too interesting either. And in typical home lab conditions I suppose Sn²⁺ is also quite hydrolysed. ^_^

Not to mention that aqueous cations are just one part of what "pre-transition" means. If we consider the measure of whether there is significant redox chemistry in oxidation states differing by one (like self-respecting transition metals ought to have), then in the 4d and 5d rows you mostly have to wait till molybdenum and tungsten. ^_^ Double sharp (talk) 07:34, 24 June 2020 (UTC)

I thought I had posted the "normal" pH scale previously but it seems not. Sandbh (talk) 04:35, 28 June 2020 (UTC)

@Sandbh: And how's that relevant when the periodic table has lots of elements whose chemistry is not exactly within domestic reach? For laboratory purposes you have to consider pH going a bit beyond 0 and 14. Concentrated hydrochloric acid at pH −1.1 is extremely common. Double sharp (talk) 05:22, 28 June 2020 (UTC)

@Double sharp: It shows the "normal" range of pH values. Thus:

"The pH Scale: a scale of range 0–14 used for expressing level of acidity. The pH scale has become a popular method for expressing level of acidity because the values are usually small positive numbers in the range of 0–14 for common solutions."

Gilleland J 1982, Introduction to general, organic, and biological chemistry, West Publishing, St. Paul, p. 262

An average mono-cation for each of groups 1–3 (including the Ln, and An from Pa to Bk; I have no E-pH diags for the post-Bk An) is capable of existing in the pH range of water, say 6–8. Frex Sc = ~4; Y = 6; La = 7¾; Ac = 9¼, average = 6¾. That is not the case for group 4 (as Ti-Th), with an average appearance onset of a very acidic pH 1½. Nor is it the case for groups 5 to 12, to the extent that one can speak of an average mono-cation for some of them. In the p-block, only Tl, Pb, and Po show mono-cations within the water threshold.

It is odd that group 4 forms a kind of neutral water wall, whereas on the other side of the wall there is river of metals that can appear as mono-cations in neutral water starting with V and then going Cr-Mn-Fe-Co-Ni-Ag-Zn-Cd-Tl-Pb, with Po as a forgotten pond, on the other side of Bi. Sandbh (talk) 07:47, 28 June 2020 (UTC)

“

The logarithmic pH scale ... is open-ended, allowing for pH values below 0 or above 14. Nevertheless, there is much confusion about the permissible range of the pH scale (e.g., 1–16). The misconception that pH lies between 0 and 14 has been perpetuated in popular-science books (1–3), textbooks (4–8), revision guides (9), and reference books (10–16).

Although many chemistry texts state or infer that negative pH values are possible, typically no examples are given. This may be because negative pH values are difficult to measure experimentally (17, 18) and there has been a lack of suitable buffer standards for pH < 1. It is easier to report H₃O⁺ concentrations or total acid concentrations in the 10⁰–10¹ mol L⁻¹ range than imprecise negative pH values. ...

The misconception might be minimized by using pH scale diagrams [that are open-ended] and listing examples of solutions, with pH outside the 0–14 range, in textbooks. For example, commercially available concentrated HCl solution (37% by mass) has pH ≈ −1.1, while saturated NaOH solution has pH ≈ 15.0 (22). Hot springs near Ebeko volcano, with naturally occurring HCl and H₂SO₄, have estimated pH values as low as –1.7 (23, 24). Waters from the Richmond Mine at Iron Mountain, CA, have pH = −3.6 (25, 26).

”

— Negative pH Does Exist, Kieran F. Lim, J. Chem. Ed., Vol. 83 No. 10

@Sandbh: In reality this is purely a matter of cation acidity. The more acidic your cation is, the lower pH is necessary for it to predominate in water. And cation acidity rises with increasing charge and decreasing radius. You may easily see the trend by looking at Cs⁺ (which will be a cation even at ridiculously alkaline pH and not much hydrolysed), and then Li⁺ or Ba²⁺ (at pH 14, the predominant species finally are hydrolysed), then Co²⁺ (starts precipitating as the hydroxide in neutral or slightly basic solutions), Al³⁺ (starts precipitating even at weakly acidic pH), then Th⁴⁺ (already significantly hydrolysed at strongly acidic pH). And only after that do you get to cations like Sn⁴⁺ which are too acidic to exist in water at all at any pH. If you focus only on neutral pH, you miss this trend from species like Cs⁺ to species like Ti⁴⁺, all of which can exist in water. Double sharp (talk) 13:09, 28 June 2020 (UTC)

The argument of keeping the "rare earths" category as a spooled line Sc-Y-La-...-Lu

What kind of a trend is that? The only reasonable extrapolation from Sc-Y-La is Ac. And where does that go, with its chemistry basically that of a rare earth coming even before La in the sequence? There's no reason to exclude it except tradition and where it's usually encountered.

And what about hydrogen being so far away from all the other nonmetals? Double sharp (talk) 13:29, 21 June 2020 (UTC)

The argument of 234 oxidation states

What are we looking at? If it's maximum oxidation states, you're by definition going to be considering some unusual states. Many things can be done at nonstandard conditions. Suppose somebody really does discover HgF₄ in some years. That would break a 234 oxidation state triad. And how much would that mean considering that that compound would still be quite off the norm for mercury chemistry? (5d participation in Hg chemistry is not at issue here, you can have that even if the oxidation state doesn't surpass +2.) And then the argument fails horribly for the poster children of great group trends (alkali metals, halogens, noble gases) thanks to the noble gases surpassing 0 once we get to krypton and below. It seems to me that if a measure concludes that some other group actually has a more consistent trend than the alkali metals, then something is wrong with that measure.

But if it's restricted to maximum stable oxidation states, you don't have this either. Lead is not terribly happy in +4, neither is thallium in +3. And all of a sudden Sc-Y-Lu improves because nobelium prefers +2 to oxidising +3. And woe to the poor halogens who have to deal with not only the chalcogens but also themselves changing their most stable oxidation state as you go down the table, despite being, again, a poster child of great group trends in the first four elements. For which it still does not work because we get oxygen −2 and then sulfur +6 and then selenium and tellurium +4.

Element placement is not just about similar chemical behaviour or even just similar oxidation states! Otherwise, what are nitrogen and bismuth doing in the same group? Double sharp (talk) 07:12, 24 June 2020 (UTC)

Double periodicity

Is not about matching the two tranches, but about making sure the elements at the end of each tranche behave like a half-filled or full-filled subshell element ought to. Such a subshell should be harder to delocalise. Therefore you should see lower melting and boiling points (weaker metallic bonding), a more stable +2 state (not going beyond the outer s electrons), that kind of thing.

That's precisely why it supports a La-Yb f block with Eu and Yb naturally acting like the ends of families. They act in every way more like Mn and Zn do in the 3d row than Cr and Cu do. Double sharp (talk) 07:18, 24 June 2020 (UTC)

I must depart from this discussion.

As of recently, I've been experiencing increased mental health issues (including depressive episodes) and will need to take a Wikibreak of indeterminate length. Thanks for your understanding. ― Дрейгорич / Dreigorich Talk 16:40, 29 May 2020 (UTC)

All the best. Hope you'll be OK. -DePiep (talk) 17:20, 29 May 2020 (UTC)

Sad to hear. I wish you have good people nearby. All the best for you. -DePiep (talk) 21:24, 29 May 2020 (UTC)

Thanks for your concerns. hug ― Дрейгорич / Dreigorich Talk 21:31, 29 May 2020 (UTC)

@Дрейгорич: I've experienced and survived clinical depression. Happy to chat via pm about this, if you feel that could help. Sandbh (talk) 02:39, 30 May 2020 (UTC)

Thanks for reaching out. ― Дрейгорич / Dreigorich Talk 04:51, 30 May 2020 (UTC)

@Дрейгорич: What DePiep said. I am confident you will come out of this stronger! ^_^ Double sharp (talk) 05:22, 30 May 2020 (UTC)

Thanks. It may take months (years?), but I hope so as well. This won't be something that resolves tomorrow. ― Дрейгорич / Dreigorich Talk 05:32, 30 May 2020 (UTC)

My best wishes. There's not much to say that hasn't been said by the others, but by all means, you have my sincerest sympathy with this. Take care for yourself.--R8R (talk) 10:47, 30 May 2020 (UTC)

Thanks for your concerns. ― Дрейгорич / Dreigorich Talk 14:47, 30 May 2020 (UTC)

[Greenwood&Earnshaw-1] Cite error: The named reference Greenwood&Earnshaw was invoked but never defined (see the help page).

[HOWI1-2] Holleman, p. 1937.

[dtv1-3] tv-Atlas zur Chemie 1981, Vol. 1, p. 220.

[1]

[2]

[3]

Very serious questions for Sandbh

Sc-Y-La lack consensus

Question A

Chemistry is quantitative and qualitative

All the other vectors

For your amusement

The scientific method

R8R's views

Naturalness of conventions

Landau and Lifschitz

How conventions are established

Straw poll among participants

Comments

The beginning: how Sandbh switched to La

Coordination numbers

How long has this gone on for?!

Old ideas wrong. cont.

The consensus

PT article victimised?

Calling an admin and chemist, as well as the previous closer, after myself

Metrics

Officer781

R8R

Дрейгорич

Sandbox update

In fact, Sc-Y-Lu is probably older (1895!) than Sc-Y-La

Solid-state electron configurations

Observations

Double sharp

Officer781

s-block metals

p-block elements

Incipient metals

f-block metals

Band structures

Actinium

Phase changes of some rare earths at standard pressure

4f in Ln complexes

Spectra of singly ionised La and Ac (1957)

Band structures of period 6 and 7 elements

A challenge, based on Gschneidner

Molar magnetic susceptibilities

A funny case where class-A-ness matters more than forming aqueous cations

MP and BP of the Ln

Electronegativity

Representativeness

The idea that La3+ is not part of the f-block contraction because it has no f electrons

The argument that nothing changed in the chemistry of lutetium

The argument of differentiating electrons

The argument of keeping pre-transition-like groups 1 to 3 together

The argument of keeping the "rare earths" category as a spooled line Sc-Y-La-...-Lu

The argument of 234 oxidation states

Double periodicity

I must depart from this discussion.

The idea that La³⁺ is not part of the f-block contraction because it has no f electrons