Wikipedia talk:WikiProject Elements/Archive 38

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A conclusive argument for group 3, and He above Be?

I believe I may have a conclusive argument for group 3 as Sc, Y, La, Ac, and the placement of He above Be, based on the concept of optimal blocks.

An optimal block is a periodic table block in which the proportion of elements that have a predominance of either s-, p-, d-, and f- differentiating electrons, as applicable, is maximised.

The idea of an optimal block has its roots in the work of Scerri and Parsons (2018, p. 151):

“…for the purposes of selecting an optimal periodic table we prefer to consider block membership as a global property in which we focus on the predominate differentiating electron. We readily acknowledge the fact that the atoms of Mn, Zn, Tc, Cd, Pt [?], Hg, Lr, La, Gd, Ac, Th, and Cm are all anomalous in that they have a differentiating electron that is atypical of the block that they are situated in. These anomalies should not challenge our attempts to establish the overall structure of the periodic table in terms of sequences of blocks in the periodic table and as a result our recommendations for the membership of group 3 of the periodic table.”

I had thought that the left-step periodic table (LSTP) would have blocks showing the fewest discrepancies between block membership and differentiating electrons, but this turned out to be not the case. The least optimal periodic table is the IUPAC-agreed format. The best is an La-Ac table with He above Be.

Here are the number of discrepancies between block membership and differentiating electrons in each form of periodic table:

Table	Discrepancies	Details
IUPAC	14	He, Mn, Zn, Tc, Ag, Cd, La, Gd, Lu, Hg, Ac, Th, Cm, Lr
Lu-Lr	13	He, Mn, Zn, Tc, Ag, Cd, La, Gd, Hg, Ac, Th, Cm, Lr
La-Ac	12	He, Mn, Zn, Tc, Ag, Cd, Gd, Lu, Hg, Th, Cm, Lr
LSPT	12	Mn, Zn, Tc, Ag, Cd, La, Gd, Hg, Ac, Th, Cm, Lr
La-Ac w/He on Be^	11	Mn, Zn, Tc, Ag, Cd, Gd, Lu, Hg, Th, Cm, Lr

^ For an example in 32-column format see Van Spronsen JW 1969, The periodic system of elements: A history of the first hundred years, Elsevier, inside front covers

Only the last table has four optimal blocks.

At the present time the chemical community is unlikely to be receptive to He over Be.

That said, group 3 as Sc, Y, La and Ac should be relatively uncontroversial.

I’ve spent about a week trying to break this argument, without success. I’m too close to it or too tired, or I’ve made a mistake somewhere, or overlooked something. Either that or it really is, subject your thoughts, a conclusive argument.

Reference

Scerri ER & Parsons W 2018, "What elements belong in group 3 of the periodic table?", in ER Scerri & G Restrepo (eds), Mendeleev to Oganesson: A multidisciplinary perspective on the periodic table, Oxford University Press, New York, [1], pre-publication draft here

— Preceding unsigned comment added by Sandbh (talk • contribs) 2018-12-25 23:15:00 (UTC)

Double sharp comments

Differentiating electrons

I remain sceptical about differentiating electrons; as I recall Scerri himself has criticised the idea of making the next element by adding a proton and an electron when it comes to the Aufbau principle. I would rather stick to the element itself and ask which orbitals are active in its chemistry (handwaving a bit for the end of blocks like He, Ne, and Zn). Double sharp (talk) 04:38, 26 December 2018 (UTC)

Well, doubts about the concept of a differentiating electron was something I hadn’t considered.

What is there is to be sceptical about? The group 3 controversy was ignited with Jensen’s 1982 paper in which he referred to the same concept. It has been around since the 1930s and is still in use in 2018. The Aufbau principle is not required to determine the differentiating electron. For example, we know that Ca is [Ar] 4s2 and Sc is [Ar] 3d1 4s2. The differentiating electron is thus a d-electron.

What the Aufbau principle says wrongly about the order of electron filling in Sc is another matter, unrelated to the much simpler differentiating electron concept i.e. Scerri and Parson also said, “The distinction between order of filling in a particular atom starting from a bare nucleus [Aufbau] and order of filling as one progresses through the periodic table [differentiating electron] has recently been stressed in the literature.” Scerri and Parsons then go on to rely on the same differentiating electron concept in their paper.

So, I think I’m in the clear here. Sandbh (talk) 12:19, 26 December 2018 (UTC)

Relevance

What I'm sceptical about is its relevance. For instance, both Lr and Nh have a 7p differentiating electron from the previous element (please take this and the following with the understanding that what I say about Nh here is all predicted, of course). The argument for putting Nh in the p-block and not Lr is not so much because it makes more sense to consider Lr an anomaly when you widen the net to look at the differentiating electrons of Rf through Cn, but rather because Nh shows p-block eka-thallium chemistry while Lr shows eka-lutetium chemistry. In other words, we are assigning the places of Lr and Nh by the contributions of the 5f, 6d, 7s, and 7p orbitals to their chemistry, deciding the block by the chemically active orbital with the highest azimuthal quantum number, and not by looking at what electron happens to distinguish them from the previous element. Just like Scerri's criticism of the Aufbau principle, comparing No to Lr is fairly off-topic, whereas comparing Lr⁺ to Lr is at least more on point because both are a part of the chemistry of the same element. The question underpinning the choice of La or Lu in group 3 is instead which one has more 4f involvement, as the start and ends of blocks (in this case f⁰ and f¹⁴) can get pretty fuzzy. It's just like looking at 3d involvement to ask if Ca or Zn should go under Mg; it's not big for either of them, but you have to pick one, because the d-block has to have ten columns. Looking at Sr, Ba, Ra, Cd, Hg, and Cn as well makes sense, as unless you want a mess your choice must be the one that fits all periods the best. But looking at other groups seems to be mostly irrelevant.

As for He, the block concept is admittedly of questionable relevance for He and Ne because of their complete chemical inertness. We can rationalise He, Ne, and Ar as being chemically s⁰ elements of the next shell (HArF is still Ar(0), after all), while Kr, Xe, and Rn which can break the full shell have a claim to also be p⁶ elements. Similarly I would say that Zn is both formally d¹⁰ and chemically more like s²p⁰ (I add "p⁰" to show its PTM character). But I would still put He, Ne, and Ar in group 18 because of their great chemical analogy to Kr, Xe, and Rn in the bulk of the (lack of) chemistry of the latter three, rather than create an immense "first-row anomaly" with He over Be. This is also why we put E168 under Fl and not Og, even though under Og it makes sense as a case of an "inert quartet effect" affecting the 8s and 8p_1/2 electrons; when the second-order course corrections overwhelm the first-order prediction, it seems sensible to alter the first-order prediction. Double sharp (talk) 01:20, 27 December 2018 (UTC)

Some context for my response
1. As a philosopher of science, Scerri is not especially interested in the drill-down details (like the extent of f-orbital involvement in La and Lu). He advocates stepping back and taking a global view. He is looking for the equivalent of using atomic numbers to sort the elements into their proper sequence.

2. That said, he is of the opinion that the difference between La and Lu in terms of the drill-down details is neither definitive nor significant, or words to that effect. By drill-down details I mean physical and chemical data, including electron configuration arguments of the kind put forward by Jensen (Scerri & Parsons 2018, pp. 145—146).

My response
On relevance, I have followed the lead given by Scerri in his paper with Parsons (2018). As you can see, their argument is based on differentiating electrons, and the first and second quantum numbers of those electrons.

AFAIK, the placement of Lr and Nh was properly informed by the sequence of atomic numbers (noting the open question of whether Lr belonged at the end of the An or in group 3). While there has been some speculation of cracks showing in the periodic law, none of this has so far come to pass.

Per Scerri, the question of f-orbital involvement is another of the inconclusive arguments canvassed by previous authors.

The Ca or Zn issue is not relevant. Restrepo’s 2017 paper on similarities among binary compounds of the elements pretty much led me to abandon this line of inquiry.^ Schwarz (2010) addressed the Ca or Zn question and found significant differences between the two. [Scerri has a high regard for Schwarz’s works.] Schwarz also looked at Ba and Hg, and extended his conclusion to groups 2 and 12, as we know them, generally.

^ For what it is worth, Restrepo (2018, pp. 94–95) found that La should go under Y on the basis of the approach taken in his 2017 paper.

There is no need to be concerned about the block membership of He and Ne from the perspective of their differentiating electrons.

An immense first anomaly would be consistent with Jensen’s observation that the anomaly effect is found in all blocks, and manifests as s >> p > d > f. There has been a recent paper (Grochala 2018) advocating He over Be, including on the basis of extrapolating the IE and EA of He from the other group 2 elements. Sandbh (talk) 06:58, 30 December 2018 (UTC)

References

Grochala W 2018, "On the position of helium and neon in the Periodic Table of Elements", Foundations of Chemistry, doi:10.1007/s10698-017-9302-7 [open access]

Restrepo G 2017, "Building classes of similar chemical elements from binary compounds and their stoichiometries", in Elements old and new: Discoveries, developments, challenges, and environmental implications, pp. 95-110, doi:10.1021/bk-2017-1263.ch005
—— 2018, "The periodic system: A mathematical approach", in E Scerri & G Restrepo (eds), Mendeleev to Oganesson: A multidisciplinary perspective on the Periodic Table, Oxford University Press, New York
Scerri ER & Parsons W 2018, "What elements belong in group 3 of the periodic table?", in ER Scerri & G Restrepo (eds), Mendeleev to Oganesson: A multidisciplinary perspective on the periodic table, Oxford University Press, New York, [2], pre-publication draft here
Schwarz WH& Rich RL 2010, Theoretical basis and correct explanation of the periodic system: Review and ipdate, Journal of Chemical Education, vol. 87, no. 4

Cart before the horse

The idea that one uses atomic numbers to sort the elements into their proper sequence is already IMHO putting the cart before the horse. The atomic number order would not mean anything if it did not correspond to periodicities in chemical properties: atomic number on its own just gives you something like list of elements. The table is 2D, not 1D; but we know where each period starts and ends because of the periodicity of properties that tells us that Li, Na, K, Rb, Cs, and Fr belong in the same group, for instance. These properties are certainly informed by analogies in electron configuration (ns¹ for all these cases), which is why we place some emphasis on that: when we discuss whether La is a d-block or an f-block element by asking about the strength of its 4f contribution, we are using that as a proxy for arguing about what box fits its chemistry better, because the degree of 4f contribution translates to observable facts about La chemistry. But electron configuration and physical and chemical properties are not at all the same thing, even though of course the first has a very strong impact on the second. That is why hydrogen, despite its 1s¹ configuration, is often floated above the rest of the table. And even more importantly, that is why helium, despite its 1s² configuration, is almost always placed as the first noble gas, because all its properties point decisively to it being one (the chemistry of H is more equivocal). So I would say that we do not start with atomic numbers and electron configuration. We start from the physical and chemical properties that we directly observe, and we arrange the elements to reflect the periodicities in these. Atomic number order and electron configuration order certainly correlate very well with these, but the case of helium shows that that which one the periodic table is really seen as being based on by the vast majority of chemists. And Mendeleev himself provided the precedent by reversing tellurium and iodine from the order of atomic weights; when the supposed "global view" does not match what we see locally, we go for the local view instead, trusting that there is some deeper principle at work explaining it. If the predictions are right, and E172 acts like a noble gas while E168 acts like dvi-lead, I would be willing to bet that no active chemist would put E168 in the noble gas group just because Aufbau says that it must be so. That is putting theory on a pedestal even when it conflicts with the real world that it is trying to explain. When that happens, you find a better theory, as we did when we moved from atomic weights to atomic numbers; and when relativistic effects swamp periodicity in the 8th period, I am sure we will find something better again.

Double sharp (talk) 08:04, 30 December 2018 (UTC)

Double sharp, I respectfully ask you to please drop the discussion of E168 etc. Those elements are so incomprehensibly far, far away from being synthesised that I see no value in discussing them, at this time.

You are right; Moseley discovered in 1914 that it was better to order the elements according to atomic number rather than atomic weight, thus resolving Mendeleev's decision to reverse the order of tellurium and iodine (Scerri 2012).

I feel you are discounting what I said about my interpretation of Scerri's personal position in all of these things. The focus on physical and chemical properties is like examining the number of petals or some such details on some particular flowers in order to decide which species they belong to. Scerri, as a philosopher of science is more interested in a categorical argument to resolve the group 3 question. He is not interested in indulging in the game of "a little bit here and a little bit there".

Per his article with Parsons, he is looking for the philosophical equivalent of the Van den Broek/Moseley resolution of pair reversals. Such things as the extent to which La or Lu do show a little bit of an f-electron, in certain highly specific conditions, is of no great interest to him.

Reference

Scerri E 2012, "Mendeleev's Periodic Table is finally completed and what to do about group 3?", Chemistry International, vol. 34, no. 2

A little bit here, a little bit there

I understand your interpretation of Scerri's position. I nevertheless disagree with it. If we did not have "a little bit here and a little bit there" we would have nothing to suggest any categorical arguments at all. All the categorical arguments to place Li, Na, K, Rb, Cs, and Fr together would be worth nothing if they did not show the amazing chemical and physical similarities that they do. It seems to me that we have to start from the observed physical and chemical properties and then come up with a theory that matches them, not the other way round. The Van der Broek/Moseley resolution of pair reversals was spectacular in how it justified putting tellurium before iodine theoretically, but we must also note that everyone was putting tellurium before iodine anyway even before the concept of atomic number was discovered.

I am prepared to take Mendeleev completely seriously when he wrote in his 6 March presentation to the Russian Chemical Society:

The atomic weight of an element may sometimes be amended by a knowledge of those of its contiguous elements. Thus the atomic weight of tellurium must lie between 123 and 126, and cannot be 128.

Now, we know that while his premise was correct (Te and I are chemically analogous to Se and Br respectively, not the other way round), his conclusion was wrong because it was not imaginative enough; he did not expect there to be some better theory than atomic weights to justify his positioning of the elements. But notice what he did here. He stood by the chemistry of tellurium and iodine, and not the order that atomic numbers produced. This is why I was bringing in superheavy examples, even if they were unlikely to be synthesised within the near future. But we already have something close to an example in the 7p elements: Fl and Og are in groups 14 and 18 respectively, but they have some properties that resemble groups 18 and 14 respectively (the other way round). If, hypothetically, those were the normal chemistries of the elements – meaning that flerovium behaved totally like a noble gas (eka-Rn) and oganesson behave totally like a post-transition metal (eka-Pb) – the principle that elements must be ordered by increasing atomic numbers would have been dead too. This is, thankfully for the periodic law as it stands, not what has been observed. But we must be prepared for it to happen in period 8.

When it comes to the arguments you have showed for considering He an immense first anomaly, I am strongly reminded of something Droog Andrey told us back in Archive 33:

Suppose we decided to start every period with group 2 element and end it with group 1 element. Your arguments will stand in that situation. Well, the periodicity is still here. The extreme properties of the penultimate elements of each period are just because of the filled p⁶ configuration, like d¹⁰ in Cu and Ag. All is clear, isn't it?
...
You know, I have a feeling that I'm saying "the coal is black", while you are responding "no, let's compare it to snow, the coal is even whiter". I think you are too enthralled by formal chemistry like electron configurations and hybridizations, while the periodic table mostly explains the real properties of real compounds.

So we agree that the details of electron configurations and hybridisation are indeed details, but we disagree on where we should look to instead. I understand that Scerri suggests that we should look for some deeper global principle. Well, I think that takes us one step further from the whole raison d'être of the table in the first place, and that we would be better off looking at real chemistry, which at least electron configurations and hybridisation are not as far removed from. Double sharp (talk) 08:11, 31 December 2018 (UTC)

Well, we all know Scerri is trying to sort out the group 3 question. In his view comparing the physical and chemical properties etc of La and Lu, "a little bit here, a little bit there", will not lead to a conclusive solution. On that basis, I cannot fault his quest for a conclusive argument analogous to atomic numbers. And that is what I've attempted to do wrt to optimal blocks. Now, the chemistry community views the periodic table as a practical tool representing the periodic law. In this context, He over Be killed the adoption of the LSPT. And the way the LSPT disrupts the L to R metal to nonmetal progression is impractical. So, what are we left with? The next most optimal table is Sc, Y, La, Ac, with He over Ne. As I said at the top of the section, He over Be will be a step too far, while Sc-Y-La would be a doddle. Sandbh (talk) 05:56, 1 January 2019 (UTC)

Real chemistry

Only in his view, though. I cannot bring myself to accept that you can get a conclusive solution without comparing the physical and chemical properties of La and Lu, and given how many attempts to justify one or the other's placement under Y are based on these considerations, most chemists seem to agree that those must have some importance. A deeper explanation of these differences is certainly welcome, but it must truly explain them, not just ignore them. In other words, the explanation must hinge upon some properties of the elements concerned, and it should certainly not work just as well regardless of what those properties actually are. The fact that most d-block elements have d-block differentiating electrons would mean absolutely nothing if their chemistry did not consistently (with a few cases near the edge, of course) show the effects of their kind of d-orbital involvement, common to them and no other elements. That's why He over Be is a step too far in the first place for most chemists: we can justify it all we like by differentiating electrons and the Madelung rule, but it ignores that the physical and chemical properties of He are obviously far closer to those of Ne than those of Be. And yet, the arguments for putting He over Be don't seem to take this into account at all; if He had more alkaline-earth-metal-like properties, but had the same electron configurations, we could be making the exact same arguments, and the only reason why they would then be more accepted is because the physical and chemical properties would match better (and indeed we have such a situation with H). So I have a hard time accepting the premises here. Double sharp (talk) 15:38, 1 January 2019 (UTC)

I don’t know of a strong argument based on a physical or chemical property. Failing that we can try and tally up all the various arguments one way or the other, and see if one pile is bigger than the other. I doubt this can be done objectively or decisively to the satisfaction of either camp. What then? Presumably we look for a conclusive argument of the type that Scerri and Parsons attempted to put forward? Sandbh (talk) 12:27, 2 January 2019 (UTC)

Archive 33

Well, there is no really simple argument based on physical or chemical properties, or the debate would have been concluded long ago like it was for putting He over Ne. But since the f-block and the d-block have average representative physical and chemical behaviour (which isn't so true for the p-block, or indeed the s-block because of H and He), we can use block assignment as a proxy. Just run the calculations and compare the involvement of the valence f subshell in homologous La and Lu compounds. If La showed more 4f involvement in its compounds than Lu did, it would be enough to change my mind. (I don't ask for Ac and Lr because this far down the table, the collapse of orbitals becomes very delayed, presumably due to relativistic effects; Rf is something like a pre-transition metal, though part of it is because Rf⁴⁺ is so large. If we add the 8th period in, there's going to be so much mixing that splitting the d-block isn't going to say anything very useful anymore, especially because you'll need to split the f-block as well and have two s-blocks in the same period, so extending the table would actually strengthen the argument from Occam's razor for Sc-Y-Lu. I only don't go this far because I'm uncomfortable with having the predicted unknown half of chemistry dictate how we think of the known half.) As a control, we can use d-involvement in homologous Ca/Sr/Ba and Zn/Cd/Hg compounds. Indeed, this was the one hangup I still have that hasn't fully convinced me to Droog Andrey's archive 33 arguments. Double sharp (talk) 15:29, 2 January 2019 (UTC)

@Double sharp: I went back and read through the formidable Archive 33, several times. It's an astonishing thread in terms of the expertise on display.

As expected, there are a lot arguments and counter arguments

Setting that content aside, here are some key extracts, plus my comments.

1. "The real chemistry is shown in the compounds." [Droog Andrey]

I agree, and note Restrepo’s support doi:10.1021/bk-2017-1263.ch005 for La-Ac on this basis, as you did also.

2. "However, Sc-Y-La-Ac implores Occam's razor…We are eventually close to shared vision :) Indeed, in some sense Sc-Y-La-Ac could be better, but is it enough to justify the d-block rupture? My point is that simpler is better (q.v. Occam's razor)…" [Droog Andrey]

I note DA’s acknowledgement that in some sense Sc-Y-La-Ac could be better.

On Occam's razor, the optimal blocks argument (which supports Sc-Y-La-Ac) is the simplest wholistic solution around.

3. "But since we have universally decided in favour of the Be-Mg-Ca choice, I think the analogy makes a pretty strong argument to go for Sc-Y-La (the choice without the insertions of the contractions)." [Double sharp]

Agree.

4. "This suggests that the situation is a toss-up for the lanthanides and is in favour of Lr having more 5f involvement than Ac for the actinides, which skews things in favour of -La-Ac again, if I am not mistaken." [Double sharp]

This is the answer to your suggestion about running the calculations and comparing the involvement of the valence f sub-shell in homologous La and Lu compounds. You may have forgotten you’d written this in archive 33.

5. "I prefer the "pre-f" character of La to the "non-f" character of Lu." [Double sharp]

Agree in the sense of Ca, Sr, Ba being pre-transition elements.

How are you seeing all of this now? Sandbh (talk) 05:36, 5 January 2019 (UTC)

Archive 33, part 2

Well, how I am seeing all of this now is coloured by how I've just reread the thing and been practically convinced to accept Sc-Y-Lu again – which I believe Droog Andrey and R8R may be pleasantly surprised by. ^_^ (Look at me, I can't make up my mind, and if you look at the end of my new comment, I'm using this inability to make up my mind as a reason to make up my mind one way! ^_^)

Certainly, the real chemistry is shown in the compounds. However, it seems to me that comparing La and Lu to Sc and Y is, while very important, not the only important comparison one needs to make when looking at the group 3 question. We need to also consider how Sc and Y fit in their periods, and compare how La or Lu would fit in at the d¹ position. If we compare the hardnesses of the metals in bulk, for instance, Sc and Y seem to show a greater kinship to the 3d and 4d metals after them than to the 4s and 5s metals before, and even than to Ga and In, the 4p and 5p metals further after them which should have the same valence. Similarly, look at the densities of La and Lu and compare them to the following metals, and then the melting points. Finally, we can graduate from looking at just the pure metals, and look at their coordination chemistry (not surprising, as Lu is the smallest lanthanide and is only slightly larger than Sc, which is halfway between rare-earth and transition metal behaviour). All this was suggested by Droog Andrey already at the end of part 5 of archive 33, and seems to make a good argument that grouping by resemblances should result in Lu and not La going under Y, because (and you can see this in Restrepo's chart as well) if we average the distances from La to Hf, Ta, W, all the way through Hg, and then do the same for those from Lu to Hf, Ta, W, all the way through Hg, Lu will have a smaller average. That is why the main force of one of our strongest arguments for Sc-Y-La was to focus on trends, because focusing on resemblances tends to lead to Sc-Y-Lu. And, after all, while O, S, Se, Te, Po certainly is better described as a trend than by talking about resemblances between the elements, we would not be putting them as a group if the six valence electrons on each of them did not result in at least some resemblances.
I would think instead that Occam's razor would support the solution with the simplest possible blocks drawn that still makes chemical sense. In other words, the simplest possible solution is to have purely rectangular blocks (something like the Janet table, with He over Be and Lu under Y), and if you want to change it, you need a very good reason why the blocks should be broken. Is this the case for helium? Yes, as it has pretty much zero resemblance to beryllium under any normal circumstances, and is obviously a lighter congener of neon in about 99.999% of its properties. Is this the case for lanthanum? Well, we can talk about it, just like we can for group 2; as Droog Andrey himself mentions, Sc-Y-La "in some sense" could be better. It is clearly not chemical nonsense like He over Be is. But this is clearly a much smaller problem than helium over beryllium, which is where the Occam's razor argument comes in: it may not be worth breaking the d-block just because of the small pedagogical advantages (privileging the usual trend of increasing basicity down the table and the "delayed collapse") that Sc-Y-La brings. Even though Sc-Y-La is the most popular form, I think you could persuade most chemists to accept Sc-Y-Lu instead, as it is chemically also very reasonable. I think, however, that if the IUPAC decision included He over Be, it would be near-universally rejected.
Well, as I said in the next paragraph: "If I were trying to counter this in favour of Sc-Y-Lu, I'd say that Sc-Y-Lu avoids breaking the blocks and like you appeal to Occam's razor instead of the analogy. Since the blocks are really drawn for bookkeeping according to Madelung's rule and they provide a solid basis, even though there is of course a lot of mixing going on (consider that 6p involvement in the lanthanides), it would make sense to draw them as pure rectangles and just add refinements later by saying that Zn-Cd-Hg don't behave like transition metals and that the f-shells don't collapse until Ce and Th (making La and Ac in a sense "pre-f" elements). But I think moving He and our willingness to ignore blocks in the 8th row shows that we can override the blocks when chemistry suggests something else, and if group 3 chemistry has more similarities with groups 1 and 2 than 4 and 5, then the choice to go for the left fork in the road like we did for Be-Mg-Ca vs. Be-Mg-Zn seems to be recommended." Of course, it should be noted that the anomalies for He and E168 (predicted) are much bigger than the ones for La and Lu, so one can very well consistently support Sc-Y-Lu with He in group 18; it just means that you draw the line slightly higher for when a block rupture is justified (and I was increasingly being convinced back to Sc-Y-Lu by Droog Andrey's arguments, in favour of considering these things something to be introduced at a higher level than right when one learns the periodic table).
Droog Andrey however replied to it by saying "it seems for me that MP2 is not a good choice for correlation test. I'll try to use CASSCF if I have some spare CPU days", so I mentally reopened the question awaiting his spare CPU days. ^_^
What I meant by saying that is that all things being equal, if La had some pre-f character and Lu had no f character at all, I would rather La go in the f-block than Lu do (i.e. a Sc-Y-Lu table). This would not be the same situation as the one for Ba and Hg, say, where both have some 5d character; for this I would now appeal not only to the trends, but also to Droog Andrey's similarity argument:

The width of the d-block is limited to 10 elements, so we can't include both Ba and Hg, although both of them show some kind of 5d activity. My vote is for Hg because it is closer to 6p elements than to 6s, while placing Ba in group 2 makes here a pretty accompaniment to group 1.
Generally, groups 1 and 2 should be considered standalone because of preemptive filling of ns subshells. They are the only groups lacking secondary periodicity (even vs. odd periods), although it reverberates somehow from Na to K. That's why I insist on reconsidering the arguments of W. Jensen, most of which were rejected in the style "OK, but let's look at the group 2".
If we allow Sc and Y to stand above La and Ac succumbing to the temptation of group 1 and group 2 weird smoothness, then a lot of questions will arise about B-Al-Sc-Y, Ti-Zr-Ce-Th and so on. [Ds: Originally I didn't think this would cause problems, as only for Sc-Y-La-Ac vs -Lu-Lr is the d¹ configuration always kept. But since He and Ne obviously have different configurations but are still put together, we have a precedent for going against those when the properties are too different.] So my point is that we don't need to pull that "dark-side" border into the d-block. It's better to leave it between s-block and the remainder of the PT.
I hope we agree on the fact that 4f in Lu and 5f in Lr are much less chemically involved than 3d in Zn. Going down group 12, we see that the participation of (n-1)d subshell in bonding rises to significant for Hg and to full-scale for Cn, completely destroying the parallel between group 12 and Lu/Lr.
So the only problem is the slow start of 5f in Ac-Th-Pa. But that seems to be normal for heavy elements (6d for Lr-Rf, 5g for 121-126). When (not if) atoms are positively ionized, these inner subshells become more available. Yes, that reminds 5d in Ba, but I'll rather consider that as specific fate for group 2: all chemically accessible unoccupied subshells have angular momentum number larger than 0, but that's hardly the reason to stop considering them as s-elements.

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)

If I may expand a little bit more: I agree that what we have with the differences between La and Lu are "a little bit". As a result I am rather disinclined to say that either Sc-Y-La or Sc-Y-Lu is "wrong". One can multiply so many good arguments for each of them. However, the principle of reflecting the "delayed collapse" for Sc-Y-La is going to create a complete mess in the 8th period, and all that for not much use: the manmade categories and manmade blocks imply a sort of discontinuity that is not there except maybe after the six natural noble gases. (It reminds me of the music history joke that goes "on December 31, 1599, all the Renaissance composers died".) Obviously the early d-block will have some s-block-like tendencies and the late d-block will have some p-block-like tendencies! Even moving the boundaries and annexing groups 3 and 12 to the main-group elements doesn't help because of the increasingly delayed collapses: as a rule, if something happens in one group in the 4th period, it happens in the next group in the 5th and 6th, and in the next group again in the 7th. The weirdo among the blocks is the s-block which only ever has one active orbital outside a noble gas core (at least until E119 when that noble gas core might become active) and has absolutely no funky shielding effects. Now, that makes it easier to learn, but it also makes it deeply weird. In much the same way, the 2p elements we all know and love are the weirdos of the p-block because of how good sp^x hybridisation works for them. So at this point, I am tempted to throw up my hands, paraphrase Leopold Kronecker, and say: "God created the elements, all else is the work of Man". We have asked indeed for some organisational principles, and Mendeleev noticed the similarities. He was, after all, noting them to help organise his chemistry textbook. But we must remain aware that periods and groups do not exist in the way that elements do. They are just better or worse ways in which we classify things. So when I ask, "is La a group 3 element", I do not mean that there is something real called "group 3". Lanthanum is lanthanum, it comes with no classifications automatically attached. It is for us to look at its properties and see if it helps our understanding more to draw things one way or another. So I am prepared to say: let there be a hundred thousand inconsistent forms of the periodic table, emphasising more or less different things. Put La under Y if you are talking about delayed collapses. Put Be and Mg over Zn if you wish to emphasise their similar class-B character. You may even put He over Be if you are just emphasising electron configurations. I only ask that if we crown one table as standard that it give the maximum effect from minimal meddling. And, you know what, while putting He and E172 in group 18 is a must if you want to avoid chemical nonsense, Lu in group 3 is fine. I don't want to have to have two s-blocks in the same 8th period. The 8th period is so smeared out that I might as well just have formal rectangular g-, f-, d-, and p-blocks: perhaps those will inoculate students against taking the blocks too seriously. So, with apologies for bringing up E168 yet again, I dare to use period 8 as a justification for Sc-Y-Lu; our current extended table is not consistent, as if it was the g-block shouldn't start till E125, and we have a problem because 18 + 14 + 10 + 6 + 2 = 50 and we have four more elements till the next noble gas. So I say, Sc-Y-Lu-Lr-E157 at least gets a point for consistently not worrying about delayed collapses and exact block assignments with the right number of elements in each block and just drawing more or less rectangular blocks that are more or less reasonable. So, we can just say that Ba is formally an s-block element of the pre-d persuasion, La is formally an f-block element of the pre-f persuasion, Lu is formally a d-block element of the post-f persuasion, and E124 is formally a g-block element of the everything-else persuasion. Not the slightest problem, since these are all formal anyway.

TL:DR; If you try to reflect all the details you end up with a mess (Rayner-Canham's table gamely tries, but I can think of many more things that should join that mess). The periodic table is the first thing you show to students that screams "chemistry": why not just make it as simple as possible and teach the mess later? I think this is about as conclusive an argument we can ever hope for here. Double sharp (talk) 02:17, 7 January 2019 (UTC)

Note incidentally that I still think appeal to symmetry would mean absolutely nothing without having made the big pile of Sc-Y-La and Sc-Y-Lu arguments, because without it you cannot gauge the scale of the differences. Obviously if you made a big pile of He-Be-Mg and He-Ne-Ar arguments the latter side would win almost everything, in contrast, so we have to play the game in order to figure out if it is a little bit here and a little bit there, or if the division is markedly less equitable. I also don't appeal to the Madelung rule for the same reason, as I consider that chemical and physical properties should be able to trump it, and it's just that for Sc-Y-La the difference is probably too small to justify it for all cases. And I simultaneously accept that "in some sense" putting La in the d-block is not wrong and in some instances may be more illuminating; as the difference is smaller, so too are the differences between the areas where the different tables may be useful. We can have a lot of room for Sc-Y-La and Sc-Y-Lu tables, in contrast to the tiny amount of room where He-Be-Mg tables have something to say. And I freely admit that using the 8th period mess to justify Sc-Y-Lu is also to some extent banking on predictions before that house is actually built. But given that we are already slotting Mt, Ds, Rg, and Mc through Og in the table based on only predictions, it's not a new problem, and similarly here we have also chosen the path of least resistance that will still probably be chemically sensible as the default one where we're not making a special point. Double sharp (talk) 02:12, 8 January 2019 (UTC)

Symmetry and simplicity

I've been thinking about how to write a response about the symmetry question, and happened to look again at the relevance section. Here you said you prefer to use the chemically active orbital with the highest azimuthal quantum number. It occurred to me that this wouldn't pass the Occam's Razor test, IMO, compared to the differentiating electron criterion. More later. Sandbh (talk) 11:42, 12 January 2019 (UTC)

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)

Deep red, La as 4f, and symmetry (breaking)

At an energy of 1.884 eV, which corresponds to a deep red colour, an isolated neutral gaseous atom of lanthanum has an electron configuration of [Xe] 4f¹6s², rather than its ordinary gas phase configuration of [Xe]5d¹6s². Bearing in mind that the first ionisation energy of lanthanum is 5.58 eV this is quite a way off from La¹⁺. (From 0.0 eV to the point at which lanthanum becomes La¹⁺, ~54% of configurations have one or more 5d electrons; the remainder nearly all include a 4f electron.)

In this condition the f-block can be taken as starting at lanthanum rather than cerium.

I wondered what the rest of such a periodic table would look like, including lutetium, lawrencium, and actinium. Here it is, noting the energy levels for Z > 99 are calculated:

Points of interest (most also shown on the Deep red PT)

Shaded elements, of which there are 17, have an anomalous differentiating electron. For example, although titanium is a d-block element it has an s- differentiating electron.

Just over a third of s-block elements have a p- rather than an s-differentiating electron.

The p-block is unchanged.

The d- and f-blocks show a few anomalies.

The 3d sub-shell is full at nickel but opens again at copper.

Lutetium has a p-electron, emulating its congener lawrencium, which also has a p-electron in its ordinary 0.0 eV ground state.

Actinium is 6d¹7s¹6p¹. It retains a d-electron all the way up to its first ionisation energy of 6.17 eV.

Together the blocks show true tetrahedral symmetry, with no interruptions in the progression of Z.

Significance

I wondered why block symmetry was present at 1.884 eV but not at 0.0 eV.

It seems that a theoretical tetrahedral symmetry can be regarded as arising from the limitations placed on the values of the four electron quantum numbers n, l, m, and s for the elements generally (Stewart 2016, pp. 116, 118). This is beautifully exemplified in the Periodic Cube.

For lanthanum at 0.0 eV this symmetry breaks. The nuclear charge is insufficient to stabilise the 4f orbital in preference to the 5d orbital (Rossotti 1998, pp. 425, 427). I don’t know precisely why this occurs but I've read that the electron energy levels of atoms are impacted by electronic repulsions, relativistic effects, and spin-orbit couplings. These effects are referred to by Atkins as "rogue interactions", which give rise to symmetry breaking (2004, pp. 266–272). Perhaps variable shielding by each atom’s inner electrons also plays a role (Schwarz & Rich 2010, pp. 435–436; Stewart 2018, pp. 116–117).

I now think that while true tetrahedral symmetry, in a theoretical sense, may underly the periodic table, it just so happens that the periodic table realised in our universe doesn’t show true tetrahedral symmetry whereas in another universe, with different fundamental constants (resulting in lanthanum with a 4f electron), it may.

Scerri once wrote along similar lines: "While it may be…that the deepest, most general laws of physics are symmetrical…this may not be so for a mere representation of macroscopic properties of different substances. It may be completely misleading to demand that the Periodic Table…should be symmetrical." (Scerri 2004 p. 149)

Whereas I used to be dismissive of HeBe; LuLr; and IUPAC style tables, I now appreciate that most of them have their place, alongside LaAc tables. I’d even agree that the Janet LSPT may be the most elegant of the HeBeLuLr 32-column tables. Thus:

DIFFERENTIATING ELECTRON SCALE OF PERIODIC TABLES

Table                       #  Notes
===========================================================================
0.  Madelung rule (1928)    0  Idealised form
---------------------------------------------------------------------------
1.  La-Ac w/HeBe           11  Physics-based optimal block solution
---------------------------------------------------------------------------
2a. LSPT                   12  Elegant 32-column version showing theoretical tetrahedral symmetry
---------------------------------------------------------------------------
2b. Lu-Lr w/HeBe           12  18-column version of LSPT
---------------------------------------------------------------------------
2c. La-Ac w/HeNe           12  Recommended for IUPAC as it places He over Ne
---------------------------------------------------------------------------
3a. Lu-Lr w/HeNe           13  A compromise (?) between 2c. and 4a
---------------------------------------------------------------------------
3b. Volumetric (1949)      13  La-Ac, He-Ne, and groups 11–12 as s-block members, here
---------------------------------------------------------------------------
4a. IUPAC, current         14  Further along the chemistry end of the scale, here
---------------------------------------------------------------------------
4b. Metallurgist's (1994)  14  La-Ac w/HeNe, HF, and AlSc, here
---------------------------------------------------------------------------
5.  Remy’s (1956)          15  La-Ac w/H-F, Th-Pa-U as d-block elements, and Np+ as transuranic elements, analogous to Pm+, here
---------------------------------------------------------------------------
7.  Rayner-Canham (2002)   17  aka the Inorganic Chemist's Periodic Table, here
---------------------------------------------------------------------------
11. Pauling (1980)         21  La-Ac w/HeNe; Sc-La as s-block;* Th–Pu as d-block and as f-block; Ku (104) as f-block
    
 # = differentiating electron discrepancies
 * Pauling's table is ambiguous but in the text he treats Sc, Y, and La as the congeners of B and Al

References

Atkins P 2004, Galileo's finger: The ten great ideas of science, e-book ed., Oxford University, Oxford
Pauling L 1980, General chemistry, 3rd ed., Dover Publications, New York, p. 135
Rossotti H 1998, Diverse atoms: Profiles of the chemical elements, Oxford University, Oxford
Scerri E 2004, "The best representation of the periodic system: The role of the n + l rule and of the concept of an element as a basic substance", in DH Rouvray and RB King, The periodic table: Into the 21st century, Research Studies Press, Baldock, England
Schwarz WHE & Rich RL 2010, "Theoretical basis and correct explanation of the periodic system: Review and update", Journal of Chemical Education, vol. 87, no. 4, pp 435–443
Stewart PJ 2018, "Tetrahedral and spherical representations of the periodic system", Foundations of Chemistry, vol. 20, no. 2, pp. 111–120

Sandbh (talk) 11:29, 13 February 2019 (UTC)

Parsimony and science

The parsimony argument doesn't stand up, really. The differentiating electron criterion requires one operation namely subtraction. The chemically active orbital with the highest ℓ can't be established that easily, and in the case of the elements in the margins, becomes quite difficult.

Regarding He over Be, the optimal blocks suggestion yields a quantitative way of assessing the various ways of organising the table. He over Be, and La in group 3, is the optimally compliant way of showing electron structure. If we want to move up the chemistry scale, noting the unique features of row 1, we can move He over Ne, to give us the traditional table (at least in chemistry). If we want to introduce more chemistry, we can use the IUPAC table. I don't actually know what the LSTP purports to show aside from matching the Madelung rule, which has no empirical or theoretical basis, nor do I know what the Lr-Lu form is supposed to represent.

With the superheavy elements, should they ever be synthesised, nothing untoward will happen. We'll still have an 18-column table, with a footnoted g block starting after, say, 125. The prospect of synthesising these elements seems unlikely.

Your original position on the super-heavies namely that we are worrying about predictions before the house is built was more reasoned. You have probably seen the paper that suggested that elements with an atomic weight > ~300 maybe replaced with udQM matter. Already it has been suggested that the electrons in Og may be smeared out rather than in "fixed" orbitals. Sure, we have already slotted Mt, Ds, Rg, and Mc through Og in the table based on only predictions, but we have synthesised these elements and, so far, with the possible exception of Og, we have not seen anything untoward.

Getting back to the symmetry question. It's nice if it works out that way, but its niceness is a Western concept.

In The new ambidextrous universe (2005, p. 34) Martin Gardner wrote that:

Japanese art, in marked contrast to Western and even Chinese art, strives to avoid symmetry. As Everett F. Bleiler points out in his introduction to The Book of Tea, Kakuzo Okakura (Dover, 1964), the Taoist and Zen notion of perfection, which so strongly influenced Japanese art, emphasizes dynamic growth, whereas symmetric patterns suggest repetition and completeness. Japanese aversion to symmetry extends even into the ritual of serving tea. “In placing a vase on an incense burner on the tokonoma," Bleiler writes, “care should be taken not to put it in the exact centre, lest it divide the space into equal halves."

Writing in 2004, Scerri had this to say:

Returning now to the Periodic System, we must face another question. While it may be granted that the deepest, most general laws of physics are symmetrical, elegant and true, this may not be so for a mere representation of macroscopic properties of different substances. It may be completely misleading to demand that the Periodic Table itself should be symmetrical. Perhaps we could conclude, at this point, that beauty and elegance might be at least two criteria for selecting one particular Periodic System over another, but certainly not the sole criteria for doing so.

Scerri ER 2004, "The best representation for the periodic system: The role of the n+l rule and of the concept of an element as a basic substance", in DH Rouvray & RB King, The periodic table: Into the 21st Century, Research Studies Press.

Earlier, he wrote:

Dirac, the founder of the quantum field theory went even further, by claiming that in seeking the deepest laws of physics what matters most is beauty and elegance in the equations and not correspondence with experimental facts. It would appear that Dirac was exaggerating. What he probably meant to say was "…not initial correspondence with experimental facts." Unless a theory is eventually supported by experimental data then surely no amount of beauty and elegance is of any importance whatsoever.

Kragh (1990, p. 290), writing in Dirac: A scientific biography, has this to say about Dirac’s view on beauty and elegance:

It is one thing to boldly maintain belief in a theory in spite of some empirical counter-evidence, but it is another thing to stick obstinately to the theory and disregard any kind of conflicting experimental results. Neither Dirac nor other adherents of mathematical beauty would accept an extreme Cartesianism, divorced form any empirical considerations. Dirac’s advice, that one should disregard experimental results which are "ugly," was wisely but somewhat inconsequently supplemented with the proviso that "of course one must not be too obstinate over these matters" (Dirac M 1972, "Basic beliefs and fundamental research," unpublished talk, University of Miami.)."

In summary, I feel like you are advocating symmetry and I'm advocating the science-based, real depiction of what's going on (as far as we can understand it). Nature still has its surprises. Sandbh (talk) 05:46, 13 January 2019 (UTC)

In itself, the periodic table as we draw it is not a "real depiction of what's going on". There is too much that is going on to draw it all. Let's look at the usual form – where are the A-B group bifurcations and the relationships they create shown? Where is the inert pair effect shown? Where are the pseudohomologies between the early actinides and the transition metal groups shown? They're not shown, of course. The periodic law governs too many things to show in any simple table, and so we only show the simplest manifestations of it. So, if we cannot ever have real, complete depictions of what's going on, I would like one that comes closest to being so with our limited means. Both Sc-Y-La and Sc-Y-Lu depict things admirably well for such simplifications, and that is why we can come up with many arguments for them. It is because the difference is so small that arguing that Sc-Y-Lu is symmetrical and that it ought to be a default makes sense – because breaking symmetry for Sc-Y-La makes it look like there is a big reason to do so, which there is not. He-Be-Mg is surely more symmetrical (it makes the s-block a pure rectangle) than He-Ne-Ar, too, but in this case I am definitely not advocating symmetry because He-Ne-Ar obviously comes closer to depicting what's going on than He-Be-Mg does. But to claim that the differences between Y-La and Y-Lu are the same order as those between He-Be and He-Ne is absurd. The latter may serve as a precedent that allows us to break the symmetrical blocks when they depict reality too badly, but it's a nuclear option. If we allow the nuclear option for Sc-Y-La, what's really stopping us from doing it for the only slightly less defensible cases of Be-Mg-Zn, B-Al-Sc, and Ti-Zr-Ce? The first one even has consistent electron configurations throughout, like Sc-Y-La. I prefer it to save our nuclear option for the times when we really need it, i.e. in period 1 and period 8.

Many untoward things will happen once you get past the first few superheavies. All right, just like ds² is a typical covering shell for the lanthanides and actinides in the sense that one electron is usually promoted from the "reserve valence" orbitals, so f²s²p² should be so for the superactinides. Then we already have a problem. E119 and E120 can go under Fr and Ra all right, but what do we do with E121–E124? We seem to be wanting to skip straight to the p-block and then fill up the f-block, while ignoring the d-block, which breaks the shape of the La-Ac table established with periods 6 and 7. Yes, 7d¹8s² is quite low-energy for E121, but evidently this is not so later, since at E160 7d is far closer in energy to 9s than to the long-since drowned 8p_1/2, so putting E121 below Ac is already a bit dangerous for what it implies later. But suppose we ignore this, just expect people to know that the "covering shell" is f²s²p², and then add a g-block. Well, if we are being this fussy about counting electrons, the g-block needs to end eighteen elements later, i.e. at E142. Now what? If we finish the f-block, we get to E154, which is a problem because even at E155 the 6f shell should still be breachable: E155 should have a lower fourth IP than Dy, and Dy^IV is certainly known. The basic problem is that the orbital filling is stretched out so much: already 4f starts being active at La and isn't a core orbital yet at Lu, but in this case putting Lu in the d-block is more palatable because while Lu may use the 4f subshell to strengthen its bonds it certainly isn't giving up those electrons. And somewhere beyond that we need to fit in an extra s-block and an extra bit of p-block because 9s and 9p_1/2 are now low enough in energy. No, I really don't think this will work out. But if we are willing to compromise to show a nice-looking table, saying that it's okay not to show E122–E124 directly under Th–U and just accept it as implicit secondary periodicity, then why don't we do it for La and Ac? It is not as if Lu is a complete stranger to Y in the way that Be is a complete stranger to He. So, Sc-Y-Lu with He above Ne is trying to show a table that is quite close to reality and only tries to show primary periodicity in its simplest form. The blocks are formal anyway and we should not be having people's heads explode over whether La or Lu is the real d-block element. These generic default descriptions are going to be overridden sooner or later anyway by actual knowledge of their chemistry and we should not treat them with so much reverence that they become more than generic default descriptions in our minds. I'm OK with having a He-Be or a Sc-Y-La table to make a specific point with, and especially the latter can make a lot of good points. But I want my default table to have the ability to take me through the worst possible conditions for periodicity and still come out reasonably OK, and the simplest way to do that in the expected mess of period 8 seems to be to just not worry about the details of what electron goes into what orbital and go for the neatest-looking arrangement that distorts reality the least. Double sharp (talk) 07:44, 13 January 2019 (UTC)

P.S. Differentiating electrons need more than subtraction to define them. What is the differentiating electron between vanadium with [Ar]3d³4s² and chromium with [Ar]3d⁵4s¹? There isn't only one.

Also, if we consider the d-block to run from group 2 to 11 instead of 3 to 12, and then shunt Be and Mg over to group 12 (creating a split s-block), it strikes me that you have not changed the number of anomalies as far as the electron configurations are experimentally known (till Hs). All the anomalies from groups 3 to 11 are still anomalies, since they haven't changed their blocks; and three previous group 12 anomalies have been swapped for three group 2 anomalies. Okay, so copernicium fixes this, but I find the idea that the best block assignments are the ones that minimise all anomalies across the table quite distasteful because it pays no attention to the elements themselves. We shouldn't have to look at copernicium to decide what block calcium is in, but differentiating electrons seem to have us do exactly that. Whereas looking for chemically active orbitals, while more complicates, seems more relevant.

For this same reason, I do not like using differentiating electrons and minimising anomalies across the periodic table to decide on the La-Ac vs Lu-Lr question. The only reason why this argument decides on La-Ac is because Lr is an anomaly both ways; otherwise, it would be like the group 2 vs. 12 situation, as what is an anomaly in one table is not in the other. In other words, we are using the weird relativistic behaviour of lawrencium to decide the placement of the much less relativistic lanthanum. This is prioritising the weird relativistic effects on electron configurations that we see in Lr and Cn in particular, i.e the stabilisation of the s and p_1/2 orbitals and the destabilisation of the p_3/2, d, and f ones. We are using an anomalous part of the table to judge how we draw the parts unaffected by the anomalies – and then not looking at the non-anomalous part at all.

At least when I have been saying "meh, La-Ac and Lu-Lr are both okay as far as period 7, but the increased flexibility of Lu-Lr helps you draw period 8 more sanely", I am looking at the non-anomalous part first to see that La-Ac and Lu-Lr both have their merits. And, crucially, I am talking about drawing. Saying that Lr's or E157's anomalous configuration suggests that we draw Lu here rather than there is fine as far as we are clear that we are drawing a description of some of reality, and especially because I'm deliberately trying not to take the blocks too seriously (my answer now to "is La a d-block or an f-block element" would probably be "yes"), but I would draw the line before saying that Lu is here or there in reality and it is because of the electron configuration of something else at least 32 elements away. Also, I am saying that rectangles are nice pedagogically and don't get us stuck in the quagmire of delayed collapses which is already an anomalous relativistic effect, so I also have an argument that doesn't require talking about an unbuilt house. ^_^ Double sharp (talk) 06:22, 14 January 2019 (UTC)

May I leave a comment on this last phrase. There is no such thing as "the science-based, real depiction of what's going on" on a matter that hasn't been agreed on yet. As for "science-based": If you imply that science can be used to back -La-Ac, well, it can equally be used to back -Lu-Lr, and your choice from there depends on what you like better. Science, by the way, can have multiple depictions of what's going on: the most obvious example is that scientifically speaking, light is both a wave and a particle (you mentioned somewhere the words "classification science"); but I digress. If you mean that -La-Ac is the actual natural truth, well, such truth simply is not to be found. Especially if you add to that the fact that the problem at hand, in itself, is not bothered with trying to use science to gather or predict more knowledge about the universe from its theoretical constructs (like theoretical physics) or trying to have an explanation for the existing experimental knowledge that would help us predict results of future experiments (like classical mechanics), but rather trying to sort of spot the pattern in the knowledge that we have today as we don't intend to use it to go Mendeleev and try to predict properties of the future elements as the periodic law is expected to fall apart (you, very reasonably if you ask me, asked DS not not go far from the 118 elements we know today because we're rather concerned with them; should we ever get to element 168, we may need to revisit the block/group 3 issue, if not before then, to think how to structure the knowledge we'll have at that moment). As for "real": what is real when what we are discussing is pure theory (classification)? I'd argue this word is meaningless in this context.

You mentioned Scerri was an philosopher of science and sought to apply that in seeking an answer to the problem at hand. By a pure accident, I had an exam on philosophy of science on the fifth, so I guess that after having prepared to it (and passed) I have a little bit of knowledge on that. Not too much but something. The current philosophy of science includes that we're long past the 17-18-19th-centuries idea of how there is a single truth to be uncovered by science irregardless of what we think of it. Rather than that, science today is commonly seen as having been made by scientists, and it cannot be separated by those who create it. To quote Werner Heisenberg, "What we observe is not nature itself, but nature exposed to our method of questioning." Equally, the common modern understanding of science is that it is inseparable from the scientific community, and more rarely the society in general, that it is produced in. (I initially typed down a story as an example of that but it came out too long and I no longer can find the proof in Google so I deleted it but I accidentally also deleted the phrase the example was supposed to illustrate.) I think that Scerri's ideas won't be very useful in solving the group 3 question unless they are widely accepted by the scientific community. How should that be achieved? Well, presumably, it should be based on something that the critical minds of the scientists can largely agree on as the number one priority in classification. I think we'll have at best an "oh yeah, seems okay, let's just get this over with" (and I'm not even sure we'll have that), a statement which is sort of asking for a "now wait a minute" (again, I hope to be proven wrong).

I admire you for actually trying to defend a position resorting to science. (As you can see, despite having a favorite, I'm not actually defending a position using some killer arguments, mostly because I can't even convince myself there are arguments I could call killer arguments for either option to begin with, not to mention convincing anybody else.) Just remember that the other positions may be valid, too.--R8R (talk) 08:40, 13 January 2019 (UTC)

Science and multiple depictions

§ A fundamental criterion

Oh, I didn't intend for my comment about symmetry v a science-based real depiction of what was going to be as sweeping in scope as it was interpreted. My bad. What I mean to summarise was that my suggestion was based on a "fundamental" quantitative criterion whereas the arguments that've been made against it have been qualitative. I used the adjective "fundamental" since differentiating electrons underly the structure of the periodic table.

The question about vanadium with [Ar]3d³4s² and chromium with [Ar]3d⁵4s¹, and what is the differentiating electron is a good one. In this case the answer is +d2 and –s1. Cleary, the differentiating electron, is a d-electron.

I see no reason to discuss a table in which the d-block is groups 2−11.

But if such a table is so obviously inferior that there is no reason to think about it, then the differentiating electron criterion should be able to tell us so. Instead it requires us to stand on the unknown electron configuration of Rg to resolve it, which is just as much a prediction as that about how 5g is not yet active in E122. When we do synthesise elements beyond 118, we will have to give them provisional places based solely on predictions, just like we did wth roentgenium. So shouldn't we at least prepare for having to do this consistently? Either predictions are acceptable for both Rg and E165, in which case we can talk about both; or they are not for either, in which case we can't even put Rg in a periodic table yet, because we don't know anything about its non-nuclear properties that are supposed to guide periodic table placement. Double sharp (talk) 11:18, 14 January 2019 (UTC)

An LuLr table with the d-block as groups 2-11 would have 15 discrepancies. Sandbh (talk) 07:14, 17 January 2019 (UTC)

Only because roentgenium is predicted to have a 6d⁹7s² configuration. If it had a 6d¹⁰7s¹ configuration, like all its lighter congeners, then Lu-Lr with groups 3–12 as the d-block has Cn as an additional exception, which is traded for Ra if you let groups 2−11 be the d-block instead. In other words, we have to stand on the unknown electron configuration of Rg to resolve it, like I said. Double sharp (talk) 16:02, 17 January 2019 (UTC)

I was referring to the whole of group 2 being added to groups 3-11. Did you instead mean Ca|Sr|Ba + groups 3-11 being the d-block? Sandbh (talk) 03:48, 18 January 2019 (UTC)

Yes. When I originally mentioned the possibility of such a table, I wrote "if we consider the d-block to run from group 2 to 11 instead of 3 to 12, and then shunt Be and Mg over to group 12", so that Be and Mg would go over the Zn group in the table I am thinking of, and the d-block would be Ca+Sr+Ba+Ra + the current groups 3 through 11. I apologise for not being more explicit. Double sharp (talk) 04:35, 18 January 2019 (UTC)

@Double sharp: I may be missing something. What is the justification for starting the d block at group 2? Sandbh (talk) 08:51, 18 January 2019 (UTC)

If we are talking about differentiating electrons as a sole criterion only, there is none for starting it at group 2, and none for starting it at group 3. The justification would have to come from which table results in fewer exceptions – but that gives no result. If we are speaking externally, of course, there are reasons stemming from the d-orbital activity in Ca, Sr, Ba, and Ra. But if we are going to give differentiating electrons a status like that of atomic numbers, it strikes me that it should be able to resolve this on its own, especially if we are using it as the only justification to resolve the La vs Lu problem. The fact that it can't is not a good sign IMHO. Double sharp (talk) 16:25, 18 January 2019 (UTC)

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)

I understood Jensen's claim applied only to the spectroscopy of the valence electrons. I presume physicists would look a bit more deeply and check out the differences in underlying cores i.e. "In group 2, the underlying core is uniformly a noble gas. In Zn the underlying core is Zn²⁺ = [Ar]d¹⁰." Sandbh (talk) 10:32, 22 January 2019 (UTC)

Except that the same thing is true in groups 13 through 18; B, Al, Sc, Y, La, and Ac all have an underlying noble gas core, but in Ga and In the core is [Ng]d¹⁰, and in Tl and Nh it is [Ng]f¹⁴d¹⁰. And also in groups 4 through 12; Ti and Zr have noble gas cores, but Hf and Rf have [Ng]f⁴ cores. Indeed, in this case group 1, the model of great group trends, is the weird one; it has no secondary periodicity because it is unarguable that for it all the cores are [Ng]. Now, the questions are whether groups II and III should follow it or not. Following group 1 leads to Be-Mg-Ca in group 2 and Sc-Y-La in group 3; following everyone else leads to Be-Mg-Zn in group 12 and Sc-Y-Lu in group 3. But it is not necessarily true that both solutions should be resolved the same way, especially because 4f involvement in Lu is much weaker than 3d involvement in Zn. I would prefer to plead similarity and horizontal trends. Ca, Sr, Ba, and Ra are very much like the alkali metals, and the s-block is more homogeneous if it includes them instead of the Zn group, whose members are more similar to the d-block and p-block metals. Similarly, Lu and Lr are clearly more similar to the unequivocal 5d and 6d transition metals than La and Ac are (just plot any properties, really, starting with density, electronegativity, and reactivity as the most obvious; I know Restrepo's article disagrees, but the weight of evidence seems to support Lu-Lr as more similar to Hf through Hg and Rf through Cn); so the d-block is more homogeneous with Lu and Lr in group 3. This is of course something like your premise 2 in favour of homogeneous blocks, except that I'm trying to use the many chemical and physical properties as many criteria instead of choosing differentiating electrons as just one. Is it subjective? Sure, it is. As R8R has mentioned, so is your choice of criterion; the criterion itself works as far as it goes, but saying that it is the main one is subjective (I have said before that the La-Ac vs Lu-Lr choice to some extent reflects what you think is more important for the periodic system to show). So I think that if we are trying to be as objective as possible, we should indeed be piling up everything we can find and see "a little bit here and a little bit there", to avoid as far as possible subjectively assigning weights to the arguments. Double sharp (talk) 01:20, 25 January 2019 (UTC)

I worry about similarity and horizontal trends. On similarity, we know Spedding and Beadry (1968, p. 377), wrote, "Since 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." And we know about Restrepo, who said that, Lu is more similar to the Ln, and that La is more similar to the TM. On horizontal trends the IE, frex, of La looks like a better fit between Ba and Hf. And we know that Laing (2009, p. 12) said a reasonable case could be made for La below Y on the basis of comparing the horizontal pairs Ca-Sc and Sr-Y with Ba-La. It looks to me like we are again descending into the slough of a little bit of this and a little bit of that (ALBOT2). My criterion happens to be "the" main one from a physics perspective since it is the building of the electron sub-shells in the sequence that we observe, that gives rise to the series of blocks, which come together as the periodic table. Mind you, I recall R8R has challenged this, which is something I'll get to. Sandbh (talk) 11:55, 26 January 2019 (UTC)

§ Lawrencium

I make no apologies for Lr and the fact that relativistic effects [damn! spelling "relativistic" gets me every time] are responsible for its unexpected electron configuration. Sandbh as a scientist doesn't care. Just as I don't care about all of the other reasons for unexpected electron configurations. The differentiating electron based suggestion calls it as it is.

Maybe, but to say that the anomalous s²p configuration for Lr has a bearing on the position of La seems to be going a bit too far. This suggests to me that before the conflicting predictions were resolved by experiment for lawrencium, the placement of La was up in the air, and then suddenly became resolved by data about another element. I cannot bring myself to accept this. That this placement can be resolved by considering lanthanum's properties: sure, that makes perfect sense. That it can be resolved by comparing lanthanum's situation with the analogous cases of other elements: sure, that is also relevant. But to resolve it by appealing to another element entirely with no analogy to the situation of La offered: that seems too hard to swallow. Double sharp (talk) 11:18, 14 January 2019 (UTC)

Historically, by a sizeable margin, La and Ac have been in group 3. Ditto Lu and Lr at the end the f-block.

Jensen stirred up a flurry of interest in the placement of La and Lr, but nothing came of it.

There were some other suggestions that Lr, with its p-electon, was a prospect for eka-Tl, until the discovery of 113. That fate for Lr was nixed by another element.

So the situation is that neither La and Ac, nor Lu and Lr, are f-elements. Strictly from this perspective it makes no difference which pair ends up in the f-block. We do know that the sudden contraction and reduction in the energy of the 4f orbitals happens immediately after La. And we know that Goldschmidt’s "lanthanide" contraction starts at Ce and finishes at Lu.

We could (1) keep La and Ac in the d-block or (2) replace them with Lu and Lr. From a physics perspective, option 1 retains the status quo in terms of something (the d-block in this case) being optimally representative of its label. Option 2 makes the d-block less representative of its label since, while Lu is OK, Lr is a p-block element.

And this is the same global approach taken across the periodic table, and it gets us to HeBe and LaAc.

I respectfully think there is something here that is much more than one element (Lr) resolving the position of another element (La). Sandbh (talk) 07:14, 17 January 2019 (UTC)

Respectfully, I don't think the mere differentiating electron should prove that La or Lu is a d-block element. Given that everyone universally thinks that Mn, Tc, and Re are d-block elements, that flies in the face of the term's actual usage. Which is precisely why I have been saying that block membership should instead be based on the orbitals with the highest angular momentum being used for chemistry, so that it accords better with actual usage and actual chemistry. Mn, Tc, and Re have the chemistry characteristic of an element with d-orbitals actively being used, and are certainly very far-removed from something like Li in the s-block. Similarly, whatever Lr is, it certainly shouldn't be a p-block element, as it has no significant similarities to Tl. If the terms "s-block element" and "p-block element" and so forth are going to have any meaning other than being randomly assorted sets of elements, the elements they encompass should have some sort of relationship, and calling Lr a p-block element and Mn an s-block element on the grounds of their differentiating electron flies in the face of that. Maybe the Madelung rule as a smoothed-out version of the pattern has not yet gotten any first-principles justification, but there's a lot of chemical and physical reality behind considering the series it produces (1s, 2s, 2p, and so on till 7p) to actually be series that are continuous, even if there is some blurriness at their starts and ends. Double sharp (talk) 16:02, 17 January 2019 (UTC)

P.S. One can just as well start the Ln contraction at La, as La³⁺ is bigger than Ce³⁺ and so on down to Lu³⁺, so it fits perfectly at the start of the series. Double sharp (talk) 04:45, 18 January 2019 (UTC)

Hmm. I haven't claimed to prove anything. I haven't referred to Mn, Tc, and Re as "s-block elements". I've noted how important the electron filling sequence is in relation to the structure of the periodic table. I've mentioned that blocks are so dubbed on the basis of the dominant differentiating electron, which is a clear cut quantitative criterion in contrast to the difficulties associated with determining the chemically active orbital with the highest azimuthal quantum number.

Goldschmidt's Ln contraction, which is caused by poor shielding from the f-electrons, starts at Ce³⁺ [Xe]4f¹ and finishes in Lu, since Yb³⁺ is [Xe]4^f13, and Lu³⁺ is [Xe]4^f14. Same thing happens with actinides. Sandbh (talk) 08:06, 18 January 2019 (UTC)

But you're referring to Lr as a p-block element just because its differentiating electron from No goes in a 7p subshell; so what definition allows this but keeps Mn and Tc as d-block elements? (I made a mistake by including Re; apparently I'm too used to talking about Tc and Re in the same breadth because they are so similar. Sorry!)

I agree that determining the chemically active orbital with the highest azimuthal quantum number is more difficult, and in some cases it even gives unwanted results like eleven-element-wide d-blocks (Ba and Hg both show 5d involvement) and fifteen-element-wide f-blocks (Ac and Lr both show 5f involvement) without deciding to prune them to ten and fourteen based on "a little bit here and a little bit there". But I think the case of Lr shows that it is by far more useful, and that is why I think Occam's razor would go for it because talking about differentiating electrons is simply too simple to be simple (heh). Lr may have a 7p differentiating electron, but the chemically active orbital for it with the highest azimuthal quantum number is certainly not 7p. And indeed, Lr shows similarities to 5f and 6d elements, but not the 7p elements at all. At least Ba shows similarities to both 5d and 6s elements. Double sharp (talk) 16:23, 18 January 2019 (UTC)

:) I laughed out loud when I read, "talking about differentiating electrons is simply too simple to be simple (heh)"! That was a good'un! :)

I regret referring to Lr as a "p-block element"; I should've confined myself to the differentiating electron distinction. Sorry. I don't think Bohr would've regarded talking about differentiating electrons as being too simple. Whilst he had a reputation for talking in complicated ways, and introducing new (unexplained) terminology, and occasional hand-waving, he certainly referred to, spoke, and wrote about, the concept of differentiating electrons. Sandbh (talk) 01:34, 19 January 2019 (UTC)

§ Lu–Lr and the left step table

I agree with R8R that science can have multiple depictions. I acknowledged the validity of a van Spronsen table, the traditional form, and the IUPAC form. As I said, I don't see any science-based argument for an Lu-Lr table, or an LSPT table.

Surely Jensen has collected many arguments based on chemical and physical properties? I have never disputed that the trends he shows are valid. When I was arguing about it, it was because there are other valid trends that show the opposite. But we could very well argue that while group 3 doesn't share the chemical properties of most of the TM's, there are indeed resemblances, and that physical properties show group 3 closer to group 4 than to group 2 on average; the s-block-like properties can then be explained well by the noble gas core without any other orbitals extending far from it and the low enough nuclear charge (indeed, this not only explains group 3 and the Ln and An, but also Al, Zr, Hf, and Rf). See, we can rationalise Lu-Lr just as well, too; as I have been saying, if you set all the properties before you (including differentiating electrons, yes!) and weigh them, your answer will depend a lot on what you consider to have more weight in the construction of the periodic system. I don't think any of these supposedly conclusive arguments are really doing any more than just adding another one to the pile, so that we can play the game of "a little bit here and a little bit there" all over again. Double sharp (talk) 11:18, 14 January 2019 (UTC)

Relevant xkcd (just replace "competing standards" with "competing foundational principles"). Double sharp (talk) 13:57, 16 January 2019 (UTC)

Nice. Stupid, I agree. Fortunately, as I see it, the foundational principles for the periodic table don't compete so much as being in a hierarchy, starting with 1. atomic numbers, 2. differentiating electrons, 3. chemistry (HeBe) Sandbh (talk) 07:14, 17 January 2019 (UTC)

I agree that they don't compete, but I disagree on their position in this hierarchy. Let me quote Droog Andrey's table again as he translated it in Archive 33: "The properties of chemical elements, as well as the composition and the properties of their compounds are subject to periodical dependence on the charge of atomic nuclei". In other words, the periodic law states that chemistry varies periodically with atomic number. So if you want to know where each period starts and ends you need the chemistry to tell you when you have reached a noble gas, and thus at the very least your 3 should come before your 1. Otherwise there is nothing telling us that breaking each period at the intervals 2-8-8-18-18-32-32 is the way to do it. Double sharp (talk) 16:02, 17 January 2019 (UTC)

Jensen did himself no favours by e.g. re-relying on the 2nd ionisation energies of La and Lr. He did collect several arguments and, as we agreed, his focus was on similarities rather than trends. I find none of his "a little bit here and a little bit there" arguments are quantitive and global. The differentiating electron argument is. Per aufbauprinzip, the differentiating electrons underly the structure of the periodic system. Sandbh (talk) 07:14, 17 January 2019 (UTC)

Except that the Aufbau principle is exactly the Madelung rule, which you have criticised elsewhere in this thread as having "no empirical or theoretical basis". But by coming up with blocks that have to be ironed out as much as possible of exceptions, you are implicitly stepping away from the real somewhat messy filling up of electrons and holding up an abstract pattern that is close to it as the ideal that the real world doesn't quite match up to. No doubt the periodic table with the least anomalies would be a messy one where Ca, Mn, and Zn were somehow all s-block elements, but no one can draw that. The standard Aufbau principle is such an abstract pattern, as is the slightly modified one that lets one electron of 5d and 6d fill before interpolating the 4f and 5f series. So if one wants to come out with an abstract pattern that approximately describes what is going on, and smooths out reality, why do we have to stop just before smoothing out the delayed collapse of the f-subshells? Why not just take the unadorned Aufbau principle as one's basis and go for Sc-Y-Lu, especially when Lu makes just as good a heavier congener to Y as Hf does to Zr, which is more than can be said for He over Be or (predicted) E168 under Og? Double sharp (talk) 16:06, 17 January 2019 (UTC)

Oh. It was my understanding that the aufbau principle (1921) said that in the ground state of an atom, electrons always occupy the lowest available energy sublevels. That is all. Then, the Madelung Rule (of thumb) (1926) gives an approximate order in which the subshells fill. Hund's rule of thumb, and Pauli's exclusion principle were both 1925.

I don't care about the MR of thumb and its 20 incorrect predictions.

I acknowledge the messy filling of electrons. I haven't attempted to smooth out reality, as far as I know; if I had there wouldn't be a split d-block.

I've looked at the structure of the periodic table and what underlies that, and then suggested a way of assessing the taxonomic congruity of each option, which can vary along the physics−chemistry spectrum. Sandbh (talk) 07:40, 18 January 2019 (UTC)

But what are the "lowest available energy sublevels"? They mostly follow the Madelung rule. Sure, it makes 20 incorrect predictions, but using even your optimally smooth blocks makes 11 incorrect predictions of differentiating electrons, all of which are still tied to some of those very same Madelung rule exceptions. Yes, putting La and Ac under Y gets rid of the consistent exception that starts the f-block (the "pair out of place"), but it does nothing to get rid of exceptions like Mn and Gd. And by putting all those messy electron configurations into blocks, you do have to accept some of those incorrect predictions, which is what I meant by "smoothing out reality" when drawing a periodic table. You have to draw some elements in places that lead to incorrect predictions, because otherwise you can't draw any clear pattern. Double sharp (talk) 16:10, 18 January 2019 (UTC)

I'm not sure we can seriously say the MR makes predictions. It's a rule of thumb based on empirical observations rather than a hypothesis built from the ground up. Counting differentiating electrons is not a predictive algorithm. I didn't come up with the idea of identifying the s-, p, d-, and f-blocks, which inform the structure of periodic table. I only observed that a set of items is presumably more representative of its label the more the individual items in it match the label. Sandbh (talk) 01:16, 19 January 2019 (UTC)

§ Element 125

On what may lie before us wrt to period 8 I've made my views about this clear. Cries of the sky will fall down come to mind, despite the view that period 8 may grind to a halt after ~120. If by, say, 2095 we have actually gotten to the point where we can synthesise E125, we can reassess the situation then. That's the way science works.

What possible difference can synthesising E125 make? Suppose we do that. Then we still don't know its electron configuration, we don't know its chemical properties, and we don't know its physical properties. Since atomic weight has been superseded as a property determining periodic table placement, we will have exactly one property that we can use: that Z = 125. Which we already knew would be true of E125 by definition before we synthesised it, so we don't have any new information at all! So either we take a hard line and say that we're not going to put anything on the periodic table till we at least determine its electron configuration – in which case meitnerium has been waiting since 1982 – or we accept that some predictions are necessary before we place anything. In which case we might as well use the best predictions we have. If E164 miraculously gets synthesised now, I would rather we put it as dvi-platinum and not dvi-lead, as both are predictions but the first is the state of the art. And that sentence applies whether it is written now when E164 is a pipe dream, or in 2119 when it begins to look seriously within reach. Double sharp (talk) 11:18, 14 January 2019 (UTC)

We place E125 according to best empirical or theoretical data we have available to us at the time. E121 will go under Ac; E122 under Th, etc until we get to point where the g sub-shell starts filling at which time we will have a second footnoted block under the f-block (in an 18-column table). Sandbh (talk) 07:14, 17 January 2019 (UTC)

But with only differentiating electrons as an argument, how do you know that E122 should go under Th? E122 is expected to have the electron configuration [Og]7d¹8s²8p¹. It seems to me that it is an anomaly no matter where you put it, so how do we know if it's an f-block or a g-block element? You say that it should be "where the g sub-shell starts filling", but this is stepping away from using only differentiating electrons. In fact it comes rather closer to my previous suggestion (and Droog Andrey's) to look for the chemically active orbital with the highest angular momentum, so that you know that the g-block should start only when 5g actually becomes chemically active. Double sharp (talk) 16:02, 17 January 2019 (UTC)

119 and 120, if we ever synthesise them, are predicted to be [Og] 8s¹ and [Og] 8s². I don't know whether these configurations will ever transpire given Og has been predicted to have smeared-out electrons. That aside, 119 and 120 will fit nicely under Fr and Ra. I'll put 121, with its predicted [Og] 8s² 8p¹ configuration under Ac, and I'll put 122 under Th until I have evidence or a strong theoretical prediction to the contrary i.e. that the 5g shell has started filling. If not, it'll be +2 anomalies for the f-block. Sandbh (talk) 06:03, 18 January 2019 (UTC)

But again here we can see that some other criterion needs to be used to arbitrate the placement of some elements, if you adopt differentiating electrons as the first criterion – whereas as much as atomic numbers don't show the 2D placements in groups, they at least fix the order of the elements. To show that E122 isn't a g-block element, you have to appeal to predictions about whether or not its 5g subshell has started filling. But again, this criterion taken by itself quickly finds itself in hot water; in thorium, the 5f subshell has not started filling, so how do we know that it is an f-element? If you say that it's because the 5f subshell is contributing to thorium chemistry, then the 4f subshell is also contributing to lanthanum chemistry, and the 5d subshell is also contributing to barium chemistry. I prefer to accept the inconsistencies resulting from delayed collapses and relativistic smearing out, and say that elements can have characteristics of multiple blocks indeed, but we smooth things out according to the Madelung rule, which at least until E138 always agrees with at least one of the blocks being mixed. So Ba can be a pre-d s-block element, Og can be a pre-s p-block element, La, Ac, and Th can be pre-f elements, and so on. Anyway, I am more willing to allow pre-f elements into the f-block than post-f elements, because the important orbitals are usually the highest occupied and lowest unoccupied ones. In La, 4f and 5d can be considered HO and LU once the 6s electrons are ionised away (the s-electrons usually are); in Lu, 4f is not the highest occupied orbital and it isn't even as active chemically as 3d in Zn. Double sharp (talk) 16:06, 18 January 2019 (UTC)

The approach you are suggesting seems more involved than it needs to be. Th, Pa, and U were simply placed under Hf, Ta, and W until Seaborg developed his An hypothesis. We accept Th is in the f-block because, globally, this minimises the number of exceptions to the MR. We simply place E122 under Th until there is evidence or a strong theoretical prediction to the contrary i.e. that the 5g shell has started filling.

Re HOMO/LUMO. I understand La³⁺ is [Xe], and that HOMO is 5p and LUMO is 5d. For lutetium, Lu³⁺ is [Xe]4f¹⁴, HOMO is 4f, and LUMO is 5d. Is that right? Sandbh (talk) 00:49, 19 January 2019 (UTC)

Re HOMO/LUMO, I'm apparently just confused when it's late in my timezone; if you ionise 6s away, it must be contributing somehow, since the next electron wants to go into it in Lu (La²⁺ is [Xe]5d¹ but Lu²⁺ is [Xe]4f¹⁴6s¹). So here's what I really meant: in neutral La, 6s is HOMO and 4f is LUMO (La [Xe]5d¹6s², La⁺ [Xe]5d², La²⁺ [Xe]5d¹, La³⁺ [Xe]); in neutral Lu, 5d is HOMO and I'm not sure what LUMO is, but I think it's 6p, and as long as it's not 5f it doesn't refute my argument (Lu [Xe]4f¹⁴5d¹6s², Lu⁺ [Xe]4f¹⁴6s², Lu²⁺ [Xe]4f¹⁴6s¹, Lu³⁺ [Xe]4f¹⁴). Now, this needs some work, because mostly in the f- and d-block elements the covering s-shell is lost first, and it's only good fortune that for Lu it isn't the case. So what I would really want to talk about is HOMO and LUMO excluding covering s-shells, which is what I meant by "once the 6s electrons are ionised away" (albeit badly expressed). Unfortunately Gd nixes this because it loses a 6s electron, then the other 6s electron, and then the 5d electron. So I have revamped this idea into thinking about the "reserve electrons" status of f-orbitals in the Ln and the late An for the most part, which you can see below. ^_^

Redirection note: See my response below in the Double Periodicity section, near the "f→d promotion" chart. Sandbh (talk) 07:24, 25 January 2019 (UTC)

You've mentioned "this minimises the number of exceptions to the MR", but if the MR is the Madelung rule, then doesn't this support Sc-Y-Lu instead? You get Sc-Y-La with differentiating electrons, not the Madelung rule.

You're right. Meant to say D/E. Sorry. Sandbh (talk) 03:32, 21 January 2019 (UTC)

Also, this makes me think of something: how do you know, based on differentiating electrons, that the 5f series doesn't really start at Pa and end at Rf? If you do that, because Th and Rf both have 6d differentiating electrons, there's still the same number of anomalies. Yes, it's really ugly to have a cut in a different place in each period, like the Sc-Y-La-Lr table that DePiep drew in Archive 32. But what tells us that this isn't the case? After all, in the same section you linked to a YouTube video with Professor Martyn Poliakoff entertaining a Sc-Y-La-Lr table but saying "What we are interested in is what nature is like not how easy it is to draw it." (Now, I would temper this into saying that we cannot actually draw the full complexity of what nature is like, so I would like a balance between ease of teaching and drawing the lie-to-children that we inevitably have to come up with, and making it as close as possible to reality. Fortunately, Sc-Y-Lu-Lr seems to me now to be closer to reality for other reasons, too, especially one I have just expounded on below in its own subsection. ^_^) Double sharp (talk) 16:29, 19 January 2019 (UTC)

The conclusion deducted from the two premises that make up my argument is that HeBe LaAc is the single best form of structuring the table. This does not nullify the existence or utility of next best solutions. He over Ne, the 2/12 issue, and 5f series running from Pa to Rf, in chemistry, have been settled by other, science based means. Sandbh (talk) 03:35, 21 January 2019 (UTC)

I think that if differentiating electrons can't solve any of these issues satisfactorily, whereas looking at real chemistry, real compounds, and real trends can, it is manifestly clear that the latter is better. And since it is so obvious to everybody that He-Ne beats He-Be, it suggests rather than your premises do not reflect what most chemists think of the purpose of the periodic system, which is almost certainly much closer to real chemistry than to differentiating electrons. If Lr has an anomalous differentiating electron that doesn't affect its chemistry, then I don't see why that anomaly ought to be put on a pedestal and used as an argument for where to place it in the periodic table. Double sharp (talk) 02:59, 22 January 2019 (UTC)

I understand.

Per my observation, here, "The existence of a single best solution doesn’t extinguish the existence or utility of next best solutions, e.g. He over Ne".

If you like, from a physics point of view the solution is HeBeLa [11 anomalies]. I'd recommend IUPAC goes for HeNeLa [12 anomalies]. Going deeper into the chemistry end of the wading pool, the current IUPAC agreed form [14 anomalies] is fine if you want to focus on the Ln as a whole.

I feel this approach should provide chemists and physicists, and others, with the flexibility to use different tables for different purposes. Sandbh (talk) 04:02, 22 January 2019 (UTC)

While I certainly agree that different tables are differently suited for different purposes, I would think that the Sc-Y-Lu table has a purpose too – and given that the periodic table is an icon of chemistry, whereas it only applies to a small part of physics, I would think that tables nearer the chemistry point of view have a better claim to being better solutions. I think the majority of chemists would agree that, for all that there are a few residual similarities between He and Be, putting He in the alkaline earth group does not improve the table. If a table is supposed to be the "best", then I think it ought to be the one that caters to the most use cases, which suggests one built on many criteria and compromise, rather than one with only one overarching one. Double sharp (talk) 08:48, 22 January 2019 (UTC)

I thought that's what I was doing: a compromise between physics and chemistry i.e. between HeBeLa (11) and HeNe* ** (14) to give HeNeLa (12). We cannot build our table on many criteria if we are looking for a conclusive solution. Sandbh (talk) 07:12, 25 January 2019 (UTC)

But any compromise itself demands that you have multiple criteria to compromise between. If you are compromising between differentiating electrons and chemical properties, then you are using both as criteria, not to mention the consistent-cores argument that justifies putting Be and Mg above Ca instead of Zn. If it's okay to have three criteria, then, why not look at everything possible? In any case, I do not mean to set down one form of the periodic table up to Og by fiat and say that that is the conclusive answer and the question is closed. I want a simple one that gets you all the major points, with the understanding that a hundred thousand others can flourish, and each helps illuminate a more minor point or correction. So even while supporting HeNeLu I do not think HeBeLa, HeBeLu, HeNe* **, and so forth are "wrong" or even worse than HeNeLu in their contexts. My support of HeNeLu is simply based on it agreeing very well with chemical and physical properties and trends even as it by necessity simplifies them down to the Madelung rule as an organisational principle. Double sharp (talk) 08:42, 25 January 2019 (UTC)

I think you are inflating the d/e principle beyond a scope it does not address, and criticising it on that basis. I don't want to say there is "one" table either. The d/e deductive argument is designed to address only one question, namely the composition of group 3, for IUPAC. The context is the LaLr slough of a little bit of this and a little bit of that. The d/e criterion very simply addresses this question, and it can be applied to any periodic table. The physicists can use their HeBeLa table; the chemists can use the HeNeLa table. There is no compromise in that sense; everyone is a winner. Upon reflection, "compromise" was not such a good choice of words. I worry about relying on the MR as an organisational principle. The rule of thumb itself is based on experimental evidence and it would then be used to justify the same experimental evidence. I will see if I can address anymore the physical and chemical evidence for Lu, as I remove my o/s placeholders. Sandbh (talk) 11:12, 25 January 2019 (UTC)

I am not using the Madelung rule of thumb to circularly justify the experimental evidence, though. The Madelung rule is indeed based on and hence accords well with experimental data; that makes it a useful way to organise that data into a periodic table. But the periodic table is not the experimental evidence, it is only based on it, and tries to show as much as possible of it in a simple format, not all of it. (All those A-and-B relationships you see in the 8-column form of the table are hardly present in the 18-column form, but they are still part of periodicity.) Hence I see no circularity in going from the experimental evidence to a pattern based on it to a table based on that pattern, only two necessary steps to see the underlying order in the real chemistry that we need in order to begin to learn and understand it.

In any case, I don't think we should have special principles just to resolve one question. You have in any case already been applying differentiating electrons to many other regions of the periodic table, when they happen to work; many of the anomalies you list are nowhere near group 3, you've been listing He as an anomaly when put over Ne, and when I suggested a Pr/Pa to Hf/Rf f-block you responded that it would give two more anomalies. So judging from these, it seems to be elevated beyond a group-3-only principle to the whole table. But the moment it doesn't work, as in the problem of telling where Be and Mg should go, we hear other arguments instead, in this case common cores. And that doesn't even work outside the group 2 question, because absolutely none of groups 4 through 18 have consistent cores anyway, and I don't think there's any way to quibble with the composition of group 18 from Ne to Rn at least. So we seem to have one specific organisational principle that addresses one set of specific problems and is completely silent on the other sets, and then another one carried in to address the other sets, at the expense of giving the "wrong" answer for nearly everything else. No, I'm not convinced that two organisational principles this mutually antagonistic can work together and create anything effective. Whereas the extended Madelung rule I have been advocating can be applied to every element (it correctly predicts which orbitals are chemically active, and by defining blocks by the orbital controlling most of the chemistry), and when it doesn't give a conclusive result, it can similarly be supplemented by the idea that a block is better drawn if its members are more homogeneous (which is amusingly needed to resolve the group 2/12 problem but not the group 3 problem). Double sharp (talk) 15:33, 25 January 2019 (UTC)

I think this is due to bad language on my part. The impetus for the d/e approach was the group 3 question. To use it, however, you have to apply it to the whole of the particular table at hand. So yes, He over Ne = +1 anomaly, and a Pr/Pa to Hf/Rf f-block = +2. You are right in that Be and Mg over Zn, with the d-block spanning groups 2-11 is as good as He over Be, and La in group 3! So I've been thinking about that for a while. The problem seems to have arisen due the lack of a definition of a block. People know what a block is when then see one but they can't define it objectively. My definition would be something like, "A region of the periodic table subtended by the appearance of a new type of differentiating electron." This would rule out both the d-block = groups 2 to 11 layout and an ordinary Lu table. We made a similar argument in the IUPAC submission. Indeed we still seem to thinking along similar lines above! Are you able to express your approach in the form of a deductive argument? Sandbh (talk) 06:25, 28 January 2019 (UTC)

PS. How will you define "chemically active" orbitals? How will you unambiguously determine this. How will it apply to Ca, Sr and Ba? Sandbh (talk) 09:53, 28 January 2019 (UTC)

§ Symmetry and simplicity

I reiterate my arguments about the cultural bias towards symmetry, and Dirac's views on this matter.

Perhaps an aesthetic preference for symmetry is culturally dependent, but surely no one could argue that a symmetric object is somehow not simpler to describe than a non-symmetric one. After all, part of the description is already done for you by the symmetry! In such a case, if a simpler and a not-so-simple model agree about equally well with reality, should not Occam's razor apply, especially when the clearly defined blocks either mandates are both constructs? Double sharp (talk) 11:18, 14 January 2019 (UTC)

I think Occam’s razor applies to the explanation that leads to the outcome rather than the outcome itself. There is no simple periodic-table based explanation that supports Lu. There is for La. And it’s symmetric (per Stowe’s physicists table).

Surely the Madelung rule supports Lu? It is an ideal that the real world doesn't perfectly follow, but then again so are optimal blocks (from the point of view of differentiating electrons) with the anomalies smoothed out. Double sharp (talk) 15:58, 18 January 2019 (UTC)

Hmmm…<sips from coffee>…If you focus solely on Lu then its placement in group 3 is consistent with the MR. If you focus on the entire periodic table, the MR supports La and Ac in group 3, and Lu and Lr at the end of the f block. Sandbh (talk) 23:51, 18 January 2019 (UTC)

If we are talking about the Madelung rule, and not differentiating electrons, then it is manifestly obvious that you want a Sc-Y-Lu table because otherwise almost every f-block element is an exception to the altered Madelung rule implied by the Sc-Y-La table ("6s, one 5d, 4f, nine 5d, 6p"). Double sharp (talk) 02:54, 22 January 2019 (UTC)

You're right. I mixed the two concepts. Sandbh (talk) 08:15, 25 January 2019 (UTC)

§ Groups 2 and 12, and the like

For Be-Mg-Zn, B-Al-Sc, and Ti-Zr-Ce, I'm happy to reiterate a lack of support by Restrepo, per doi:10.1021/bk-2017-1263.ch005.

Saying that Be and Mg are not closer to the Zn group than to the Ca group contradicts a lot of descriptive chemistry, and the fact that similarly sized and equally charged cations will of course be more similar to each other than if the sizes and charges are more different. It also seems quite inconsistent to me to have to appeal to similarities of compounds to argue against Be-Mg-Zn when differentiating electrons were supposed to be the conclusive argument (except that it doesn't suffice to rule out Be-Mg-Zn without invoking predictions), and especially while supporting He over Be. If we compromise on it to fit chemistry, then it seems that the idea that differentiating electrons are the conclusive argument has been thrown out the window. Double sharp (talk) 11:18, 14 January 2019 (UTC)

Differentiating electrons are the conclusive argument for the entire periodic table. After that, from a chemistry based view, the case for He over Ne is solid. I read a fair amount of descriptive chemistry about Be-Mg-Zn. I recall this was never taken up on account of a lack of an underlying d10 sub-shell in Be and Mg. Sandbh (talk) 07:14, 17 January 2019 (UTC)

And yet B-Al-Ga has been universally taken up, even though B and Al lack the underlying d¹⁰ subshell that Ga has, so there must be more to it than that. Double sharp (talk) 16:02, 17 January 2019 (UTC)

It would've been clearer for me to say that in group 2, the underlying core is uniformly a noble gas. In Zn the underlying core is Zn²⁺ = [Ar]d¹⁰. Sandbh (talk) 05:45, 18 January 2019 (UTC)

But again, that cannot be the whole story. Ti⁴⁺, Zr⁴⁺, Ce⁴⁺ and Th⁴⁺ all have the electron configuration of a noble gas, too. So why does everyone put Hf and Rf under Ti and Zr instead? I am inclined to instead take the distinctness of the s-block seriously instead, as Droog Andrey stated in one of the quotes from him above. Double sharp (talk) 09:57, 18 January 2019 (UTC)

I believe my answer here is that, given a choice between group 2 and group 12, BeMg in group 2 results in more consistent underlying cores. If you place Ce and Th under Ti and Zr, where will you place Hf and Rf? At the end of the f-block = +2 differentiating electron anomalies? Sandbh (talk) 10:30, 18 January 2019 (UTC)

Indeed, the reason for not putting Ce and Th under Ti and Zr is because Hf and Rf are clearly not f-block elements, which is fine as it stands (even though I think block assignment should be considered differently). But this criterion alone fails to solve the group 2/12 question, just like the other criterion of uniform cores fails to solve the group 4 question mentioned here. That seems to imply that you can't just say that differentiating electrons decide the block placement of elements with the decisive finality that atomic number decides their ordering; we need to call in other criteria to arbitrate. Double sharp (talk) 15:56, 18 January 2019 (UTC)

Agree. You've lost me with the second half of your response (・・? I thought I'd addressed group 2/12. BeMg in group 2 results in more consistent underlying cores. Sandbh (talk) 23:25, 18 January 2019 (UTC)

Yes, you have addressed it, but each problem has been addressed differently. You're addressing Ti-Zr-Ce-Th by appealing to differentiating electrons, but you're addressing group 2/12 by appealing to consistent underlying cores. The problem is that while each criterion solves the problem it has been chosen to solve, it doesn't solve the other problem (or, in the case of Ti-Zr-Ce-Th, it solves the problem wrongly). As a result neither seems to be complete enough to serve as a foundational principle for periodic table placement on its own. Double sharp (talk) 16:07, 19 January 2019 (UTC)

The conclusion deducted from the two premises that make up my argument is that HeBe LaAc is the single best form of structuring the table. This does not nullify the existence or utility of next best solutions. He over Ne, and the 2/12 issue, in chemistry, have been settled by other, science based means. Sandbh (talk) 03:34, 21 January 2019 (UTC)

I think that if differentiating electrons can't solve any of these issues satisfactorily, whereas looking at real chemistry, real compounds, and real trends can, it is manifestly clear that the latter is better. And since it is so obvious to everybody that He-Ne beats He-Be, it suggests rather than your premises do not reflect what most chemists think of the purpose of the periodic system, which is almost certainly much closer to real chemistry than to differentiating electrons. If Lr has an anomalous differentiating electron that doesn't affect its chemistry, then I don't see why that anomaly ought to be put on a pedestal and used as an argument for where to place it in the periodic table. Double sharp (talk) 03:03, 22 January 2019 (UTC)

Yes, I agree. While d/e underlie the structure of the periodic table from a physics point of view, many chemists would certainly be more comfortable with, for example, HeNe than HeBe. And that is fine since we still look to the physics of what is going on here for an explanation. The p electron of Lr is chemically significant; the unusually low ionisation energy of Lr is attributed to the presence of an easily ionisable outer 7p-electron. That aside, and if we accept Scerri's a "little bit of this and a little bit of that" viewpoint for LaLu, how else would you propose to resolve the situation? Sandbh (talk) 07:13, 25 January 2019 (UTC)

I'm not even sure that differentiating electrons are the real underlying structure. Electrons, sure. Electrons filling shells and subshells, sure. Homologous valence electron configurations, sure with a pinch of salt (Nb might be d⁴s where Ta is d³s², but it doesn't affect their great similarity). But differentiating electrons specifically don't let us know whether Be and Mg are better placed in group IIA or group IIB. What resolves that is recognisng the global filling. A d-subshell can hold ten electrons and they fill more or less one after the other. That is why I think if we're going to formalise an approximate order of activity of atomic orbitals that governs the table, the Madelung rule is better. Differentiating electrons are essentially saying "well, if we add a proton and an electron, we turn a H atom into a He atom", and such a nuclear process happens only at such high energies that we would be wise to give it a wide berth, perhaps of about 150 million kilometres. Now look at the Madelung rule approach. It asks: why are we looking to put elements into blocks and classify them so? Well, it is because the active electron shells an element has, and the number of electrons in these active shells, define its chemistry. There are elements where only the outer s-electrons are active that have hard noble gas cores, and they behave like strongly reactive, electronegative metals. There are elements where outer s- and p-orbitals are active, with hybridisation between them often prominent, and a general preference for covalent bonding. There are elements whose chemistry is controlled by their inner d-electrons which show variable oxidation states, coloured compounds, and significant coordination chemistry. There are elements whose chemistry is manipulated from behind the shadows by deeply buried f- and g-electrons, which appear for the most part as a gang of identical siblings, but whose deeply buried indirectly valent electrons grant them different magnetic properties. If you believe in a table based on chemistry, that is what the blocks are there for, to unite elements that behave similarly because of the orbitals their chemically active electrons are in. So we are now looking at each element on its own and are finding an approximate pattern that predicts more or less what each one will show. We expect Ca from this pattern to have 4s active and have two electrons in it, and indeed it happens. We expect Cu to have 4s, 4p, and 3d active, with mostly the last controlling the chemistry, and have eleven electrons in total in both of them (9 + 2); while the prediction of 9+2 is wrong, the total number is correct. We expect La to have 4f, 5d, 6s, and 6p active, with three electrons in them in total, with 4f controlling chemistry behind the shadows by donating electrons to 5d; that is more or less what we see since 4f¹ is a low-lying excites state that often makes a contribution. We expect Lu to have only 5d, 6s, and 6p active, with three electrons in them in total with 4f not contributing any funny properties, like scandium and yttrium which have no f-orbitals in the core and indeed that is what we see. So by simply distributing electrons among orbitals for each element according to the rule we have more or less totally banished the idea of "add one proton and one electron, there's the next element" that can hardly happen in conditions suited to do chemistry and not nuclear physics in. That is why I think the Madelung rule, predicting the configuration for one element at a time, must surely be superior to anything that compares things to the previous element. Sure, we cannot derive it from first principles; but we cannot so derive the actual electron configurations we got differentiating electrons from, either.

The effect of the anomalous configuration of Lr is surely overstated by this measure, too. OK, the 103rd electron goes into 7p, and it's easier to remove than expected. But we still see 6d mostly controlling the chemistry, and certainly the result is chemically and physically nothing like the superficially similar Tl; you never see unipositive lawrencium like you do unipositive thallium and as we are expected to see unipositive nihonium. Everything about Lr chemistry is absolutely homologous with Lu. This is a deviation in degree and not in type, which is perfectly normal, since homologues are not expected to continue trends exactly, just be close; the 5d transition metals are also anomalously small because of the 4f contraction, but that's just a second-order correction. Anyway, the dip at the end of the the actinide series with Lr is also seen at the end of the lanthanide series with Lu, which strongly suggests again that Lu and Lr are opening a new block as the new unpaired electron from a higher-energy subshell is easier to remove. Double sharp (talk) 09:16, 25 January 2019 (UTC)

I addressed the circular nature of your proposed application of the MR of thumb at the end of the Element 125 section. I also discussed inflating the scope of the d/e argument and then criticising it on that basis. You are extending the MR of thumb beyond its scope by saying, "We expect La to have 4f, 5d, 6s, and 6p active. Rather the MR of thumb only "predicts" La to be [Xe]4f¹⁴s²; instead it has [Xe]5^d16s². There is no comparison between the MR of thumb and determining a d/e. The former is an approximation that attempts to predict electron configurations. The latter is a known criterion, based on the actual configurations of the elements involved. Sandbh (talk) 11:30, 25 January 2019 (UTC)

Yes, I'm extending it based on the format of the periodic table. After all, the sets of orbitals with the same number of nodes ({1s}, {2s}, {2p, 3s}, {3p, 4s}, {3d, 4p, 5s}, {4d, 5p, 6s}, {4f, 5d, 6p, 7s}, {5f, 6d, 7p, 8s}, and so on) that organise the Janet table, have the problem that the core is always finished at each p-orbital in this set, and the next s-orbital is easily removed and indeed is still easily removed until the next p-orbital is finished. That's why we move them all over to create the period sets {1s}, {2s, 2p}, {3s, 3p}, {4s, 3d, 4p}, {5s, 4d, 5p}, {6s, 4f, 5d, 6p}, {7s, 5f, 6d, 7p}, and so on. This order is still exactly what the Madelung rule gives, and the Madelung rule still tells you which orbital is the one that should theoretically be filling and fixes the row and position (just fill them up; for example, vanadium is expected to fill up everything to 4s and add three 3d electrons, so it must be in the 3d row in the third position, and so on). All I have added is a statement that the inert core is untouchable, and that all orbitals in one set can theoretically be involved in the bonding (though orbitals with azimuthal quantum number 3 and up usually do not contribute even indirectly outside their blocks as they are buried too quickly). But if you prefer the unadorned Madelung rule, consider this: it predicts La to be [Xe]4f¹s² and thus to be an f-block element with significant 4f involvement in chemistry, whereas Lu is predicted to be [Xe]4f¹⁴5d¹6s² and hence to be a d-block element with 5d and no significant 4f involvement in chemistry. And the resulting block and hence chemical prediction is what we see even if the predicted configuration for La is wrong. Double sharp (talk) 04:37, 26 January 2019 (UTC)

Well, the MR does not tell us the orbital "that should theoretically be filling". We all know the MR is not a theory, and that it has no first principles basis. What the unadorned MR tell us about La and Lu strikes me as an interesting coincidence. What concerns me about the UMR is its lack of consistency, Frex it tells us that Ag should be a well-behaved transition metals, whereas it behaves mainly like a main-group metal. Sandbh (talk) 06:10, 28 January 2019 (UTC)

Yes, the MR is less than a theory, as it doesn't so much explain what happens in reality as describe approximately what happens in reality. But, like I said, the periodic table is also a way of organising and describing what happens in reality, and so the MR seems a good match. It should be noted that Cu, Ag, and Au all behave kind of like main-group metals when they are in the +1 state because then they have a filled d-shell. The difference is just that Ag is most stable in the +1 state, whereas Cu is most stable in the +2 state and Au in the +3 state; when Ag is oxidised beyond +1 it starts to display normal transition-metal character. So the MR prediction of significant 4d involvement in Ag chemistry is not really wrong. We may, of course, refine it, as in a certain sense Ag is the normal group 11 element with a "normal" 4d-to-5s gap; the 3d-to-4s gap for Cu is shrunk (radial nodes again), as is the 5d-to-6s gap for Au (relativistic destabilisation of 5d). It strikes me therefore that a more telling test for the UMR is group 12, which is predicted to have d-involvement and behave like transition metals, but generally disappoints (the normal one in the group is cadmium, which disappoints totally). But this is not unusual at the end of a block; a filled shell is generally hard to break open, especially the first one of its quantum number. When we get further down the table, it gets easier to do so. Contrast helium (which I agree is an s-block element; I just don't think it needs to be put with the others), for which 1s² is nigh-on impossible to breach, with beryllium where 2s² is easily persuaded to involve itself in bonding (and the rest of the alkaline earths have it even easier). Contrast the basically impregnable p-shells of Ne and Ar with the tentative steps towards activity made by Kr, Xe, and Rn blooming into full ignobility at Og. Contrast the core-like d-shells of Zn, Cd, and Hg contrasting with how Cn gives up its 6d electrons before its 7s ones. (E166 and E172 are not directly comparable since they are using 9s and 9p_1/2 instead of 8s and 8p_1/2.) So the only problem is that Yb-No-E156 and Lu-Lr-E157 both show the wrong trend (5f is buried deeper than 4f at the end of the series). But since every other end-of-block column has some elements showing activity eventually, the former seems better since the f-shell never gets breached in Lu, Lr, or E157. Double sharp (talk) 07:26, 28 January 2019 (UTC)

Placeholder. Sandbh (talk) 10:30, 28 January 2019 (UTC)

§ Equal justice

R8R: Sandbh, thank you for your response. Even though it's only 3 PM or 15:00 local time, I'm already falling asleep after another exam and thus will probably respond tomorrow or whenever I can find enough time. I've got a quick question before that, though. You said, "The question about vanadium with [Ar]3d³4s² and chromium with [Ar]3d⁵4s¹, and what is the differentiating electron is a good one. In this case the answer is +d2 and –s1. Cleary, the differentiating electron, is a d-electron." Okay, sure. What about chromium ([Ar]3d⁵4s¹) and manganese ([Ar]3d⁵4s²)? It's even more clear that the differentiating electron is an s electron. Why does Sandbh as a scientist accept this flaw and put Mn into the d block regardless, but when it comes to a similar problem with Lr and its potential placement in the d block, its flaw becomes prohibitive. Not disturbing yet acceptable under some conditions like with Mn---prohibitive all by itself? If a criterion doesn't do equal justice to different elements, is the criterion all that good in the first place?--R8R (talk) 12:15, 14 January 2019 (UTC)

As I understand it, there is a little more to Sandbh's argument than that. La, Lu, and Ac all have a d-electron differentiating them from the previous element, but Lr has a p-electron. In a La-Ac table, Lu is anomalous because it has a d-electron instead of the f one we would expect from the table, while La is exactly as we would expect. In a Lu-Lr table, this is reversed. But because Lr has that weird p-electron thanks to relativistic effects, it is anomalous regardless of which table you use, whereas Ac is not anomalous in a La-Ac table. The result is that in a Lu-Lr table, both Ac and Lr have anomalous configurations, but in a La-Ac table, only Lr does. However, I still find myself uncomfortable with such an argument, chiefly because I don't accept that the anomalous configuration of Lr can lead to the conclusion that La is a d-block element. To my mind, "La is a d-block element" is a statement about La, and therefore it must be justified or debunked with references to some properties of La. Double sharp (talk) 15:15, 14 January 2019 (UTC)

Double sharp, you are right in a sense, and I’ve addressed your other concerns earlier in the Q & A part of the thread. Sandbh (talk) 07:14, 17 January 2019 (UTC)

R8R, Mn is an anomaly rather than a flaw. I looked for the periodic table with the fewest anomalies, and was astonished to find that it was HeBe + La, that is all. (I had to check and recheck my results, such was my doubt). The criterion is applied equally across the periodic table. Sandbh (talk) 07:14, 17 January 2019 (UTC)

May I take a minute to appreciate the debate you and DS are having here. Both of you have your scientific (what would those be? hypotheses? suggestions?) ideas, which you use to describe the reality as you see it. I admire both of you for doing so. I can barely keep up with the discussion by watching it unfold on this page. As much as I'd love to take part in some of the discussions, I simply find myself unable to devote enough time to do so. Some of the points raised here do indeed trigger a desire to criticize them in me. A couple of times those were DS's, the rest of them were yours. (Then again, while I'm trying to look past my bias, which I openly acknowledge, I find myself not very successful at it, so maybe that's a part of that. I don't think so but can't deny it, either.)

I took the time to think again what exactly we were discussing here. The section started essentially with your idea that minimization of the differing electron anomalies should be the main principle, the "conclusive argument," as you put it in the title of the section. I took the time to check the exact meaning of "conclusive." Since I'd want to be sure we're talking about the same thing here, I tried to find an Australian dictionary, but then again, since I'm not sure which one to use, I went with the safe choice for English in general, Oxford Dictionary, and it says, "having or likely to have the effect of proving a case; decisive." Now that makes the title ("A conclusive argument for group 3, and He above Be?") quite a claim so let's test it.

It was for a reason that I asked the question that currently stands in the top post of this level 5 subsection. I must say, I'm not particularly satisfied with your response, bearing in mind that we're talking about a potentially decisive argument. Re "that is all": that is clearly not all when put into the context of you trying to use this as a decisive argument for a different question. What I meant by "flaw" was the particular Mn's property of having a differentiating s electron instead of the expected d electron. But you know, call it a flaw or an anomaly, that doesn't really matter. ("What’s in a name? That which we call a rose, // By any other word would smell as sweet.") My point was that there are anomalies that don't ruin the concept of a block; they sit more or less with it. If these anomalies were only limited to the La-Lu-Ac-Lr quartet, then the idea of the Lr's anomaly being an exception in both -La-Ac and -Lu-Lr would be more solid. (Still not the killing argument for me, but that's a different story.) However, there are a plenty of other exceptions. The total is no less than 11, the lowest estimate of the number of them that you have brought up. Now would you say, really, that if at least a tenth of the elements (11 or more) are exceptions anyway, must we then strive for a minimalization of these exceptions at any cost since they are abundant anyway and dismiss the idea of having another one just because of this incomplete minimalization? Doesn't the idea of this being the criterion sound really artificial given that alone? To me, it does. And I'm fairly positive I wouldn't be alone in that.

I agree these anomalies don't ruin the concept of a block. I agree we don't strive to minimalise these anomalies at any cost; we still need to show the elements in order of their Z. Consistent with the concept of a block, my first premise is, "A set of items is more representative of its label the more the individual items in it match the label." So yes, I am arguing we do strive to minimise the number of anomalies. Sandbh (talk) 02:02, 22 January 2019 (UTC)

Now that's the second premise?

Actually, yes, I wanted to write about that, but then, as it so often happens, I got carried away by my thoughts and forgot. I am skeptical of the absolute character of your second premise. While I certainly agree that there is some clear correlation between the number of elements that match the differing electron label issued by the block, I don't see why this correlation is absolute, i.e., what we have is a clear unambiguous casuality. I would genuinely assume that if characteristics of Lu were profoundly closer to something you would expect from a d-block element than La, people, in particular Scerri, who wants to base his solution of the group 3 question on the idea of blocks, would go with that. And some think so, and so they do. Some don't, which is generally also understandable but inconsistent with Scerri's block-based approach.

So if I were to alter your deductive argument, my second premise would be "A set of items is usually considered more representative of its label the more the individual items in it match the label," which would change the conclusion to "A periodic table with HeBe and LaAc is the single best solution to the group 3 question based on electron configurations alone in absence of any other data that, if provided, may or may not change the outcome."--R8R (talk) 07:38, 22 January 2019 (UTC)

Now let's add one more thing. I presume that we are having this discussion having in mind that Scerri wants to solve the group 3 issue. What is Scerri's opinion of these anomalies? Well, quoting your quote of his quote, "These anomalies should not challenge our attempts to establish the overall structure of the periodic table in terms of sequences of blocks in the periodic table and as a result our recommendations for the membership of group 3 of the periodic table." I know I said this before, but it seems to me that I need to reiterate it. The anomalies are not the decisive factor for him, they are not important at all, and I think I see why. (If you want me to write more on this particular why, just let me know.) You've written before that fewer anomalies meant purer blocks but I still refuse to see how this matters. Not only the decrease of the impurity is less than 10% (this is not neglibile, but certainly not a deal breaker if you ask me), but the impurity decreased in something that, according to Scerri, shouldn't matter in the first place. So is this criterion for Scerri's problem decisive? I'd say no, and I'd say so firmly.

There is some important context to Scerri's opinion, as expressed in the full quote. Here it is:

“Moreover for the purposes of selecting an optimal periodic we prefer to consider block membership as a global property in which we focus on the predominant differentiating electron. We readily acknowledge the fact that the atoms of Mn, Zn, Tc, Cd, Pt [?], Hg, Lr, La, Gd, Ac, Th, and Cm are all anomalous in that they have a differentiating electron that is atypical of the block that they are situated in. These anomalies should not challenge our attempts to establish the overall structure of the periodic table in terms of sequences of blocks in the periodic table and as a result our recommendations for the membership of group 3 of the periodic table.”

I agree with Scerri. I accept the anomalies. I agree we focus on the predominant differentiating electron. I agree we should strive to establish the overall structure of the periodic table in terms of sequences of blocks in the periodic table and, as a result, my recommendation for the membership of group 3 of the periodic table. Please then continue to my first premise. Sandbh (talk) 02:02, 22 January 2019 (UTC)

It appears funny to me that you have added two more sentences to my quote and then referred exclusively to those two sentences you added and did not explicitly refer to the one that I highlighted. Scerri says exceptions don't matter, exceptions are exceptions; and I agree. I personally think that the concept of blocks includes more than that, things like what electrons are involved in bonding, something that puts Mn back into the safe d-block zone by any means. Scerri provides an oversimplified criterion for inclusion into a block but he seems to diminish the negative aspects of that by saying that exceptions are exceptions, they shouldn't matter. I'm calling for you to do the same.--R8R (talk) 07:38, 22 January 2019 (UTC)

Now you've tried to refer to some other aspects of the problem, and so did DS. And I think you were right to do that, because the picture is complex. A simple criterion would be great. Yours, however, appears to be an oversimplification.

While we're still at the criterion, I honestly don't see why it would have to be quantitative (I sense that you mean here some binary/ternary/etc. divisions, not differences in figures after the decimal point like the electronegativity trend, for example; if I'm wrong, please let me know). I would honestly assume the criterion would need to be qualitative that could alternatively be interpreted as quantitative (something like "this substance is a base because its pH is 12"). This kind of a criterion seems more general in its scope, and thus more legitimate to be the criterion, than "12 exceptions instead of 13 is the way to go." I'm really unfavorable on the idea of counting what would allow us to have fewer exceptions. They're exceptions for a reason: the topic underneath the periodic table is very complex, and the reality needs to be looked more closely at than judging by an inevitably oversimplified perception.--R8R (talk) 18:20, 21 January 2019 (UTC)

Quantitative is measurable; qualitative is subjective. Sandbh (talk) 02:02, 22 January 2019 (UTC)

Dunno. If you have a quantitative criterion, don't you also require some subjectivity to determine where to break stuff up? It's like saying that an element needs to have a conductivity of at least X to be considered a metal; why does it have to be X instead of X+1 or X−1? If we are cherry-picking X to give the "obvious" definition then it suggests that there are other reasons why that definition is obvious, but it has nothing to do with X. Anyway, I agree with R8R's question. If you have to accept some exception, and they shouldn't matter to block placement, then what is the point of breaking blocks so that there are a few less? You could drop the exceptions to zero by shoving Ca, Mn, and Zn all in the 4s² differentiating electron position, but we wouldn't do that for other reasons. You could have the same number of exceptions by letting the 5f series be Pa through Rf, but we wouldn't do that for other reasons. You could have the same number of exceptions by putting Be and Mg atop Zn and letting the d-block run from the Ca group to the Cu group, but we wouldn't do that for other reasons. To which I want to say: if we need to look at electron configurations, d- and f-electron involvement, and even the possibility of drawing stuff in a table, to resolve so many matters, then at the very least differentiating electrons are not everything. Indeed, since we are quite willing to depart from them to put He over Ne, I think they are not that important at all, since chemistry not only supplements them but trumps them in this case. I am more inclined to say that the periodic table is about real elements, real chemistry, real compounds, and real trends, and if Lr happens to have an anomalous s²p configuration that does not affect any of these, then it should not be reflected, and it should not impact anything. And since this Sc-Y-La argument depends on Lr being s²p, I am inclined to think that it is not seeing the chemical forest for the differentiating electron trees. If we are going to mention all the formal stuff, it should at least be explaining something about chemistry, rather than just being there for the sake of it. Double sharp (talk) 02:51, 22 January 2019 (UTC)

Part 1 of my response is: No subjectivity is involved in my quantitative suggestion. My deductive argument has no arbitrary line of demarcation. Part 2 of my response is: Yes, you have to accept some anomalies. My approach is (subject to observing an increasing order of Z) that the optimal periodic table is the one that, from a physics point of view, most closely matches the observed filling sequence of the electron sub-shells namely:

1s²

2s² 2p⁶

3s² 3p⁶

4s² 3d¹⁰ 4p⁶

5s² 4d¹⁰ 5p⁶

6s² 5d¹ 4f¹⁴ 5d⁹ 6p²

7a² 6d¹ 5f¹⁴ 6d⁹ 7p²

Many, many chemists will look at that and say, helium is better positioned over Ne, from a chemistry point of view. And I would agree with them, at the expense of one more d/e discrepancy. A chemistry teacher might say, I'd like a 15 -element wide footnote, rather than 14 wide. And I'd say, good to go, at the expense of two more differentiating electrons.

A few other chemists will be quite happy with HeBe (open access).

Yes I'm looking at the d/e forest and I can see the chemistry trees too, but I can't yet see an LuLr one, that has any solid foundation. Sandbh (talk) 05:37, 25 January 2019 (UTC)

(response to ~~an unfinished comment~~ Part 1) I beg to differ on this one. Your criterion is indeed subjective. The part "-La-Ac makes one less exception to the differentiating electron rule" is not subjective. However, "let's use that as the best possible justification for a -La-Ac table" is: there couldn't possibly be a way to impartially conclude that one criterion is "better" than another without applying some subjective thinking. You may conclude from my reasoning that any criterion produced by you or me or DS or even Scerri will be subjective---and you will be right. Subjectivity is inevitable.--R8R (talk) 08:59, 24 January 2019 (UTC)

I must be missing something. What is it that is subjective about my deductive argument, namely "Premise 1: A periodic table block is named according to the predominant differentiating electron among its members"; and Premise 2: "A set of items is more representative of its label the more the individual items in it match the label?" (Perhaps you have in mind something like what you say below about "our whole issue is entirely subjective". I'll get to that when I can). Sandbh (talk) 05:13, 25 January 2019 (UTC)

First of all, you are entirely right about how I base my opinion on that "our issue is entirely subjective." But since you respond to that below, my answer to that will be there.

The rest is very closely related to the aforementioned thesis but I will describe it greater detail. First of all, I am critical of the absolute character of your second premise (you can find more of my criticism in this very level 5 subsection; look up for the sentence "now that's the second premise?"). Second of all, your arguments only leads to a conclusion from the premises that you have provided. You have not, however, included all premises that could be made; you only included those that you found reasonable. That very choice was deliberate and thus subjective. There could be more premises of strength that would be roughly equal to that of your second premise after my reworking I had mentioned during its criticism, like "Premise 3: a block shows similar (you could quantify that if you wish) vertical trends throughout its groups"; "Premise 4: an element that adds an electron to a complete shell is regularly not considered a member of the block the filled shell corresponds to"; "Premise 5: a block is preferably contiguous" (I really like that last one. It is a direct analog of your second premise, although a little more general in its scope, and is just as easily quantifiable: one split block or zero split blocks. We do want to minimize the number of exceptions, don't we?). Whether you want only premises 1 and 2 (which gives us -La-Ac), or 1 and 5 (which gives us -Lu-Lr), or all five (which requires the "a little bit of this and that" approach to make a conclusion), or maybe more is entirely up to you, i.e. subjective.--R8R (talk) 15:09, 25 January 2019 (UTC)

But our whole issue is entirely subjective. The concept of a "block" is something people explicitly made up. This isn't gravity which exists regardless of how we describe it; this is an entirely, 100% human-made approach, a way to describe what we perceive as similarities (notice the subjectivity of this term) between various elements. It is subjective by definition.

I probably haven't made this entirely clear, but there are different kinds of "quantitative." Those can be either binary/ternary/etc. classifications or measurements exposed by real numbers. I'm calling to abandon the former (because then we would be again puzzled with counting exceptions) and accept the latter, making from there qualitative conclusions if you need them (which you presumably will). Something like "Lr is [Rn]5f¹⁴7s²7p¹ but its [Rn]5f¹⁴7s²6d¹ state is only XX eV away and it behaves like a d-block element because look at those mp/bp/IE trends, the numbers clearly tell us this is in great agreement with what we have in other d-block groups, whereas numbers show that Sc-Y-La-Ac is an uncommon trend for the d-block" (or the opposite). It doesn't have to be exactly what I described, and even the result can be different, but this is the kind of thinking that I'd be more likely to recognize than counting exceptions because then I'd want to look at your exceptions and see why they are exceptions and figure if their exceptionality matters, which brings us back to the thinking I just described as preferable.--R8R (talk) 07:38, 22 January 2019 (UTC)

Actually no. They didn't make it up. The sub-shell filling sequence was discovered, and the blocks fell out of that. Not only in terms of the physics of the filling sequence but also in terms of the distinct characteristics—in a global sense—of the s-, d-, p, and f-blocks. OK the latter part has some subjectivity because we are getting into the chemistry here. But I still agree with Scerri that the blocks can be objectively discerned, at least in a global sense. Like I said above, I must be missing something. What exactly is it that is subjective about my deductive argument, as outlined above? Consider two identically sized fields of oats. Looking closer, field A has signs of poppy contamination. Field B has no such contamination. Which field is more representative of a field of oats? Sandbh (talk) 06:00, 25 January 2019 (UTC)

Yes! But watch your words there. "The blocks fell out of that." They were not discovered; they were invented as a means to describe the similarities between the different elements throughout that very filling sequence. But similarities don't exist, and neither does anything that is based on that. A block is not a tangible thing or even a physical phenomenon; it is a concept only. You cannot measure (which is an action based on observation of actual physical phenomena) a block, you can only describe it. You can touch your laptop or you can experience the gravity to the Earth; there is nothing of that sort that a block would help you do. Therefore, a block does not exist in any physical sense.

Can a block be described objectively? I'd argue that no, it cannot. Very close to that at a given time maybe, but not absolutely. If block is a concept, and a concept is something that people have agreed on, then what would prevent them from changing their opinion over time (like going from premises 1 and 2 to 1 and 5 or vice versa. Remember that DS and even yourself previously changed your opinion on what d and f blocks would consist of?) and therefore changing the concept itself? This would render the previous description---as well as all future ones---subjective. In fact, this has already been done by the very possibility of such a future change.

Now to your oat example. To this, I would say that from the data that you have provided, it indeed seems that the second field seems a better representation. This conclusion, however, rests on two implicit premises: that oat fields usually don't have poppy contamination (which sounds plausible but I'm no agrarian to confirm or deny that) and that the fields are identical in any other respects. Say, if the first field were in England and the second were in Antarctica, I think I'd see why some would argue that the former is a better representation.

(I admire you for accepting that you may be missing something. I have come to do that in my life when I'm not entirely sure about something or lack enough knowledge to make an unambiguous conclusion. It is for similar reasons that I don't argue for either version; as you could see, my contribution to this discussion has only been in reviewing the arguments themselves. I'm not sure there is at all a kind of argument everyone would agree on, and in an absence of such an argument, I don't make it. I, however, cannot see what I could be missing here.)--R8R (talk) 15:09, 25 January 2019 (UTC)

I wonder if objectivity matters. "Everyone" knows a periodic table block when they see it even if they cannot quite put their finger on precisely quite what makes a block a block. They know it has to do with the order in which the sub-shells of the periodic table are filled. Surely a block is a region of the periodic table characterised by similarity in most recently occupied sub-shell?

Gravity as something objective is not quite the same as what I'm claiming. My approach is concerned with providing an objective measurable criterion. I guess this is something like a theory/description(?) of gravity. Originally based on classical mechanics our understanding of gravity was superseded by general relativity. And we think we still don't have it right over very-long distances. Nobody queried the objectivity of any of these stages in the development of our understanding of gravity. And I think the same can be said of the differentiating electron concept.

We can't handle blocks just like we can't handle numbers. We can still make objective arguments about them, can't we? Sandbh (talk) 05:54, 28 January 2019 (UTC)

Re "I wonder if objectivity matters": I wrote my previous message in particular in response to this phrase: "But I still agree with Scerri that the blocks can be objectively discerned, at least in a global sense." I argue that no, blocks cannot be objectively discerned because the whole foundation of objectivity crumbles on the subjectivity of the term "block" (also, I find it very curious indeed that two people, who argue that blocks can be objectively discerned, arrive, at least preliminarily, at different blocks---now what if not that screams that the issue is subjective). To me, this is something to acknowledge as a given and move on. But I do find it important that this is realized: if Scerri makes his conclusion without acknowledging that the issue is indeed subjective if you look closely and claims the opposite, IUPAC or maybe other chemists may not accept his findings thinking he arrived to a conclusion based on wrong premises. If Scerri's conclusion is not accepted, then the whole group 3 task force was a bust.

Re "'Everyone' knows a periodic table block when they see it even if they cannot quite put their finger on precisely quite what makes a block a block": everybody gets the general concept, sure, filling shells, etc. Different people, however, make different accents on what indeed makes a block a block. For instance, some emphasize electronic structures; some, while admitting that the theory behind the concept is indeed those structures, focus on periodic trends within blocks: what would be the point of discussing blocks and even inventing that term in the first place if it did not help reveal interesting similarities between elements. Since it's only four elements that are in question, the concept generally remains intact one way or another.

Re "My approach is concerned with providing an objective measurable criterion": I understand that, I really do. I do believe you when you say you didn't invent this criterion just to justify the -La-Ac table; you wanted a criterion that was clear and made most sense. Since it so happened that it provided support the -La-Ac table, so then it should be. The point that I am trying to get through is that no criterion could possibly be objective. That is because by making your statement and relying on electron exceptions, you implicitly deny to acknowledge the importance of other criteria that make some people want to think about blocks. That was your decision, deliberate or not. It is your judgment that the criterion rests upon. However, if you had included those, that would have also been a decision of yours. The criterion would've still relied on your judgment. You can get through with your idea to as many people as possible, even the entire seven-billion population of the planet. Yet it would still be the decision of yours to have made that argument (and of those people's to accept it). Analogies with gravity don't really apply. Gravity exists regardless of what we think about it. The theory of gravity allows you to get predictions for future experiments and you could set up experiments to test the theory. In contrast, your criterion, and the concept of blocks in general, is only one way to systematize the knowledge that we already have. It does not allow us to make any predictions. That's why it could be that nobody doubted the objectivity/subjectivity of the gravity theories: there is always a possibility to test the theory and see if the theory stand against the tests. That's what matters. The concept of blocks is just a concept. It cannot be tested by any reproducible experiments; it can only be agreed on, expanded, or rejected in our thoughts. It is not entire impossible to think that we could have invented a different concept of blocks, with blocks d1 and d2 for the first and second halves of what we call the d-block. Or that we wouldn't be bothered with blocks altogether, and focused solely on groups and periods. In the end, the difference is that the theory of gravity describes something objective, something that does exist, and allows us to make testable predictions. The concept of blocks describes relationships (note the subjectivity implicitly tied into this word) between elements' properties, something that doesn't exist even if still quite useful to think of, and on its own, it allows to makes no predictions whatsoever.

Re "We can still make objective arguments about them": that we can do. We can thereby get some objective incomplete parts of the entire picture. What we cannot do is to make objective global conclusions from those arguments, the conclusions will inevitably be subjective. The entire picture will inevitably depend on how we look at it because we are looking at our own inventions---relationships between elements---rather than something real.

I only want you to recognize no criterion would possibly be objective. To gain ground, it doesn't need to be objective because that it cannot be; what it does need is recognition, for which you would presumably need to recognize the basic premise of inevitable subjectivity and perfect your reasoning from there. As I mentioned, I don't really like your criterion. By which I'm not trying to say it is bad in an absolute sense or anything---personally, I find that argument not very convincing, nothing more and nothing less. I perfectly recognize I'm not the most important person there could ever be in chemistry. I'm not even a chemist to begin with. I do, however, have the feeling that other people may think like me and this will stipulate your attempts to get your criterion recognized. Then again, I did mention that I think the recognition barrier seems too high for any possible definition or criterion. I remain hopeful I will be proven wrong.--R8R (talk) 04:11, 30 January 2019 (UTC)

It seems to me that part of the issue here is, as R8R says, we are not dealing with something akin to an experimental science like gravity. We are dealing with a descriptive and classification issue, something more like the nomenclature and taxonomy of biology. What should our goal be? Is it attainable? To answer that, consider the history of the periodic table. Originally, the elements were ordered by atomic weight, but then there were a few exceptions. I think everyone agreed to the exceptions before the underlying principle - atomic number - was arrived at. Our goal should be to figure out a way to organize the 2nd dimension of the PT in a way that is as satisfactory as Z is for the linear dimension. Well, maybe I'd settle for "almost as satisfactory as Z".

I've had a couple of heretical thoughts that may be of interest.

Maybe we messed up in going to the wide table. Maybe there were some benefits to Mendelev's original very narrow table.
Maybe we messed up in trying to remove ambiguity. If there are some inherit ambiguities, maybe the "ideal" PT should actually recognize the ambiguities rather than hide them.

As to ambiguities, I'm not sure how this works out in practice, but I just cannot get it out of my head. Maybe put H (or He) in two places? Maybe re-consider the much maligned Sc/Y/*/**? As to the latter, when I first saw it back in high school, I instinctively thought it meant that the footnoted elements really belonged in the main part of the table. And I understood that only two of the elements really belonged under Sc/Y, but the table didn't tell me which two. Today I see that ambiguity as a plus. Oh, and I NEVER thought Sc/Y/*/** meant that all footnoted elements were in group 3. Today, I know a bit better - I see the "all in group 3" as possibly another alternative understanding of Sc/Y/*/**, but even to this day I would never think that interpretation is the primary meaning of Sc/Y/*/**.

YBG (talk) 07:59, 30 January 2019 (UTC)

Oh, and one more thing. I think this discussion is helping us to build a better encyclopedia, but if someone asked me why this discussion is not a violation of WP:NOTFORUM (particularly point 5) I'm not sure I could provide a good answer as to how it is that we are stay[ing] on the task of creating an encyclopedia. I think there is a good answer, I just cannot express it. Maybe someone else can. YBG (talk) 08:10, 30 January 2019 (UTC)

First of all, I'm glad I could explain the nature of my concern to you.

Quick re (well, that was the intention, but I got carried away):

Wide, medium, or short---doesn't really matter for our topics of period 1 and group 3. My personal preference is the 19-column table: the regular medium-width table with a gap between either groups 2 and 3, or 3 and 4 to account for the inclusion of the f-block there. (Like our PTQ template and unlike the PTQ picture.) The 32-column table would be even better if it weren't so inconvenient. The 19-column table represents exactly the same, but in a different manner, less appealing to purists like DePiep (who is known for his advocacy of the 32-column table) but more convenient not only in print due to different width-to-height proportions, but also more appealing to the eye, I would say, because the 32-column table is not only too wide, but also creates a lot of empty space within the PT. The short PT has the downside of not being able to provide that gap.
As for ambiguities. I have a gut feeling (not very objective, granted) that a few decades after the official adoption of the -Lu-Lr, the issue may potentially, if we get very lucky, die out, but the official adoption of the -La-Ac table or the -*-** table would still leave some small opposition indefinitely. I have come to think that the success would be not in having the right decision (which is unattainable by the very nature of the problem), but rather one that everyone could agree on. The two most popular tables are -La-Ac and -*-**, both still facing some challenges from -Lu-Lr despite their prevalence over the last decades. It could be that if -Lu-Lr dominated the stage, people wouldn't see a reason to go back to -La-Ac. Maybe not, but there's a chance. I am quite certain that the -*-** would not solve the problem. I think that the interested chemists want to get down to the bottom of things (that's how I see their motivation), and to many, -*-** would feel like giving up halfway through the search. Ideally, there should be an ideal argumentation for either -La-Ac or -Lu-Lr that makes people forget their old alliances and settle on either option. The problem is that such argumentation has not appeared yet, and it is uncertain whether it will. I personally don't think this will happen because different people emphasize different things about blocks. But if it does, that will be terrific. As for double H: indeed, it is quite common for Soviet and even Russian periodic tables to have H in group I and (H) in group VII (the periodic table I had in our physics classroom in school inverted this, having (H) in group I and H is group VII, though I don't recall having seen that anywhere else). The very famous textbook Chemistry of the Elements has H and He border each other and float above the rest of the PT. I think it is that very desire to get to the bottom of things that obstructs ambiguity in this respect and makes H and He just like every other element, forcing into specific groups, both in one piece, because other options seem too artificial and that's perceived as unwanted.

As for your concern re WP:NOTFORUM. That rule is to be applied in the article space. In contrast, we are now on a WikiProject talk page. According to WP:WikiProject, "It [a WikiProject] also provides a forum where issues of interest to the editors of a subject may be discussed."--R8R (talk) 10:43, 30 January 2019 (UTC)

Totally agree with R8R on "I have a gut feeling (not very objective, granted) that a few decades after the official adoption of the -Lu-Lr, the issue may potentially, if we get very lucky, die out, but the official adoption of the -La-Ac table or the -*-** table would still leave some small opposition indefinitely." Indeed, -La-Ac is just a relic of times without f-block at all. If lutetium had been discovered earlier than lanthanum, we probably would have never rise a Group 3 problem at all. Droog Andrey (talk) 21:18, 9 February 2019 (UTC)

Who knows? If Lu had been discovered first it would still have been lumped with the other Ln. Then there would've been the problem of which element would occupy the position after Ba and below Y. La fits better when comparing Ca:Sc, and Sr:Y. In the old days it was thought that Yb was f¹³, so that the f-series finished with Lu, implying again that La with no f electron should come after Ba. Even in the real world, while some chemists in the 1920s placed Lu under Y, this never gained any traction, despite the fact that Lu occurred naturally with the yttrium earths. Go figure. Sandbh (talk) 00:07, 20 February 2019 (UTC)

If Lu had been discovered as early as La was, there would not have been that many other known rare earths to put it with. Presumably Mendeleev would have left two rows of frustrating blanks after Ba like he did in our timeline, putting Lu as dvi-yttrium as it would be about as clearly a group III member as Er, which he put there in our timeline. If La then evaded discovery for a while, Lu would very likely have then kept the eka-yttrium position by default just like La did in our timeline. In the old days we put Th and U as eka-Hf and eka-W, and though Bassett suggested as early as 1892 that these were really eka-lanthanides, his ideas never got any traction until the synthesis of the transactinides and evidence that 5f was filling here (and not 6d, as previously assumed) made it irrefutable that this was an inner transition series. Even them some chemists protested their removal to the actinides because U is a lot more like W than like Nd, but the 5f involvement makes U chemistry quite different from d-block chemistry (even if it doesn't make it much like 4f chemistry), so no one raises complaints now. So we already have a precedent for changing placements because we got the electron configuration wrong and missed subtleties of their bulk properties which are caused by their electron configuration. It just appears to be taking longer with Lu than with Th and U, which is fair as the differences are smaller (and you can't draw a table with Ac through U in the same places as Lr through Sg; don't forget ease of drawing as a necessary caveat!).

Oh and I disagree that La fits better in the way you mentioned, among other reasons because that would certainly support putting Al over Sc instead of Ga. ^_^ Double sharp (talk) 05:57, 20 February 2019 (UTC)

@R8R: We have spoken a lot about objectivity and subjectivity. Was the decision to organise the periodic table on the basis of Z objective or subjective? It was done since that brought out the recurring similarities among the elements better than atomic weight. But we know that the repetition of properties involved is still only approximate. In this sense, using Z as our organising criterion seems to be subjective. The line I am exploring is that if the differentiating electron criterion is to be regarded as subjective then it is so because (like Z) we so far have nothing comparably better. Sandbh (talk) 02:02, 15 February 2019 (UTC)

I'm sorry for not having responded earlier. I did see it and I immediately got the idea of what my answer would be like but I didn't write it down and then it slipped my mind.

You are entirely correct in that classification in order of increasing Z is subjective. However, there is one phrase that puts me off (you'll see why it's relevant shortly): "we so far have nothing comparably better." This is, again, almost a pretension that it is our best bet is best in an absolute sense---something there isn't at all for this question. The correct phrase would be "we so far have nothing that we would find comparably better." I can't stress enough that we can only judge from our perception. If you think something (about classification of the natural phenomena), it is subjective. If we both think that, it is still subjective but has a little better grounds in the society (though still not much). If the entire WP:ELEM agrees, the basis grows, but the view is still subjective. If the IUPAC agrees, the basis in the society is still stronger, but the view is still subjective. If the entire planet thinks something, it's unlikely that the dominating opinion will change. Yet all of its holders are subjective, and the possibility of the change is still there.

Now to why this was relevant. The idea that the differentiating electron is "the best we've got" is subjective. The objective statement would be, "I [i.e., you] think that the differentiating electron is the best we've got and therefore we should closely stick to this, minimizing the number of exceptions wherever possible." That cannot be argued with, you really do think so. However, and I think I've explained why, I don't agree with such absolute character of your statement. DS isn't convinced, either, and DS's point is also valid. Finally, Droog Andrey also made his point, and he also doesn't emphasize your premises to the same extent as you do. None of these opinions is better than the rest in any absolute sense. Yet mine, DS's, and DA's contradict yours; we don't think "we so far have nothing comparably better." I don't want to speak for the other two, but I think that what is comparably better is a combination of a number of factors, including your adherence to the "minimum number of exceptions" criterion, but more that that. In my opinion, such a combination should yield -Lu-Lr. You may disagree and that's fine as long as you accept your opinion is not better than DS's; it may, however, gain enough ground and become effectively dominant, but that would still not make it better. (I don't think, however, that people have made or are willing to make that bet to ensure there is nothing "better" as in "more popular" if they were to really think things through. Though, of course, it is just my intuition and nothing more.) Equally, DS's opinion cannot be better than yours, either. It may become more appealing to the others at best, and that's it.

I see that I'm being very formal here but I think formality is favored so that our language does not interfere with our discussion and people won't think something along the lines of "lanthanum must be in the d-block because it cannot be a lanthanide. It is not 'like lanthanum,' it is exactly lanthanum, and we keep lanthanum in the d-block away from the lanthanides in the f-block." (I don't recall the details, but I have once heard this silly argument. Had lutetium been discovered in 1700 and the series been called "lutetides," would that alone have changed the presentation of the periodic law? Of course, both science and language are both human constructs, but they shouldn't influence each other this much.)--R8R (talk) 16:26, 18 February 2019 (UTC)

@R8R: I largely agree. I tend not to agree with you where you said:

"…what is comparably better is a combination of a number of factors, including your adherence to the "minimum number of exceptions" criterion, but more that that. In my opinion, such a combination should yield -Lu-Lr."

This reads too much like "-Lu-Lr" is the right solution and we should be able to retrofit some combination of factors to support this. The d/e criterion works the other way round. I didn't develop it to support any particular outcome. I had thought it would point to LuLr given how strongly this was associated with the LST, and variations of that such as the ADOMAH "perfect periodic table", and the Madelung Rule etc., but I was nearly astonished to find that LaAc was the closest to the pure Madelung Rule.

I'll refrain from describing my deductive argument as being objective. I'll now refer to it as being quantitative. I understand that the objectivity of quantitative > qualitative, and I'd be quite happy with that.

Oh, nearly forget. What is it about LuLr that you find so appealing? Sandbh (talk) 22:52, 19 February 2019 (UTC)

Reading his comment, I don't think R8R means to start with Sc-Y-Lu and then accentuate the arguments that lead to it. Instead what he writes sounds closer to my position, which is that relying on one criterion alone will be inadequate and we should look at multiple ones (for me, in proportion to their impact on real bulk properties), and that on the balance this will conclude in favour of Sc-Y-Lu. Double sharp (talk) 23:49, 19 February 2019 (UTC)

I'd worry that the use of multiple criteria won't be able to be done sufficiently objectively or decisively to the satisfaction of either camp. Sandbh (talk) 04:44, 20 February 2019 (UTC)

Yet it is far more objective than picking just one. That way the other camp can say that important points have been missed and can dispute the importance of your chosen criterion. If you look at them all, the other camp may argue on the weight each should be given, but it is much harder to question which conclusion each of them separately leads to. Double sharp (talk) 05:42, 20 February 2019 (UTC)

DS got the right impression. I simply wanted to avoid a focus in that particular on why I liked -Lu-Lr better and thought this should be the result because that wasn't the point of what I was meaning to write. I indeed don't favor -Lu-Lr just for the sake of favoring -Lu-Lr; there are particular reasons that make me think that. First of all, I don't favor excluding group 3 or even group 12 from the scope of the term "transition metal." The whole transit is from group IIA to group IIIA via with the insertion of groups IIIB through IIB. I see the transition, at least in its early groups, as gradual. It is okay if group 3 is not very transition-ey in the colloquial sense because that very transitionness grows stronger with groups 4, 5, etc. It has to start somewhere and I get the impression that having a d-electron in Sc(II) or Y(II) is decent enough a start. Yes, +2 is negligible for these, but +3 is not at all strong for Zr and even Ti, either, +4 for Nb and especially V is already a bit more strong, though still not the main oxidation state; see, the transit is gradual. I think there's more in this than what you might have concluded from the basis of a term; what I've described does feel right even without the concept of transitionness, but it does provide a beautiful illustration, and if it did not exist, it would be worth inventing anew.

Now, as for the placement of the f-block. Normally, I would think the beauty of contiguous blocks is a good hint that this is how things should be. This makes the concept of -Lu-Lr more intuitive. Intuitive doesn't mean right, but our problem has no right solution anyway; any would have resulted from some judgment. I see a good analogy between Lu immediately after the f-block in group 3 and Ga immediately the d-block in group 13 and it only makes sense that periodic trends are not continuous in group 3 (periodic trends are well distorted in the following groups as well, all for the same reason, the lanthanide contraction): atomic radius, mp, density. The graph that popped up in this section also provides a beautiful illustration for this idea and well enough hints that if we were to represent in our humanly ways the horizontal periodicity in filling subshells, this would be the closest to what we could have to the hidden truth. If you don't like the graph because why third IP, we could remember that Eu(II) and Yb(II) are quite common (and, on a similar note, that is also to a certain extent true for Tb(IV), which is half the 4f series away from Ce(IV)), all indications of that Eu is the half-shell element and Yb is the full-shell element of the 4f series. All of what I have written is fairly basic (and I think all of it has been referred to at some point during this discussion?), and it all points to -Lu-Lr. The evidence for -La-Ac is not nearly as convincing, in my opinion. We could dig into various properties, and you and DS do that very well, but for me, this would inevitably have less value because why would you look into details when defining a concept, and what we have on the surface seems enough for me to make a decision.

As I mentioned in my first comment, I don't think there is any judgment that would decisively resolve the dispute. If you don't like multiple criteria, consider this logic: one criterion is also multiple criteria. In a multiple-criteria choice, you explicitly decide which factors matter more: you weigh what matters more, what matters less, and what doesn't matter at all. In a one-criterion choice, the situation is identical. The only difference is that you now decide implicitly that all other factors don't matter at all; yet you still make that decision, and it is just as likely to be contested as in any other scenario. Giving more weight to several criteria seems more fair to me; again, we wouldn't have bothered with inventing (or even if we had invited it anyway, we still wouldn't use it actively) the concept of blocks if it weren't for the properties that elements within these blocks display. In contrast, I wouldn't be particularly bothered with minimizing the number of exceptions as you do; very recently, if not today, DS reasonably (per my judgment) said that we care about properties first and foremost; Scerri himself wrote, as you quoted, what I regard as a call not to worry about these exceptions, as they are not at all defining. The differentiating electron concept seems only necessary for him to produce the general concept, and that's it. If I'm reading into his words correctly, then I support this approach. DS recently said (and I think I had said that in one of my first posts) that if the unusual exception at Lr is what is the effective force that settles the dispute, then I wouldn't consider this a good result, not because of what group 3 this yields, but because this exception has no effect on actual properties, so the foundation behind the decision, in my opinion, would be very weak (sorry).

Is this a satisfactory answer to your question? I think I wanted to say more but I can't remember what it is that I'm forgetting to say.--R8R (talk) 17:50, 20 February 2019 (UTC)

Yes, one would think that the IUPAC project will need to compare the big pile of physical and chemical property based arguments, before they can conclude it's too close to call.

That article in C&EN is worth bearing in mind again.

We know that:

"Scerri thinks a focus on chemical or physical properties is misguided. He compares it to early botanists’ classification of flowers by their color or petal number."

He has a strong point given the track record of these arguments.

"You’ve got to go for something fundamental," Scerri says, like electronic configuration. "Just to amass properties is never going to give you a definitive answer."

"Not that electronic configuration is perfect either, as Scerri will tell you. Exceptions have been made for some elements in the periodic table in terms of how their orbitals are filled, like copper. By the periodic table’s logic, all d-block elements should have filled s orbitals. But copper defies that logic."

“My suggestion is simply this,” Scerri says. “Represent the periodic table in a 32-column format.”

From this you get the Janet form, with the s-block moved to the left. Lu is then below Y. Scerri makes no mention of the split d-block option. He calls this, "a rather unnatural presentation that can be safely ignored" (in the Mendeleev to Oganesson book),

Anyway I reckon the d/e proposal is something fundamental; based on electronic configurations; takes the exceptions in its stride; and the resulting HeBeLaAc (11 d/e) table can be displayed symmetrically in the form of Stowe's physicists table. This doesn't negate the utility of tables that move further away from the ideal MR table (d/e = 0). So I can see a good argument for HeNeLaAc (12). But I expect the move from there to HeNeLuLr (13) will be a bridge too far, and fail on petal counting grounds. Sandbh (talk) 07:09, 20 February 2019 (UTC)

Sure, we now have genetics to explain colour or petal number. But note that it is a true explanation: the early botanists were quite right in noting what they saw, and it is just that they did not know why they saw what they saw. I do not see differentiating electrons as such, as the very unusual anomaly at Lr translates to absolutely nothing for its chemical and physical properties, and He behaves nothing like the elements in group 2 which share its s differentiating electron. Double sharp (talk) 15:34, 20 February 2019 (UTC)

Interlude: Symmetry retrieved

This subsection interrupts thread continuity, lacking a better place to put it. It's nevertheless directly related.

I was surprised to see Timothy Stowe’s Physicists Periodic Table (1989) has He over Be, and La in group 3. I was then gobsmacked to see that, as Timothy put it:

"The chart's symmetry and beauty [my emphases] stem from the fact that its structure is mathematically derived from the quantum numbers (n, l, m, s)."

Extraordinary! Jeries Rihani has a site that further explores the symmetry of this table.

It's remarkable that a loss of symmetry would be caused by moving He over Ne, and not by having La in group 3.

Earlier, Van Spronsen published a 32-column table, with He over Be, and La in group 3, in 1951. He later reproduced it on the inside covers of his 1969 book, The periodic system of chemical elements: A history of the first hundred years. He wrote (p. 257):

In a system arranged according to electronic structure, the noble gases Ne, Ar, Kr, Xe and Rn would become members of the same column, but He would fall outside of it and head the second group because of its complete s-orbit, which it has in common with the alkaline earths. This classification was favoured by Janet… A few years ago, a system on the same basis was also published by the present writer… The agreement in chemical properties provides a better basis, even though it involves a departure from the criterion that elements in the same column of the period system must fill up or complete the orbit of the same kind in the electron shell of their atoms.

I agree with his conclusion about He over Ne, even though it comes with a loss of symmetry.

Curiously, he continues to refer to his "He over Be, group 3 with La" table (p. 280):

The [32-column] system Romanoff prepared in 1934 to celebrate the occasion of Mendeleev’s centenary deserves special attention. This was a simple two-dimensional system in which each element had been given its proper place, and was used by the present author as an example to bring the periodic system up to date (Figure on the cover).

Romanoff’s 1934 table was the same as that of van Spronsen, expect he put He over Ne. Now get this: Romanoff was the Professor of Physics at the University of Moscow! A physics professor moves He over Ne. Very cool.

Back to van Spronsen (p. 293):

The periodic system (Figure on inside cover) is composed of groups of analogous elements, each of which belongs to one of a group of periods.

And just one more time (p. 295):

The remaining irregularities can be seen from the periodic system on the cover.

Summarising, I continue to see a spectrum of tables:

The Physicist's Periodic Table, which has optimal blocks
The traditional table, as per Romanoff (a physicist), and supported by van Spronsen (a chemist)---almost as good as the physicist's table, but for He over Ne
The IUPAC(hemistry) table---good for showing the An and Ln, at the seeming expense of a 15-element wide f-block.

I continue to see no robust basis for an Lu-Lr table, or a LSPT. I may add to this interlude, with further reflection. Sandbh (talk) 03:08, 15 January 2019 (UTC)

There is surely a loss in symmetry that is obtained by putting La and Ac in group 3. It means that the 5d and 6d series, alone among all of them in the periodic table, are split into two subsets that are not continuous. Even moving He to group 18, or extending the 5g series to 22 elements to account for its delayed collapse and prolonged filling, does not do that: in the former case, there are no elements between H and He that would break the 1s series. I am also curious how he manages to derive the pattern mathematically for the quantum numbers, since the pattern is fairly obviously Madelung's rule with a symmetry-breaking exception for splitting the d-block, and no one has come up with a first-principles justification for that, even though it does match with reality fairly well.

A Lu-Lr table is simply based on a marriage between bulk properties of the elements and their compounds and the pedagogical value of supposed "distinct series" as an organisational principle. It knows that the series are not real, but it recognises that the table was created for pedagogical purposes and that we need them even as lies to children, just like the octet rule, for example. It emphasises these series by choosing to emphasise the trends that go with them instead of against them, but it is not so stubborn as to stick to them when experimental evidence is firmly against it as in the placement of He. In cases where the evidence is about evenly divided, of course, it follows what you have quoted from Dirac and Kragh and decides in favour of the more symmetrical option, because it is simpler. The periodic law has so many exceptions and exceptions to the exceptions that if you try to be less compromising you will never be able to draw anything at all consistently. In effect, Lu-Lr is a compromise, because the periodic law itself is built on compromises between many mutually antagonistic effects. And though its astonishing simplicity almost looks like over-simplicity, once we start to grasp just how many of those effects there are, and how many consequences they have, we will begin to understand the wisdom of aiming for simplicity here. For no matter how much we cram into a periodic table, there will always be more things in this world than its makers have dreamt of. It is therefore better to lower one's ambitions and prioritise the most basic things. And while the Madelung rule has never been derived from first principles indeed, we cannot deny that it is simple and approximately right even in the chaos expected for the 8th period, so it makes a good foundational construct. Double sharp (talk) 06:24, 15 January 2019 (UTC)

To paraphrase,

Mandelung Rule : Periods 1-7 :: Newtonian mechanics : v ≪ c

YBG (talk) 05:07, 16 January 2019 (UTC)

Yes, pretty much. Even more, the general idea that 8s fills before 5g fills before 6f fills before 7d fills before 8p is mostly right on the global scale in the 8th period, even if it is locally riddled with exceptions everywhere past E120, so the Madelung rule is pretty effective even there. Double sharp (talk) 05:43, 16 January 2019 (UTC)

re Timothy Stowe’s Physicists Periodic Table (1989): wow! This is an early version of the ADOMAH (QM-based) periodic table (Valery Tsimmerman, 2006; here): by the four quantum numbers.

I think it is OK to approach the chemical (Mandeleevian) and physical (QM) periodic tables differently: constructed by a fundamentally different principle. Trying to apply both pronciples into one Table will make it less (convincingly) elegant, and it seems to require compromises. On the wall in scientist's rooms & labs & classrooms, there should be two periodic tables: each one correct by its principle (choices in details might apply). Now for introductionary books and for schools, a single compromise table might be suitable (likely looking like the classic one but with QM aspects and annotations). Of course all facts in the compromise should be taken from the two original ones. BTW, at this point I think: would not Janet's Left Step (basically two repositioned columns only) form be a better start, i.e., requiring less compromises?

re "The IUPAC(hemistry) table", third in the Sandbh list here. I assume this is the latest IUPAC-publicated periodic table (1 December 2018, their Red Book (2005) peridic table filled in). Sigh. This table was abandoned some years ago by IUPAC (Scerri's "Group 3" research question did not allow to result in this 17-element group 3 at all, full stop) and we at enwiki (excplicitly preferring the Sc-Y-Lu-La construct; see Archive 33). I find it unacceptable to keep digging up a periodic table form that has been scientifically rejected. This whole thread starts out to consider the organising principles of the PT, and in the end a from is reintroduced that does not follow from that principles in any way. Occam's razor for the 'simpler solution' does not apply, because it is not a solution. Symmetry may be convincing effect, but should not be a criteria beforehand, that's so unscienetific.

re 2: Then, I repeat: a scholar or scientist should not rely on an 18-column periodic table to show their scientific claims. At best, 18-columns is an editorial change from a single table (nowadays the 32-column table), and so needlessly cutting up a coherent unit introducing extra mental steps (in the IKEA shop, the cupboards are not presented as they are in the box you take home and have to solve). At best that is. At worst, it introduces errors re the table one wants to depict (it does draw something different from what you want to show), or it hides issues (such as the group 3 question in case). Once you get the 32-column form right, the 18-column form will take care of itself, helped by editors. Final note: Mendeleev already put thorium and uranium in the main table — period. -DePiep (talk) 08:52, 17 January 2019 (UTC)

In response to Double sharp: There is no pedagogical value in an Lu-Lr table. That part of the periodic table isn't looked at closely until university. By that time students can grok the split d-table. I have:

The Usborne Illustrated Dictionary of the Chemistry, which I found in the children's section of a book shop, and which is aimed at up to year 11 high school students: it has a 32-column split d-block table;
The World Book Encyclopedia of Science volume on chemistry (my parents had a World Book Encyclopedia when I was a child): it has an 18-column LaAc table (when I went to high school we upgraded to an Encyclopaedia Britannica; it had, and still has, an LaAc table, as does the online version); and
The Periodic Table of the Elements laminated placemat for children, by Painless Learning Placements: it has an LaAc column column table.

There is no pedagogical issue associated with an LaAc table. Sandbh (talk) 11:34, 17 January 2019 (UTC)

Sure, it works, but that doesn't mean it can't be improved. I learnt from a Sc-Y-La table as well, but that leads to a problem when the Aufbau principle is introduced. Because while everyone can see that He is an s-block element that has just been moved for its chemistry, making La a d-block element means that Aufbau should technically no longer read "6s, 4f, 5d, 6p" in the sixth row, but "6s, one 5d, 4f, nine 5d, 6p". I have never seen that done. Instead what I usually see is an inconsistency where the Aufbau principle is given in the first form even though a split d-block table is shown. And yes, I wondered about that when I first saw it, because it was not actually explained (not that it could be at that level, of course). Now, while it can be explained later, given that the chemistry-based arguments for both La and Lu under Y are about equally strong, it strikes me that using Sc-Y-Lu results in having less hands raised at the back of the classroom ready to wonder about something that we really cannot give an explanation for (and an easily countered one at that) until many years later when d- and f-block chemistry is first seriously discussed. Double sharp (talk) 23:38, 17 January 2019 (UTC)

In my own case, and as far as I know this is still the case, the Janet/MR rule of thumb is introduced years after the PT is introduced. The two books I mentioned above don't talk about it. Sandbh (talk) 11:19, 18 January 2019 (UTC)

From memory I first saw them introduced more or less together while reading myself; I also don't remember the wait being that long in school, as you need the Madelung rule already to write electron configurations for anything above argon. Double sharp (talk) 02:23, 22 January 2019 (UTC)

Did the MR chart account for the anomalies? Sandbh (talk) 10:38, 22 January 2019 (UTC)

We were told separately about Cr and Cu in the 3d series, and that we would just have to memorise them. The heavier d- and f-block elements were not treated in significant detail; if they were I presume they would have been treated the same way. But for sure, we were given questions for the main-group elements, which are never anomalous as far as we know (till radium), along the lines of "write out the full electron configuration of barium"; and to do that you need to use the Madelung rule to figure out which orbitals should have been filled going up to 6s. Double sharp (talk) 02:48, 24 January 2019 (UTC)

In response to DePiep: Wow indeed. That is what I thought when I looked again, this time more closely, at Stowe's Physicist's table. About 18 column, 32 column, and Janet table, this is not within the scope of the IUPAC project. They will only make a recommendation on the composition of group 3. Your thinking about different tables for different purposes is on the money.

I made two points re the IUPAC table. Sure Scerri's remit is not about 18-vs-32 columns. But my points here are re you, calling a wrong and obfuscating depiction of the periodic table. The fact that you seriously list a PT that has 32 elements in group 3 as a representation of what this thread describes, is frustratingly substandard. This wrongfullness and deceit is a consequence of the 18-col format. IOW, exactly per the IUPAC non-preference: do draw that same IUPAC PT in 32-column format, and explain how it represents the points made in this thread. (Spoiler: it looks like this).

Whatever statement you want to make in a PT, draw it in 32-column form to prevent making such mistakes and (self-)deceits. Once drawn in 32-column form, it can easily and consistently be transformed into 18-column (editorially), so both forms are available stating the same. -DePiep (talk) 13:14, 17 January 2019 (UTC)

Out of chronological order response to DePiep: I agree the IUPAC table is deficient, because I can't work out straight away what it represents. It may have been influenced by the IUPAC Red Book referring to the Ln as La to Lu, and to the rare earths as Sc, Y and La to Lu. Doesn't help with group 3. Sandbh (talk) 03:33, 18 January 2019 (UTC)

There is not even a very good chemical reason for Sc-Y-*. I am prepared to agree that the old Sc-Y-* form (treating the f-block as degenerate members of the d-block) is just about OK for showing the chemistry of the lanthanides, as over there the 4f-electrons are only indirectly valent and can only contribute once they are promoted to the 5d orbital. I am also prepared to agree that such a messy situation may be just about OK for the 5g elements, as the same thing is likely to apply there. What kills it is the actinides, specifically the early ones where the 5f orbitals contribute directly; something similar is also expected for the 6f elements. This is just another result of the absence of radial nodes in the 4f and 5g orbitals. So it was OK as far as it went when we thought that the lanthanides were a one-off and that Ac through U were transition metals, but once Seaborg discovered more actinides, and that the actinides were actinides, Sc-Y-* should have become untenable. And knowing this I do not want to fall into what is likely to become the same error once the likely properties of the 6g elements are calculated. (From what we have calculated so far, they are very much active at E173, but inert at E184; this twelve-element distance is the same as that between Pa and No when the 5f orbital drops down from just starting to occupy to being almost totally inert, so there are probably some eka-superactinides in between with a complicated situation with 6g, 7f, and 8d all contributing before 7f and 8d start to act as a covering shell, although this is of course just my OR.) Double sharp (talk) 01:51, 18 January 2019 (UTC)

I understand the reason for sometimes having a 30 element "f-block" is that the +3 oxidation state is common to all of the metals involved. We will allocate any elements > E120, as previously described. Sandbh (talk) 11:02, 18 January 2019 (UTC)

It's only common for the Ln and the late An. The elements from Th to Am mess this up, as +3 is not common for them; indeed, for Th and Pa it is not even stable in aqueous solution. Sc–Cu, Y–Ag, and Lu–Au all show the +3 state too, but because most of them do not have it as the usual oxidation state, no one has ever collapsed the d-block this way. Double sharp (talk) 15:45, 18 January 2019 (UTC)

Agree. I could've been clearer. All the Ln and An exhibit the +3 oxidation state. Sandbh (talk) 23:15, 18 January 2019 (UTC)

In response to YBG: The analogy between the Janet/Madelung Rule and Newtonian mechanics is not good. The Janet/Madelung Rule is an approximate rule of thumb, like saying pi = 22/7. Newtonian mechanics are based on laws of physics. When Janet recognised the n + l rule he "adjusted" some experimental results in order to ensure the regularity of his periodic schemes, as he thought the experimental results must have been erroneous. Unfortunately, the experimental results were right; Nature was not as tidy as Janet had thought. Sandbh (talk) 01:08, 18 January 2019 (UTC)

Newtonian mechanics are also approximate; they work very well at low velocities, but at high velocities they need to be replaced by Einstein's equations. I agree that the anomalies seen in the Madelung rule are experimentally true. However I do not see why La and Ac should be treated specially among the anomalies if the arguments for Sc-Y-La and Sc-Y-Lu are only about equally strong. Double sharp (talk) 01:41, 18 January 2019 (UTC)

No special treatment is being applied. The differentiating electron approach is global, across the table. Same goes for a table organised according to the MR of thumb (Janet, say). Sandbh (talk) 11:10, 18 January 2019 (UTC)

Giguère's Periodic Table (1965)

I like this a lot since it's so easy to grasp what's happening with the f-block. Should able to download the animation here. H and He are missing; see here. Sandbh (talk) 09:18, 18 January 2019 (UTC)

Double periodicity

I write this, conscious of the risk of getting bogged in the slough of "a little bit of this and a little bit of that".

The following two tables show what happens to melting points as you travel along the two kinds of fourteen element 4f-rows. I've divided each row into two sub-rows of seven metals each. A "U" means the melting point goes up e.g. from Ce (1071 K) to Pr (1204). A "D" means the melting point goes down e.g. from Sm (1347) to Eu (1095). Elements in italics have half- or filled 4f shells.

Ce–Lu
Ce-Pr-Nd-Pm-Sm-Eu-Gd-
  U  U  U  U  D  U  U
Tb-Dy-Ho-Er-Tm-Yb-Lu
  U  U  U  U  D  U

La–Yb
La-Ce-Pr-Nd-Pm-Sm-Eu-
  D  U  U  U  U  D  U
Gd-Tb-Dy-Ho-Er-Tm-Yb
  U  U  U  U  U  D

Double periodicity is seen in the f-block as Ce–Lu, but not as La–Yb. For melting points, the fall from Sm to Eu is associated with the attainment in Eu of a half-filled shell. Same thing happens with Tm-Yb, as Yb attains a full 4f sub-shell. The fall from La to Ce is associated with the start of filling of the 4f sub-shell.

For the actinides, what happens with the trend in melting points gets complicated due to these metals having 5f electron itineracy, peaking at Pu. After that they behave more like the Ln. A weaker double periodicity is nevertheless seen for Th–Lr, with a half-full 5f shell at Am and Cm, and a full-shell at No and Lr. This is not evident in the An as Ac–No. Sandbh (talk) 07:44, 19 January 2019 (UTC)

But if you're saying that Eu attains a half-filled shell, and Yb attains a fully-filled shell, then that would support a table with Eu as the seventh member of the f-block and Yb as the fourteenth, i.e. Sc-Y-Lu, wouldn't it? The effects usually attributed to half- and fully-filled shells happen at Mn and Zn in the d-block, and not Cr and Cu, which suggests that Mn and Zn are the fifth and tenth members of the 3d series and hence that it starts at Sc. Similarly, the effects usually attributed to half- and fully-filled shells happen at Eu and Yb in the f-block, and not Gd and Lu, which suggests that Eu and Yb are the seventh and fourteenth members of the 4f series and hence that it starts at La. So we see something like Droog Andrey's 3rd IP plot:

Response pre the plot: Well, both Eu63 and Gd64 have half-filled shells, and Yb70 and Lu71 each have full shells. In the d-block an analogous pattern is seen with half-filled shells at Cr24 and Mn25, and Mo42 and Tc 43; and full shells at Cu29 and Zn30; Ag47 and Cd48; and Au79 and Hg80. Sandbh (talk) 10:49, 20 January 2019 (UTC)

And yet, when you plot properties against atomic numbers, Eu and Yb take positions analogous to Mn and Zn, not Cr and Cu. This suggests that the situation is different. In the d-block, the most common gas-phase configuration is dⁿs² with a few exceptions; in the f-block, it is similarly fⁿs². So in Cr-Mn and Cu-Zn, the first element is anomalous, but in Eu-Gd, the second one is (Lu is not an anomaly). If we look at dications, most of the anomalies are ironed out, and this looks even clearer. Double sharp (talk) 07:19, 21 January 2019 (UTC)

Can we back up here. For melting points, the steady increase from Sc to V plateaus at Cr(4) and crashes at Mn(5). The next big fall happens at Cu(9) and continues on into poor Zn (10). So we can see the influence of the half- and full 3d orbitals here. In the 4f row, the crash happens at Eu(6) followed by a spike at Gd(7) due the addition of a d rather than f electron. This pattern is repeated at Yb(13) and Lu(14). So we can see the analogies and yes, the effects are different, due to one involving s electrons and the other d electrons. Lu is not anomaly in the sense you were referring to; neither is La. Dications have as much relevance as 2nd ionisation energies (per Jensen). Sandbh (talk) 03:06, 22 January 2019 (UTC)

Not quite; the problem with 2nd ionisation energies is that they are inconsistent on whether we are getting rid of an s or a d electron. However, if we look at dications, this electron has already been ionised, and the electron configurations are far more consistent, as seen in Droog Andrey's table; this is the reason to look at 3rd ionisation energies in the transition groups, i.e. the energy needed to remove an electron from a dication.

Having a spike at a purportedly half- or fully-filled shell at Gd or Lu is just weird, because if the shell was really so, one would expect a crash as it should be harder to delocalise those electrons. The fact that they have a d and not an f differentiating electron has nothing to do with it, since Fe and Ru have similar spikes, and they have a normal differentiating electron for their blocks. Rather it is because Fe and Ru, like Gd and Lu, are really one electron past a half- or fully-filled shell, and that extra electron is more easily delocalised again!

At half-filled shells, there is either a crash when double periodicity is strong (first rows, usually), or the trend continues when it is weak (later rows); see Mn, Tc, and Re for an example of the first type changing into the second. But a spike seems to suggest that we have started the second half of the series already. Double sharp (talk) 03:22, 22 January 2019 (UTC)

Comparing 3rd IEs doesn't eliminate the issue of consistency, or lack of it. In the d-block this is not an issue. OTOH, in the Ln, we get rid of a d electron at La, Ce, Gd, and Lu; and all the rest are f electrons. The discrepancies in crashes and spikes occur because when the 3d-shell fills, Cr gets ahead of itself with its 3d54s1 configuration (it should be 3f⁴s²), followed by Mn with its 3d⁵4s² configuration. When the f-shell starts filling, everyone after Ce gets ahead of the count by 1 until we hit Eu with 4f⁷6s². Then, turning things around compared to the 3d row, Gd hangs on to a half-filled shell, with 4f⁷d¹6s². That is why there is 3d crash at Fe (6) whereas the crash occurs in 4f at Gd (7). For Ce to Lu, it is pleasing to see a perfect match with place and number of f electrons, in the series of +3 ions, thus: Ce³⁺ [Xe]4f1; Pr³⁺ [Xe]4f2; Nd³⁺ [Xe]4f3; etc all the way up to Tm³⁺ [Xe]4f12; Yb³⁺ [Xe]4f13; and Lu³⁺ [Xe]4f14. Sandbh (talk) 10:21, 22 January 2019 (UTC)

Actually, no. Almost all the Ln²⁺ dications are [Xe]4fⁿ, and almost all the An²⁺ dications are [Rn]5fⁿ. The exceptions in the lanthanides are La and Gd, which are [Xe]4fⁿ⁻¹5d¹, and Lu, which is instead [Xe]4f¹⁴6s¹. The exceptions in the actinides are Ac, which is [Rn]7s¹; Th and Pa, which are [Rn]5fⁿ⁻¹6d¹; and Lr, which is [Rn]5f¹⁴7s¹. In the transition metals, Lu, Os, Lr, and Db–Rg are dⁿ⁻¹s¹, and Rf and Cn are even dⁿ⁻²s².

In particular, note that Gd²⁺ is an anomaly while Cm²⁺ is not, and yet there are dips in the 3rd IE trend at both Gd, at which we are removing a d-electron, and at its congener Cm, at which we are still removing an f-electron. This suggests to me that the individual anomalies are small potatoes compared to the trend. Also note that while La and Gd are indeed trying to stay at the f⁰ and f⁷ shells of Ba and Eu rather than become the less stable f¹ and f⁸, they are doing it by promoting one 4f electron to 5d. Lu is instead putting its anomalous electron in 6s. And not only that: we cannot rationalise this as being originally a 4f electron, as there is no space for fifteen electrons in the same 4f shell. It has no need to try to stay at f¹⁴ when there is no such thing as f¹⁵! Instead it is analogous to Os; Lu and Os are behaving the same way, staying at the d⁰ and d⁵ shells of Yb and Re rather than becoming the less stable d¹ and d⁶. In the 7th period, of course, this is less clear as 7s is now quite definitively lower than 6d, so both Ac and Lr put an electron in 7s. And indeed, 5f is rather weakly involved for Ac. But again: more formally this time, we can indeed think of Ac²⁺ of having an ideal 5f¹ configuration, but a 5f¹⁵ interpretation of ideal Lr²⁺ is just nonsensical.

Now, we can compare the d-block situation. Hmm, M²⁺ is almost totally consistently dⁿs⁰ in the less relativistic fourth, fifth, and sixth periods, which is nice since it irons out most anomalies. Should we not then compare these +2 cations to +2 cations of the Ln and An? If one compars them to trications, one is subtracting one electron by fiat from the Ln and An, forcing the trend one step to the right; but that's not comparing like with like – especially since we are doing this to say where the blocks should start and end, which means that La/Ac and Lu/Lr have to be considered in both groups. Surely we cannot have Lu²⁺ considered on one side and Lu³⁺ on the other. It should be either +2 all the way or +3 all the way, and since it's correlations with the outer s-shell that are responsible for most of the anomalies, +2 (ionising that and only that away) makes the most sense. Then the result is clear without mental gymnastics needed: it's not that ten elements (Pr through Eu, Tb through Yb) are ahead of the count and five are right, it's that those ten are right and the five are behind. So we can also count and reduce anomalies, and a look at the An confirms this. Otherwise, consider the odd electron configurations of the 4d metals: Nb, Mo, Ru, Rh, and Ag are all dⁿ⁺¹s¹ and Pd is even dⁿ⁺²s². But we don't decree dⁿ⁺¹s¹ to be the normal d-block configuration just because of this impatient minority when most of 3d and 5d, and indeed all but one of 6d, are completely normal. Double sharp (talk) 11:08, 22 January 2019 (UTC)

P.S. If you plot properties, Eu and Mn always take analogous positions, and since we both agree that Mn is half-full, it seems quite reasonable to say that so is Eu. But if this isn't strong enough; remember that a half-filled configuration is supposed to be particularly stable, because you can't add another unpaired electron in the lowest-energy orbital. Well, in the p- and d-block, this checks out with s²p³ and d⁵s²; but in a La-Ac table, the "half-full" f⁷ds² configuration is hardly very stable. The f⁷s² configuration suggested by a Lu-Lr table looks more analogous and behaves more analogously. Double sharp (talk) 11:21, 22 January 2019 (UTC)

Checking with you: why you talking about Ln²⁺, which is hardly representative of Ln chemistry when I was talking about Ln³⁺, which is. Sandbh (talk) 12:01, 26 January 2019 (UTC)

For a number of reasons. Firstly, as already stated, we should pick like terms comparing between f- and d-elements. In all of them, the outer s² electrons are removed (or at least they start to be removed) first, so taking dications makes sense; we cannot speak about a common oxidation state across the d-block or indeed all of the f-block (because the early actinides are there), so this seems the next best thing. Secondly, because the definition of the 3rd IP is the energy required to remove a third electron from a dication to make a trication; if you want to look at the data the other way, then you can think of it as saying that if you add an electron to Cm³⁺ and put it in the lowest-energy orbital, that happens to be 5f, not 6d (hence Cm²⁺ is [Rn]5f⁸6s²). Thirdly, in a real chemical environment the bonds are not totally ionic, as there is always significant ligand-to-metal charge transfer due to available empty orbitals. The end result is that the charges of Ln cations in a chemical context are closer to +2 than to +3: for example, in the LuF₃ molecule the charge on the Lu atom is +2.4 (10.1021/jp803213j; this is the paper Droog Andrey linked to, showing that the 4f shell is completely inert here, and that the delocalisation of the electron density back to Lu mostly goes to the 5d shell with a little going to the 6s shell). But if you want trications; note that as Droog Andrey also mentioned back in archive 33, the first excited state of La³⁺ is 5p⁵4f¹, while 5p⁵5d¹ is 1.6 eV higher. There's obviously no analogue for Lu³⁺ as there's no such thing as 5p⁵4f¹⁵. ^_^ Double sharp (talk) 15:25, 26 January 2019 (UTC)

Placeholder. Sandbh (talk) 10:32, 28 January 2019 (UTC)

:Yes, there are other reasons for some of these properties such as the fact that in the condensed phase Eu and Yb take on different configurations from the surrounding lanthanides, but if we are talking mostly about gas-phase configurations (which makes sense because Be and Mg in the condensed phase have p-orbital involvement), then that is just a minor additional supporting factor (and anyway, Eu and Yb still show up as the anomalies, and certainly not Gd and Lu). Yes, cerium is an anomaly, but that is because it's the only lanthanide for which a filled 4f subshell is significantly more than a reserve area, and even in Ce^IV compounds the 4f valence electron is still partially held by each cerium atom and not fully ionised. (This notion of 4f as a reserve area is also a good basis for supporting Lu under Y; in La–Yb, we can consider that one 4f electron is being promoted to 5d to participate in chemistry, but that it's not feasible usually to promote the next one. La and Ce are just exceptional in that the contraction of 4f is happening as we pass through them, so that the gap is small enough that it is already feasible to promote one in the ground state of the atom itself; Gd is exceptional because the energy gap is lowered as the extra 4f electron would be the first paired one. But with Lu, 4f cannot play any role as a "reserves area" at all, as that would require chemically achieve Lu^IV, which never happens. It still impacts the bonding to some extent, but then again, 4f still impacts chemistry as far as Hg through being a poor shield.)

I wouldn't care so much that the actinides don't follow it so well; double periodicity is strongest in the first row of each new block (except the s-block, where there is no such thing as it would be rather degenerate). Double sharp (talk) 08:22, 19 January 2019 (UTC)

Bleh. I never liked this graph as it wasn't comparing like with like. It doesn't tell us anything useful, and it obfuscates the delayed start to the filling of the f shell. We do know that the 3rd IE trend going down ScYLaAc supports the group as that rather than ScYLuLr, as Eric has acknowledged. Sandbh (talk) 11:32, 20 January 2019 (UTC)

If this isn't comparing like with like, then what is? It is taking the 3rd electron from everybody, which means that the outer s-electrons are almost always ionised away already. The 3rd IE trend is not that impressive going down groups (it is more impressive across periods); within the whole d-block, only Mn-Tc-Re-Bh and Zn-Cd-Hg-Cn are monotonic trends. Double sharp (talk) 07:31, 21 January 2019 (UTC)

Same as last time: "I do not think you can compare the d-block and the f-block in quite the way you have done. In the d-block, the half-filled shells occur at the 4th and 5th members (Cr, Mn etc), and the filled shells at the 9th and 10th members (Cu, Zn etc). Whereas in the f-block you are using, the half-filled shells occur at the 7th and 8th members Eu, Gd etc), and the filled shell at the 14th member (Yb). In other words you are not comparing like with like." Sandbh (talk) 03:26, 22 January 2019 (UTC)

And here's my response from the last time: 'But if we are considering gas-phase configurations, then there is also not much similarity. The anomalies at Cr and Cu are when a half-filled subshell comes early by "grabbing" an electron from the outermost s-subshell: taking the argon cores as a given, we have K 4s¹, Ca 4s², Sc 3d¹4s², Ti 3d²4s², V 3d³4s², Cr 3d⁵4s¹ (expected 3d⁴4s²), Mn 3d⁵4s², Fe 3d⁶4s², Co 3d⁷4s², Ni 3d⁸4s², Cu 3d¹⁰4s¹ (expected 3d⁹4s²), Zn 3d¹⁰4s². The anomalies in the 4f row, if we look at gas-phase configurations, are instead at La, Ce, and Gd in their promotion of a 4f-electron to the 5d orbital: taking the xenon cores as a given, we have Cs 6s¹, Ba 6s², La 5d¹6s² (expected 4f¹6s²), Ce 4f¹5d¹6s² (expected 4f²6s²), Pr 4f³6s², Nd 4f⁴6s², Pm 4f⁵6s², Sm 4f⁶6s², Eu 4f⁷6s², Gd 4f⁷5d¹6s² (expected 4f⁸6s²), Tb 4f⁹6s², Dy 4f¹⁰6s², Ho 4f¹¹6s², Er 4f¹²6s², Tm 4f¹³6s², Yb 4f¹⁴6s², Lu 4f¹⁴5d¹6s², Hf 4f¹⁴5d²6s², and so on. Note that Lu is not an anomaly.

I'll rephrase the point to make things clear. A d-subshell can hold 10 electrons and is half-filled when it has 5; an f-subshell can hold 14 electrons and is half-filled when it has 7. Therefore Mn (3d⁵4s²) corresponds to Eu (4f⁷6s²) and Zn (3d¹⁰4s²) to Yb (4f¹⁴6s²) when considering gas-phase configurations, where the "covering shell" for the Ln is not 5d¹6s² but 6s² for the most part. Then the anomalies at Cr and Cu are of a very different sort to the one at Gd. We would have expected Cr to be 3d⁴4s², that is, one electron short of the half-filled d-shell (as it comes before Mn); so it takes one electron from an outer subshell to make the inner subshell half-full at 3d⁵4s¹. We would have expected Gd to be 4f⁸6s², that is, one electron past the half-filled f-shell (as it comes after Eu); so it removes one electron to an outer subshell to make the inner subshell half-full at 4f⁷5d¹6s². These are two different kinds of anomalous configuration and so it makes sense that they show up in different places. Then Lu is not even an anomaly, because 4f is already filled with 14 electrons and so the 71st electron cannot go there anymore. That is why I consider gas-phase configurations to solidly point to Sc-Y-Lu (which you agreed with at our IUPAC submission: "Jensen's support for -Lu(Lr) is based on gas phase electron configurations and we agree with his argument on that basis."), and to counter it there is little better than questioning the premise of using gas-phase rather than condensed-phase configurations.' [Which is itself again undesirable as it supports putting B and Al over Sc.] Double sharp (talk) 04:33, 22 January 2019 (UTC)

On reserve 4f electrons are you mixing gas phase and solid state configurations? Frex: "most of the metals are composed of a lattice of Ln^III ions with a 4fⁿ configuration and 3 electrons in the 5d/6s conduction band." There is no 4f reserve in this sense. Sandbh (talk) 03:44, 21 January 2019 (UTC)

No, I'm consistently using gas-phase configurations, because solid-state configurations are problematic in cases like groups 2 and 3 (these have p-involvement, which seems to support B-Al-Sc). Double sharp (talk) 05:04, 21 January 2019 (UTC)

Well, you are talking about 4f electrons being promoted to participate in chemistry, which is a condensed phase concept. Sandbh (talk) 03:26, 22 January 2019 (UTC)

It's not restricted to the condensed phase. 4f→5d and 5f→6d promotion energies exist in the gas phase, and they can be plotted, as done to the right. Such a plot explains both condensed- and gas-phase configurations. Once they go from negative to positive, an individual gas-phase atom has an fⁿd rather than an fⁿ⁺¹ configuration. But in the condensed phase, the energy needed to promote this electron is compensated by the increased cohesive energy from having three rather than two electrons involved in metallic bonding, so we only go to having a divalent metal when the energy passes around 210 kJ/mol. So we see that the concept of promoting reserve f-electrons to the directly valent d-subshell actually covers both the gas phase and the condensed phase. Anyway, the whole point of this is that in some situations the f-block elements are fⁿ and in some they are fⁿ⁺¹, and for sure their environment can cause them to flip from one to the other. This is a situation common to all the Ln and An but Lu and Lr, which suggests that they are qualitatively different. Double sharp (talk) 04:29, 22 January 2019 (UTC)

P.S. Let me quote Droog Andrey again, since he explained this much better than I did: "4f-electrons is more of a reserves area, so they are indirectly valent (prevail in non-bonding MOs), while 5d6s (and sometimes 6p) are directly valent (prevail in bonding MOs), but both are significant for chemistry because of electron correlation between the subshells. Such a situation is observed mostly from La to Yb, so that's another fruit in my bin :P". Double sharp (talk) 04:38, 22 January 2019 (UTC)

I'm concerned that we're starting to get bogged in the slough of a little bit of this and a little bit of that. You cite a reference pertaining to the lanthanum monochalcogenides which might, subject to your answer below, suggest 4f involvement. In our IUPAC paper we cited that reference implying 4f involvement in Lu trihalides (noting that this paper was challenged by two others. You talked about the concept of 4f electrons as a reserve, and suggesting this supports La to Yb, even though La has no 4f electrons. Something similar could be interpreted with respect to the d metals, and the use of their s electrons as kind of a reserve. Now, it's OK for Zn to be counted as a d-block metal even though it cannot add anymore s electrons. But it's not OK for Lu and its 14f electrons. The graph you posted here of f→d promotion energies, shows neither La Ac or Lu Lr. Rightly so. You said, and I agreed with you, that the possible involvement of 4f in bonding in La and Lu is not really a good criterion. I'm OK to keep discussing the theme but it seems to be running on empty. Sandbh (talk) 07:52, 25 January 2019 (UTC)

La is shown, it's just cut off from the bottom (you can see a line going down from Ce); so I presume Ac and Th are also very far down the bottom and just cut off. OTOH, we don't see any lines going from Yb, because for Lu it would be plotting nonsense (there is no f¹⁵).

TL;DR: When I said 4f involvement wasn't a good criterion, it was because if you apply it across the table without refinements the d-block becomes a problem. However, some data from Droog Andrey below seems to offer us a way out, which is good because this criterion seems so obvious.

Say rather that it needs work because while it works well for the f-block, all the elements from calcium to gallium show some 3d involvement, and we can't have a twelve-element-wide d-block. It is certainly suggestive, though rather hard to calculate, and even an obvious choice because what better way is there to tie blocks to chemistry than to argue from how the subshells represented by the blocks contribute chemically in the elements; but it needs some work. Perhaps a statement of blocks being more representative the more its elements fit the properties they imply would solve it (surely Ga is a normal post-transition metal just like β-Sn is), and indeed we already have to do a rather degenerate block assignment for H and He. I'll take it if I get nothing better, but when I want my criteria to be this fundamental, I'd like them to work for absolutely everything without any special pleading for only some elements!

Even so; I am arguing because of the type of 4f involvement for the lanthanides, and this sort of consideration can help resolve the Ga conundrum too. La through Yb share a use of 4f as a reserve and the possibility of 4fⁿ and 4fⁿ⁺¹ configurations both contributing that is not shared by Lu, and that that is the property that informs much of 4f chemistry. The early actinides show direct 5f involvement, but then the difference between using 5f as a reserve and not using it at all (No and Lr) is also stark. The analogy to Zn doesn't really hold: 4s is not a reserve in Zn, as it is directly valent, and a reserve like 4f in La through Yb is indirectly valent. 4f in La through Yb is normally non-bonding, while 5d, 6s, and sometimes 6p are normally bonding, and the reason why 4f is a reserve that isn't just part of the core is because of correlation between the two sets. In Lu, this doesn't hold any longer because there's no such correlation, and 4f is deeply buried with 5s and 5p in the core; but in Zn, even through 3d cannot be ionised chemically, it strengthens the bonding and spreads further from the core. (Anyway, since groups are similar, I would think that Zn-Cd-Hg-Cn showing an increasing trend in d-involvement gives a good argument for it, whereas Lu-Lr-E157 shows a decreasing trend in f-involvement). Now, the only problem is that d-involvement should also increase until at Nh it becomes more significant, but the bond angles proxy Droog Andrey suggested below shows that for Ga, In, and Tl it is not a directly bonding orbital (otherwise the situation would not be the same as that of Al), so the argument seems to have been saved for the most part. Double sharp (talk) 16:39, 25 January 2019 (UTC)

Placeholder. Sandbh (talk) 10:33, 28 January 2019 (UTC)

I've got two placeholders in this section which I may or may not need to respond to, subject to how I go with the following contribution.

In Treatise on inorganic chemistry, Remy (1956) wrote as follows:

"When the variation in properties of the lanthanides or their ions along the series is considered…it is found that three types of variation can be discerned.
[1] The properties may show a clear [double] periodicity…
[2] It is also possible for the properties of the Ln to vary in a symmetrical manner, so as to change with atomic number in the opposite sense, for elements standing to the left or the right of gadolinium, respectively…

[3] There are also properties which alter monotonically within the Ln series."

To which I'd add:

[4] The properties may show no discernible pattern.

I was surprised to read Remy.

Over 60 years ago he essentially anticipated Scerri's "a little bit of this and a little bit of that" position. I think he also anticipated the nub of this thread, which has been to pile up or review the various arguments one way or the other, to see if one pile is bigger than the other, and then find that this cannot be done sufficiently objectively or decisively to the satisfaction of either camp. Or at least that is how I see it now. So, my main focus now is at the balcony level, rather than the dance floor level.

Having said that, Remy was a proponent of Sc-Y-La, based on the work of Klemm (1929; 1930) who divided the Ln into two sub-groups, on the basis of the special position occupied by Gd. These two subgroups are Ce to Gd, and Tb to Lu. Equally, Remy acknowledged the relevance of the older classification of the rare earths, based on analytical-preparative behaviour, into the cerite earths (La to Sm) and the yttrium earths (Sc, Y, Eu to Lu).

On the special position of Gd, Remy associated it with the place of the noble gases, although to a much lesser degree. He observed that Tb⁴⁺ attained the same configuration as Gd³⁺; that Eu²⁺ attains the same Gd³⁺ core; and that "samarium…shows a tendency at least to approximate to the Gd²⁺ structure by functioning as a dispositive element". When I look at this rare-earth metal long term air exposure test, bearing in mind the Eu is the most reactive of the Ln, I can see where Remy was coming from (although Tb to Lu are much less reactive, so the group 17/18 analogy is not seen here).

References

Klemm W 1929, "Measurements on divalent and quadrivalent rare earth compounds. II. A system of rare earths based on periodic property changes of their ions", Zeitschrift für anorganische und allgemeine Chemie, vol. 184, p. 345

—— 1930, "Measurements on divalent and quadrivalent rare earth compounds. IV. Supplement to the communication: A system of rare earths", Zeitschrift für anorganische und allgemeine Chemie, vol. 184, p. 29

Remy H 1956, Treatise on inorganic chemistry, vol. ii, Sub-groups of the periodic table and general topics, Elsevier, Amsterdam, pp. 491–493; 480

Sandbh (talk) 10:58, 13 February 2019 (UTC)

On sending f-electrons on the pitch at half-time

Since we have reopened the can of worms that is "a little bit of this and a little bit of that", let me throw another hat in the ring! ^_^ From 10.1039/C6DT00358C, the Ln sesquioxides, excluding Pm₂O₃ which wasn't studied due to its radioactivity, can mostly be classified in three groups based on their levels of 4f involvement (n meaning the number of f-electrons in the Ln³⁺ cation):

Group A: Non-bonding 4f orbitals (Ln = La, Gd, Tb, Dy, Ho, Er). The predominant contributor to the bonding is between 5d on Ln and 2p on O. 4fⁿ and 4fⁿ⁺¹ states are both absent in the gap between the filled O 2p and Ln 5d¹ states.
Group B: Some Ln 5d–4f hybridisation (Ln = Ce, Pr, Nd). However, the effect is greatest for Ce; as we go from Ce to Pr to Nd, the properties approach group A sesquioxides. The 4fⁿ states are in the aforementioned gap, so that 5d–4f hybridisation is increased.
Group C: Some O 2p – Ln 4f mixing (Ln = Sm, Eu, Tm, Yb). The 4fⁿ⁺¹ states are in the aforementioned gap, so O 2p – Ln 4f mixing is increased.

There is an outlier, Lu₂O₃, where for obvious reasons there are no 4fⁿ⁺¹ states at all (and also there is no spin-orbit coupling). The work also discusses the divalent lanthanide cations Ln²⁺ (whose electron configurations can vary between [Xe]4fⁿ⁺¹ and 4fⁿ5d¹ depending on the environment, except again Lu for obvious reasons). This suggests to me that it is sound to take [Xe]4fⁿ⁺¹6s² as the Madelung rule suggests as the default configuration for La through Yb, as both configurations with 4fⁿ and 4fⁿ⁺¹ are always relevant. Lutetium must then be treated as the first element of the 5d series, as there is no chance of a 4f¹⁵ configuration, and the last 5d electron cannot be seen as being promoted from the 4f reserves area. I am inclined to take the "reserves / indirectly valent" character of 4f in La–Yb as an argument in its favour, as this is not a phenomenon that we see outside the 4f series with its deeply buried filling orbital (although I might speculate on its possible reappearance in the 5g series). The divalent vs. trivalent metal dichotomy for the late actinides, which is even starker, suggests to me a similar treatment. The reason why Es through No are divalent is because it is getting very difficult to promote a 5f electron to the 6d subshell; the fact that Lr is trivalent again is not because it got miraculously easier to do that, but because that 6d electron in its compounds is not coming from the 5f subshell anymore, but rather from the 7p_1/2 one. In other words, Lu and Lr's maximum trivalency has a very different explanation from that of the previous Ln and An; those 5d and 6d electrons are no longer being sent on the pitch after half-time, they were there from the beginning. And this is similar to the explanation of the maximum tetravalency of Hf and Rf, the pentavalency of Ta and Db, and so on, instead, because possible sending of 5d and 6d electrons on the pitch would make these no longer the maximum oxidation states (and, indeed, Yb and No are maximally trivalent, even if nobelium doesn't like to do it). As a result, the trend lines seen around this area of the periodic table are quite clearly lines if you stop them at No and start them again at Lr, and have a weird, huge kink if you stop them at Lr and start them again at Rf. The difficulty with La and Ac seems different; even if they are by default n = 0 if we look at La³⁺ and Ac³⁺, they certainly have excited f¹ states, and these even sometimes contribute (link is for La). This is different from Lu and Lr where there are no f¹⁵ states, excited or not.

I should add a postscript on the involvement of 4f in bonding; I am no longer convinced that this is a really good criterion. In lutetium and lawrencium, the filled 4f or 5f subshell appears to strengthens the bonding (this is from the paper I linked to in archive 33 comparing the f-activity in La, Ac, Lu, and Lr), but they are not being used the same way as they are in the filled 4f subshell in Yb, say. This gave me the idea to look at hafnium, but unfortunately the study I found (10.1103/PhysRevA.76.030501 on HfF⁺) could not actually do a compare-and-contrast with and without 4f correlation because it would have been too time-consuming. Nevertheless, they do write that neglecting 4f probably leads to smaller errors than neglecting 5s and 5p does, despite the less strong binding of 4f compared to 5s and 5p. I don't think we can use this as a good benchmark because ignoring 3d correlation in Ga compounds results in gross errors (10.1063/1.477851), even though 3d is surely already firmly in the core by Ga. Since the d-block has surely ended before we get to gallium, this seems to mean that just because 4f is contributing in lutetium compounds does not firmly prove that the f-block has or has not ended yet. But I think the consideration in the preceding paragraphs of Lu and Lr being different because n + 1 > 14 for them seems to be sound for now. Double sharp (talk) 15:59, 19 January 2019 (UTC)

P.S. Jensen has already made this argument. From his 2015 paper on lawrencium:

“

To tip the scales in favor of one pair of elements or the other requires instead a consideration of the additional chemical and physical properties discussed in my original paper of 1982 and, above all, a consideration of their available excited-state configurations (2, 4, 12). This reveals that both La and Ac have low-lying empty f-orbitals and that these are implicated in several low-lying excited configurations, whereas Lu and Lr have no available empty f-orbitals. This implies, in turn, that both La and Ac – like 25% of the other d- and f-block elements (including their nearest neighbor Th) – are best viewed as having anomalous ground-state valence configurations, which, in their case, take the place of an idealized (n-2)f¹ns² valence configuration. Since such an interpretation is not possible for Lu/Lr, it pretty much determines that this pair should be assigned to the d-block whereas the La/Ac pair should be assigned to the beginning of the f-block.

”

Although I was worried about this, this argument doesn't actually force the d-block to be Ca–Cu, even though Ca has low-lying empty d-orbitals and Zn doesn't. The reason is that the argument for f-block elements holds only because for most of them, the interplay is between the fⁿ⁺¹ and fⁿd configurations, and the directly valent f-orbitals in the early 5f and 6f series should be treated as an exception. (Indeed, at the end of the 6f series the 6f orbitals should be drowned even deeper than the 5f ones are at the end of the 5f series.) In the d-block, by contrast, the changes in configuration are between the inner d-shell and the outer s-shell, and indeed, in a chemical environment, s-occupancy is reduced in favour of d-occupancy. This allows us to have d^ms⁰ configurations all the way until group 11 (Ag^II is still a thing), whereas the group 2 elements have (n−1)d higher in energy than ns and so this doesn't happen. So the two situations are different, because in the d series the d-electrons are directly valent, and in the f series the f-electrons are mostly indirectly valent. (Yes, Ac has rather weak 5f involvement, because of the delayed collapse; but 5f also goes in the core rather more quickly than 4f does. Anyway, 5f¹ is at least a possibility for it, whereas 5f¹⁵ isn't for Lr.) And we see this eventually; the drowning gets less and less as 6d < 5d < 4d < 3d, so much so that Cn should be able to attain +3 and +4 oxidation states, whereas the drowning gets greater as 6f > 5f > 4f. 7d is of course not directly comparable as we are now comparing (n−1)d to (n+1)s rather than ns; 7d is of course far above 8s at E166, but it is some distance below 9s. (It's not just a matter of delayed collapsing because nihonium uses its 7s rather than its 6d electrons to attain the +3 oxidation state, and the absence of the +2 state in between suggests main-group character, whereas the possibility of stable +2, +3, and +4 for copernicium suggests transition metal character.) Double sharp (talk) 03:54, 20 January 2019 (UTC)

I agree with you that the possible involvement of 4f in bonding in La and Lu is not really a good criterion. Sandbh (talk) 11:48, 20 January 2019 (UTC)

Indeed. However, I think the fact that the situation of having competing 4fⁿ and 4fⁿ⁺¹ configurations holds only from La to Yb, and not Lu, should count for something, since promoting 4f electrons to 5d is very important for Ln chemistry (it explains why they are usually in the +3 state and not the +2 state). Double sharp (talk) 04:33, 21 January 2019 (UTC)

Could I just check with you on this. Where is La getting its f electrons from? Sandbh (talk) 02:09, 22 January 2019 (UTC)

Lanthanum can in some situations be 4f⁰ and in some situations be 4f¹, so we can say that it has an electron that can be transferred back and forth between 4f and 5d, and is more active chemically when it is in the latter; this is true for cerium through ytterbium as well. However, lutetium is always 4f¹⁴, and the 5d electron is never anywhere else, creating a situation more like that of hafnium through mercury. So for La to Yb, we can define a 4f-to-5d promotion energy for this electron; this happens to be negative for La, Ce, and Gd, of course, but for Lu it is even undefined because there isn't such an electron (you'd need Lu^IV for it, which never happens). Double sharp (talk) 02:29, 22 January 2019 (UTC)

Extraordinary! Under what circumstances can La be 4f¹? Sandbh (talk) 06:17, 22 January 2019 (UTC)

See this link (same as the one above), which explains the optical and MO spectra of La chalcogenides in an external magnetic field with long-lived 4f¹ excited states for La. Double sharp (talk) 06:21, 22 January 2019 (UTC)

The authors seeded their model, and based their calculations on, La having a 4f electron. That doesn't count. I'm also concerned about the picture at the top of the page showing a magnetic field strength of a whopping 60 tesla. Sandbh (talk) 11:03, 22 January 2019 (UTC)

Not quite. The section on the La chalcogenides starts on p. 308. As stated on pp. 309–310: "In these calculations the 4f states have been considered as: (1) itinerant using the local spin-density approximation [LSDA] and (2) fully localized, treating them as core states, but unoccupied." They then compare the results to the experimentally known data, and as they write on p. 314ff: "After consideration of the band structure and optical properties we turn to the magneto-optical spectra. In Fig. 3.66 we show the experimental [752] θ_K(ω) and ε_K(ω) MO Kerr spectra of LaS, as well as the spectra calculated with the LSDA, the 4f states in the core and the LSDA with shifted 4f states. This picture clearly demonstrates that the best description is given by the LSDA approach with shifted 4f states. ... A similar situation is observed in the case of LaSe. ... [On LaTe:] Theory gives a much smaller resonance structure in the Kerr rotation spectrum and fails to produce a broader structure observed experimentally at higher energies between 3 and 5 eV [752]. This feature is well recognized only in LaTe. Salghetti-Drioli et al. [752] suggested that the broad absorption developing between 3 and 5 eV is due to interband transition into empty 4f states. ... There is another important discrepancy between the theory and the experiment. The MO measurements of lanthanum monochalcogenides [752] were performed in external magnetic fields up to 13.2 T. On the other hand, to achieve the same absolute value of the Kerr rotation in LaS and LaSe we used in our calculations an external magnetic field of 60 T. In other words, to achieve the same Zeeman splitting we needed to use 5 times larger external magnetic field in comparison with the experimental conditions. The effective increase of the magnetic field may be caused by some amount of magnetic impurities. We can also imagine another, so called "self-magnetic" impurity mechanism. The ground state of lanthanum monochalcogenides have empty 4f states. The light absorption in the optical measurements leads to excited states of the La atom, which may include 5d → 4f interband electron transitions. The excited electron in 4f state may exist quite a long time on the same site depending on the degree of the localization of the 4f states in the compound. Such a 4f¹ configuration decays to the ground state most probably through the Auger process emitting an addition electron from valence band. Due to energy balance it might be La d electron. An addition hole in d valence band will not influence the optical spectra due to its small life-time." This is the context for the calculation that was described starting on the page that I linked to. As stated in their conclusion on p. 320, "To achieve the same absolute value of the Kerr rotation in LaS and LaSe we must use in our calculations an external magnetic field 5 times larger than the experimental one. This might be associated with possible creation of the long-lived La 4f¹ surface states which cause an additional polarization of the system. To accurately estimate the value of the life-time of such La 4f¹ surface quasiparticles further theoretical analysis is needed." So, they are not starting by assuming that La is 4f¹, but found that assuming so helps their theoretical calculations to explain and replicate the experimentally known results better. Double sharp (talk) 14:24, 22 January 2019 (UTC)

Checking with you. They seem to be saying they are comparing their theoretical calculations with experimental conditions up to 13.2 T. Is that how you read it? Sandbh (talk) 07:39, 25 January 2019 (UTC)

Yes, but they theoretically had to use 60 T to reproduce the conditions of 13.2 T, which they explain via magnetic self-impurities due to some La atoms being excited from 5d¹ to 4f¹. Double sharp (talk) 16:25, 25 January 2019 (UTC)

Do their conclusions apply at ambient conditions? It worries me that many things become possible at other than ambient conditions e.g. Ca, Sr, and Ba becoming transition metals at sufficiently high pressures. Sandbh (talk) 05:05, 28 January 2019 (UTC)

4f involvement from La through Lu

Well, finally I'm ready to do some calculations on CCSD(T)/cc-pVTZ-DK3 level of theory. I propose bond angle in LnF₂⁺ as a measure of 4f vs. 5d involvement. That angle could also be computed for ScF₂⁺-ZnF₂⁺, and for YF₂⁺, as a reference plot. For IIIA group it is equal to 180° (except for Nh, probably).

I expect this work to take about a month. Meanwhile, there's a high-level calculation showing a total absence of 4f involvement in LuF₃: 10.1021/jp803213j Droog Andrey (talk) 08:55, 24 January 2019 (UTC)

@Droog Andrey: Thank you so much for returning to this question! I'm really looking forward to seeing the results. And if it's not too much trouble I'd like to see at least Ac and Lr as well from the actinides. ^_^ Double sharp (talk) 11:03, 24 January 2019 (UTC)

@Double sharp: Ac-Lr computations would definitely require spin-orbit accounting which makes the whole task much heavier :( There's also a problem with good RCC basis sets beyond Cm. Droog Andrey (talk) 11:33, 24 January 2019 (UTC)

@Droog Andrey: I understand; that was just a like, so to speak. ^_^ Is problem that the MOLCAS library only includes basis sets up to Cm? The reason why I asked about the actinides was because the MP2 calculations I linked to the previous time we had this discussion suggested Lr had more 5f involvement than Ac, so I was curious what would happen with this better choice of correlation test. Still, I would expect that 5f should be even more deeply buried in Lr than 4f is in Lu, since the +2 state is always more important in the actinide than the lanthanide in the pairs Er/Fm, Tm/Md, and Yb/No (showing that 5f in the late actinides is already more buried than 4f in the late lanthanides, which is quite something since 4f is already very much a "reserve" indirectly valent subshell); I guess with a very long superactinide contraction, E157 should continue the trend, since E156 looks very analogous to nobelium. That is as you said last time definitely the opposite trend from Zn-Cd-Hg-Cn. ^_^ Double sharp (talk) 13:55, 24 January 2019 (UTC)

Further steps to formalising "look at the active orbital with the highest ℓ"

The d-block really has been causing a major headache for attempts to formalise the criterion of looking at the active orbital with the highest azimuthal quantum number. Group 2 can mostly be explained away by the fact that all chemically accessible unoccupied orbitals have a positive azimuthal quantum number, which will always beat the zero of an s-orbital (so it suffers from being at the right end of the Janet table), as Droog Andrey did back in archive 33, but the activity of the 3d shell even at Ga is harder to explain away. So I have looked in Kaupp's paper on radial nodes again, and what caught me this time was that in the 3d element compounds, pseudopotential approximations need to treat the surely core 3p electrons as valence electrons in order to obtain more accurate results! The reason of course is that the 3d orbitals have the same principal quantum number as the core 3s and 3p orbitals and thus have similar radial extents; fortunately for chemistry, the 3d orbitals spread out more from the core nonetheless. Transition metals in general already have the problem that their block-determining chemically active d-orbitals are inner orbitals, which are too small to achieve optimal overlap with ligand orbitals. The 3d metals have it even worse than the 4d and 5d metals, because the 3d orbitals lack radial nodes and are hence even smaller than they "should" be. So it seems to me that the need to consider what should have been core orbitals as valence orbitals in calculations is perfectly normal and that we should not take it too seriously. Instead we should use other proxies to measure supposed core orbital involvement, such as Droog Andrey's suggestion of bond angles.

This abnormal smallness of the 3d orbitals 3d electrons to experience greater interelectronic repulsion than 4d or 5d electrons, which is why the ground-state 3d element electron configurations are mostly regular 3dⁿ4s² to lessen this repulsion. In the 4d elements this is not necessary and lessened occupation of the 5s shell is actually slightly more common than 5s². Of course, when you get to the 5d and even more so the 6d elements, relativistic destabilisation of the 5d and 6d subshells is enough to raise their energies significantly relative to the 6s and 7s subshells respectively, and so Aufbau-like dⁿs² configurations are more common again in 5d, and by the time we get to 6d the one anomaly (Lr) is actually shovelling electrons to 7p(!) instead. But look at what happens in 7d when 9s and 9p_1/2 are relativistically contracted so much that 9p_1/2 and 8p_3/2 are nearly degenerate and 9s usurps the position that a non-relativistic 8s would take: not until E166, when it is forced on us, do we ever see 7dⁿ9s² as the ground-state electron configuration. According to Fricke's calculations, E157, E158, and E164 are 9s⁰, while E159 through E163 are 9s¹. Yes, the details might vary, but it is crystal clear just how much 9s² is out of favour. That's why I insist on considering and bringing up E157–E172 so much; if the predictions are right (and they are likely to be so, at least at the broad-brushstrokes level), they are a precious laboratory around the hypothetical second island centred on E164, because they act like orthodox, non-relativistic members of groups 3 through 18 using 7d, 9s, and a hybrid 9p_1/2+8p_3/2 shell.

Anyway, even leaving them aside, this is exactly the sort of reason why I don't like differentiating electrons that much. The differentiating electrons are anomalous for many of the 4d metals, yes. They are anomalous for Lr, yes. But what does it have to do with the chemistry? Nothing at all; Nb and Ta are like peas in a pod even though the former is d⁴s¹ where the latter is d⁵s², and Lu and Lr are like peas in a pod even though the former is ds² where the latter is s²p. So by tabulating these anomalies as though they were something really important, we are tabulating something that means absolutely nothing for chemistry, and is instead easily influenced by other effects. The upshot is that the 4d metals show up with more anomalies than the 3d, 5d, or 6d metals, even though they are the least anomalous chemically: their atomic numbers are high enough that their valence d-orbitals have radial nodes, but are not so high that relativistic effects start to kick in. But if your criterion for whether an element is a d-block element is not a differentiating d-electron, but the physical and chemical properties common to d-block members that can be attributed to the involvement of d-electrons, then groups 3–11 fulfill everything perfectly, with no exceptions at all. Yes, there are always chemical problems at the end of a block where we get the whole column of ¹S₀'s, but that's a good argument to formally add the Zn group to the d-block just like how we add the Ne group to the p-block even though they both start out with the titular orbitals completely inactive. Anyway, a few columns down, this changes with Kr among noble gases and Cn among group 12 metals. Also, physically, it seems obvious that Zn, Cd, Hg, and Cn are closer to the transition metals proper than Ca, Sr, Ba, and Ra are. (This argument is not needed for the noble gases because there is nowhere else to put them with their lack of chemistry. ^_^)

But do note that I'm not happy with my as yet not really formalised arguments either, so this is as yet still just an attempt and not a full justification of my sense of I know it when I see it. ^_^ Double sharp (talk) 16:39, 2 February 2019 (UTC)

Sitrep: Chemical & Engineering News

Lemonick S 2019, "The periodic table is an icon. But chemists still can’t agree on how to arrange it," vol. 97, no. 1, January 7

My favourite quote: "Scerri calls 32 columns a more natural form for the periodic table and attributes the current dominance of 18 columns to convenience only".

Error?: Pyykkö's has element "145" (a 2nd appearance) where my beancounter expects "154". -DePiep (talk) 14:09, 22 January 2019 (UTC)

Most objectionable: Pyykkö trashing group 3 into a bag of 65 (sixty-five) hashed elements. -DePiep (talk) 14:11, 22 January 2019 (UTC)

Additional links

"lanthanum lies one place below yttrium in the periodic table." This comes from nobody other than Scerri himself :) --R8R (talk) 10:56, 23 January 2019 (UTC)

And in context: "In order to search for other such materials scientists needed just to consult the periodic table in order to predict that compounds in which yttrium was replaced by lanthanum would also be high-temperature superconductors. This is because lanthanum lies one place below yttrium in the periodic table. It was soon discovered that analogous lanthanum-containing compounds were indeed superconductors and in fact more so than those containing yttrium."

A first-hand account of the discovery of YBCO is available online. Apparently, lutetium was also investigated. Also, the analogous lanthanum barium copper oxide seems to have been discovered in 1986, before yttrium barium copper oxide itself, in 1987, and the yttrium compound is superconducting at higher temperatures than the lanthanum one. Scerri's point is of course intact: the periodic table was indeed used as a guide to change the elements from the original formulation; the other alkaline earths, save beryllium, were tried as substitutes for Ba as well. Double sharp (talk) 14:06, 23 January 2019 (UTC)

Term symbols

I was working with term symbols (indications by Sbharris). It resuled in this table. This may be interesting here because

The Term symbol is a simple, 3-value notation of the four quantum values (reduced complexity but meaningful).
They show great periodicity in the s-, p- (8 out of 8), and d-, f- block (14/24);
Supports He above Ne, and fit La, Ac, Lu in group 3 Sc, Y.
Five Ln/Ac columns behave irregular in this: Ce, Pr, Nd, Pm and Lu. Also the d-block groups 5 (V), 6 (Cr), 8 (Fe) and 10 (Ni).

Now I don't know if this is new information; after all the terms are derived from the quantum values so are not adding new info. I guess they represent periodicity information that has been described & discussed elsewhere here. But they do aggregate the quantum info into some main QM (wave) characteristics, showing periodicity.

That's all I can say; just happy to share that I recognised the blatant periodicity and that it might have to do with this thread. ;-). If this is a duplication/expansion of an existing subtopic here, repositioning this subsection seems OK. -DePiep (talk) 10:01, 26 January 2019 (UTC)

OTOH, with Sc-Y-Lu, every block ends with a column of nothing but ¹S₀, but with Sc-Y-La this pattern is broken. Double sharp (talk) 15:30, 26 January 2019 (UTC)

(P.S. This of course needs to be taken with a pinch of salt when we get to period 8 and E156 probably isn't ¹S₀ even though it ought to act like Yb and No which are. Again, I plead bulk properties in what I am well aware is starting to look like my universal answer to everything. So I shall further plead that I'm still trying to formalise this so that it doesn't look like I can use this to justify anything I want, despite so far having pretty much used it to justify everything I wanted. I guess I'm currently just unsatisfied with anything very formal even though I know it when I see it. Perhaps in another week this will change! ^_^) Double sharp (talk) 16:55, 2 February 2019 (UTC)

Chemistry-based support for a split d-block

I'm behind on my responses due to RL.

Before I try and catch up I wanted to pass on another observation.

In our 32-column table, group 3 is adjacent to groups 1 and 2, and split from groups 4 to 12.

This is consistent with the literature, frex:

"There is…a closer configurational similarity between the lanthanide ions and the Group Ia–IIIa cations than between the lanthanide ions and the d-transition metal ions. The presence of shielded 4f electrons in the lanthanide ions does not materially alter the noble-gas core that they present to incoming chemical groups." (Moeller 1973, p. 3).

"…lanthanide chemistry is predominately the chemistry of highly electropositive metals in the +3 oxidation state, just as the chemistry of the alkali metals and alkaline earth metals is the chemistry of the highly electropositive metals in the +1 and +2 states, respectively. For this reason, the chemistry of the lanthanides is conveniently discussed in the same book as the chemistry of the alkali and alkaline earth metals." (King 1995, p. 289)

There is an echo of these observations at the other end of the d-block, with group 12 acting much more like main group metals than transition metals (Cotton et al. 1999, p. ix, 598).

In a Sc-Y-Lu 32-column table, group 3 becomes adjacent to group 4, and the nice collocation of groups 1 to 3, leading proximately into the Ln, is lost.

Double sharp and I mentioned something like this in our IUPAC paper but it never became so apparent to me until I considered the 32-column form.

I'm pleased this is a chemistry-based argument that doesn't rely on the terrible "little bit of this and a little bit of that" twins, La and Lu. Sandbh (talk) 04:01, 3 February 2019 (UTC)

I really like this observation. Sandbh (talk) 04:01, 3 February 2019 (UTC)

Isn't this exactly an argument for the -Lu-Lr config? If group 12 is not all that transition-ey, but is still treated as an unusual part of the d-block but a part of the d-block regardless, then why wouldn't it be that group 3 is one just as well and thus be displayed in a regular d-block fashion, just like group 12, which is displayed normally despite being unusual compared with the rest of the block? Then again, I may be overly influenced by Scerri's focus on blocks.

Regardless, I will admit that this argument is much nicer than your original one, and I would like to support you for this kind of approach to the problem.--R8R (talk) 10:33, 3 February 2019 (UTC)

@R8R: I don't think it is an argument for LuLr. Focusing on the outlier nature of group 3 and group 12 is a secondary argument—somewhat like a conjuring trick that relies on distraction—and does not look beyond each group. Looking beyond each group, which is the contextual and primary argument, it can be seen that group 3 sits naturally next to groups 1 and 2, and that group 12 sits naturally next to group 13. This shows up very nicely in the 18-column form. Thanks for your show of support, and refreshing perspective. Much appreciated. Sandbh (talk) 00:24, 15 February 2019 (UTC)

OTOH: the early actinides would seem to fit better with the d-block than the s-block, and while Ti is certainly a transition metal, Zr, Hf, and Rf are increasingly unhappy in the +3 state and behave more and more like main-group metals like Th does. So a gap between groups 3 and 4 is not so clear-cut that I would want to show it; the gap between groups 11 and 12 is much bigger (except for Ag which is mostly happy in +1), but showing it would mean Be-Mg-Zn which isn't that great either and creates a more artificial-looking gap between groups 1 and 2. Double sharp (talk) 00:59, 15 February 2019 (UTC)

The fit of the early An with the d-block shows nicely in the 18-column form. There is even a bit of a match with the early Ln i.e. Ce⁺⁴ and Pr⁺⁵. The gap between groups 3 and 4 is a reflection of the fact that group 4 are the first d-block elements to unambiguously show characteristic transition metal chemistry (variable oxidation state, colour, paramagnetism). The gap between 11 and 12 may be stronger, but is weakened by the preference of Ag to show main-group chemistry. Sandbh (talk) 03:30, 15 February 2019 (UTC)

References

Cotton FA, Wilkinson G, Murillo CA & Bochmann M 1999, Advanced inorganic chemistry, 6th ed., John Wiley & Sons, New York
King RB 1995, Inorganic chemistry of main group elements, Wiley-VCH, New York
Moeller T 1973, The chemistry of the lanthanides, Pergamon texts in inorganic chemistry, vol. 26, Pergamon Press, Oxford

That's a very good chemistry-based argument for -Lu-Lr. Indeed, if f-block metals are in some sense closer to s-block metals than to d-block metals, why should we place f-block inside the d-block? It's far better to place it immediately after s-block, as -Lu-Lr table suggests. Droog Andrey (talk) 22:51, 9 February 2019 (UTC)

Not only that, but whatever table you use, Lu and Lr are still next to Hf and Rf, so we still have some members of the set {group 1 and 2 metals, rare earths, actinides} next to transition metals. But also, this set doesn't even include all the electropositive metals with inert cores, as aluminium is still stuck on the other side of the table. Double sharp (talk) 03:57, 11 February 2019 (UTC)

My reply to Droog Andrey: We place the f-block inside the d-block because the chemistry of the d¹ metals is very much like that of the s¹ and s² metals. This is a reflection of the delayed start to the filling of the f orbital. Sandbh (talk) 00:56, 15 February 2019 (UTC)

Don't see any connection between "f-block inside the d-block" and "chemistry of the d¹ metals is very much like that of the s¹ and s² metals". The delayed start is not a reason to rip the block apart; otherwise there would had been several such rips (e.g. 6d between groups 4 and 5). Droog Andrey (talk) 14:35, 15 February 2019 (UTC)

I may have got the emphasis the wrong way round. What seems to be the usual case in the literature is that the split d-block is an outcome of the delayed start of filling of the 4f shell. In the 32-column form, the delayed start results in a "natural" split between groups 1 to 3, and 4-12 (i.e. main group chemistry on the left; transition metal chemistry on the right). This is not so evident in the 18-column form. So the delayed start is not so much a reason to split the d-block, it is an outcome of the delayed start. There is no basis, as far as I can see, for a rip between groups 4 and 5. Sandbh (talk) 00:09, 17 February 2019 (UTC)

He is talking about period 7, where Rf chemistry is essentially purely main-group with almost no possibility of lower oxidation states at all (Rf^III, AFAIK, should be not much more of a thing than Sc^II and its heavier congeners), but Db starts to show an unstable, easily oxidised, but well-defined +4 state. We could hence draw an analogy between Rf/Db and Y/Zr when it comes to their positions in their rows. As a general rule, when something happens in the 3d series, it happens about one element later in the 4d and 5d series, and about one element later again in the 6d series. (It would be pushed even later in 7d but for the intervention of 8s and 8p_1/2 falling into the core, which makes it look only about one element later than 3d rather than about five.) In this case that something is the onset of indisputably transition-element chemistry, which is a gap that has moved from between groups 3 and 4 in 3d, 4d, and 5d to between groups 4 and 5 in 6d. (Thanks to CsScCl₃ and such compounds one could argue that it happens between groups 2 and 3 in 3d, too; the chemistry of Sc is like that of a mini-Lu, while Y behaves exactly like the heavy lanthanides.) But that, even combined with Th being [Rn]6d²7s² as if it were a bona fide d-block element, and acting mostly as main-group as Rf does (the analogies with La and Lu beckon), is not enough for us to split the 6d series as Ac Th [Pa–Rf] Db Sg Bh Hs Mt Ds Rg Cn. So why is it enough for us to break the 5d series? Double sharp (talk) 05:17, 18 February 2019 (UTC)

I see. Our own article on Rf says it behaves like the rest of the group 4 elements. Earnshaw and Harrington (1973, p. 52) said that group 4 "is the first group in which the really characteristic transitional properties of variable oxidation state, colour, and paramagnetism are encountered." I conclude there is no basis to split groups 4 and 5. On thorium we said in our IUPAC paper, "...though nobody doubts that Th is an f-block element, this is probably due to the fact that the 5f orbitals demonstrably contribute in metallic thorium (being hybridised with the 6d and 7s levels), and that the electron configuration of the Th³⁺ ion is [Rn]5f¹, thereby showing that the 5f orbitals are low-lying and available for chemistry. AFAIK we split group 3 from group 4, as the f-block originates in period 6 at Ce. Sandbh (talk) 03:00, 19 February 2019 (UTC)

Rf behaves like the other group 4 elements indeed, but continues their trend of favouring the +4 state and disfavouring the +3 state as the group is descended. The end result is that while Rf^IV chemistry is analogous to Zr^IV and Hf^IV chemistry, Rf^III chemistry is expected to be even less of a thing than Zr^III and Hf^III. As a result, since Rf mostly shows up as Rf⁴⁺ with the closed-shell [Rn]5f¹⁴ configuration, it does not show significant variation in oxidation states, and since this configuration is closed-shell it should not show colour or paramagnetism. Indeed, neither do Zr⁴⁺ and Hf⁴⁺: the entire claim of Zr and Hf to be transition metals comes from the lower oxidation states, which are already even less stable than in Ti where they are already easily oxidised. Lower-than-group oxidation states only start becoming more of a thing later in the transition series, while the group oxidation states become less of a thing. We already see this in the 3d series when V^IV and V^V are about equally important, and we go back down to preferring lower oxidation states with Cr^III. The favouring of +2 across the rest of the 3d series (except Fe just past the half-full shell) looks a bit like a weaker version of what goes on in the 4f and 5f series, doesn't it?

I would hesitate now to say that the f-block originates at Ce. That the 4f shell collapses below 5d and 6s there, yes, there is no doubt. But it is another step to infer from that that the f-block has started there and not earlier. The collapse is a gradual process: that is why 4f can make some excited-state contributions already at La, and it is also why Pr and Nd can still reach the +4 state in somewhat normal conditions, because 4f has not fallen so far in the core yet. And we already have a precedent from Th in considering chemically relevant excited-state configurations, because there is already 5f involvement in Th metal. To say explicitly then that a block must start precisely at a collapse, as defined by when an orbital dives below some other already filled ones, runs into the problem that there is no such collapse associated with the start of the p-block and creates tons of interruptions. Even the 7th period becomes a mess because 6d hasn't collapsed below 7p_1/2 until Rf and we can't make the blocks defined so have the "right" number of elements! This sort of thing is what makes me think that we should not take the blocks too seriously, and as I've said below, treat them as a consequence, not a premise, so that it's not the end of the world when relativity starts to spoil them. Double sharp (talk) 03:45, 19 February 2019 (UTC)

Hmm. it feels to me like I refer to what the literature plainly says or supports, and then you respond by downplaying this, or drawing attention to irrelevant properties, or going down rabbit holes. For example, I said, "Our own article on Rf says [with citations] it behaves like the rest of the group 4 elements." and then quoted Earnshaw etc who said that group 4 "is the first group in which the really characteristic transitional properties of variable oxidation state, colour, and paramagnetism are encountered." You instead focus on the properties in the (IV) state, which are irrelevant to my line of reasoning.

I refer to the f-block staring to fill at Ce, which effectively 100% of the literature supports. You query this because it isn't comparable to the start of p-block. Eh? The difference between Th and La is that we know the Th3+ ion is 4f1. La has no such f involvement.

It feels like you apply different "rules" to different parts of the table in order to achieve the result you're looking for. Whereas the d/e approach applies universally.

Put another way, if I may be so bold, it is like what Droog Anthony observed, "You know, I have a feeling that I'm saying "the coal is black", while you are responding "no, let's compare it to snow, the coal is even whiter."

Now, if the d/e approach favoured Lu/Lr (which I thought it would) I feel that the shooting match would be over. To my surprise it pointed to La/Ac, and the response has ever since been, "This cannot be". Go figure.

The very good thing about all of this is that it convinced me of the legitimacy of the Madelung Rule as representing the underlying symmetry of the periodic table, which we do not see in any our tables due to symmetry breaking. Sandbh (talk) 06:03, 20 February 2019 (UTC)

My reply to Double sharp: Well, yes, some members of the set are next to the TM. (1) I don't see the "So what?" of this; and (2) Lu³⁺ and Lr³⁺ nicely pass on the effects of the Ln/An contraction to Hf and Rf. Aluminium is stuck on the other side regardless of which table use (exception: Faithi Habishi's metallurgist's table). I don't see the "So what?" here, either? Sandbh (talk) 00:56, 15 February 2019 (UTC)

Well, no matter which form you use, Sc-Y-La or Sc-Y-Lu, you're going to have groups 1, 2, 3, and the Ln/An in one continuous set. The only difference is whether the Ln/An come before or after group 3; either way, you still have some highly electropositive elements that prefer the +3 oxidation state above all others connected to group 4. Also, I don't see a really sharp distinction between groups 3 and 4. Zr, Hf, and Rf they hardly show variable oxidation states and are most commonly in +4 with the d⁰ configuration (Zr^III and Hf^III reduce water and Rf^III should be very unstable), so most of the "transition-metal" chemistry is restricted to Ti in this group (and even then they are readily oxidised to Ti^IV). Backbonding is inadequate in group 4 as it is in group 3 and both groups have organometallic chemistry dominated by cyclopentadiene and its derivatives, like the Ln. So what I'm trying to say is that I don't believe that such differences can motivate how we draw the table (because we have similar adjacencies either way), and even if they could, I don't believe the differences are big enough in this case. Double sharp (talk) 16:12, 15 February 2019 (UTC)

Wiberg says the group 3 metals are practically always found in the +3 state. There are compounds in which they appear to be divalent but these are electrides, formulated as e.g. M³⁺[S²⁻)e^–. There are only a few true lower-valency element cluster halides in which M is less than +3. In this respect they are not typical transition elements as one would expect them to form the +2 oxidation state by the loss of 2 s-electrons.

On Zr and Hf, Wiberg says they are mainly +4 in their compounds, and they also occur as +3 e.g. ZrCl₃, HfI₃, +2 e.g. ZrF₂, ZrO, HfCl₂, HfS, and +1 e.g. ZrCl, HfBr.

I'm still relying on differentiating electrons for my deductive argument. In this context, the differences between group 3 and group 4 are pleasing but are not a primary motivation for how we draw the table. Sandbh (talk) 02:05, 17 February 2019 (UTC)

I would think that lower oxidation states of Zr and Hf are kind of the same kind of thing as higher oxidation states of Ag. Yes, they exist; yes, the elements in question display more transition-metal character in them; but they are not the most stable or most common oxidation states. If HgF₄ really exists and mercury decides to show 5d character in one compound, that is very cool, but it doesn't mean we need to include Hg as a transition metal on a par with Au; that only makes sense in the context of pedantry. If we were to treat all the exotica as on a par with the common compounds we could hardly start organising the elements at all. No, we need to decide what is normal, and what is not normal, and that is usually obvious simply by comparing frequencies. But since the gap between groups 3 and 4 is more of a "nice to have" point in this context I'll return to talking about why I think we should perhaps compromise a bit with differentiating electrons in other sections. ^_^ Double sharp (talk) 15:27, 17 February 2019 (UTC)

ACS Division of Inorganic Chemistry 32-col PT

Quite nice. Sandbh (talk) 04:48, 3 February 2019 (UTC)

Leaving aside the group 3 question, I would certainly have preferred them to have added the not-so-new names of elements 113, 115, 117, and 118 by now. ^_-☆ Double sharp (talk) 03:59, 11 February 2019 (UTC)

Extended periodic table

Here, at the top of page 3.

@Double sharp: You've been talking about the potential for a mess in period 8 etc. I don't see any mess here. How does it look to you? It looks very orderly to me. Having said that I don't understand why Lu-Lr-153-203 have been split off from the f-block. If they were returned to the end of the f-block, it would become a split-d split-f table. Sandbh (talk) 01:34, 18 February 2019 (UTC)

@Sandbh: It looks to me like complete chemical nonsense, because according to all predictions element 172 should behave like a good chemical homologue of Xe and be nothing like Ce and Th. So we have two choices: either focus on chemistry and ignore that our g-block has ballooned from 18 to 22 elements, or focus on strict Aufbau-like blocks and ignore chemistry. I think the precedent of He tells us which one is more preferable. ^_^ Worse than focusing on chemistry alone would be to try to serve two masters and try to assign distinct s-, p-, d-, f-, and g-blocks in the 8th period when no such clear things exist, but as long as it puts E172 as dvi-radon and not dvi-thorium, it's better than pure Aufbau in my book. Differentiating electrons will surely not support putting E164 as dvi-lead, either. ^_^

Not only that, but we can weasel around with the definition of block (E121 through E142 should all have some 5g involvement, if only as the lowest unoccupied subshell like 5f in Ac and Th) far more than we can with chemistry: a periodic table that puts a noble gas (well, probably a noble solid or liquid for E172) as a heavier congener of cerium and thorium is hard to reconcile with the periodic law being about periodicity of all properties (physical, chemical, atomic, you name it), but that alternate viewpoint on blocks is totally consistent with the part of the periodic table we know and love. Yes, it does mean that we can't draw a table ad infinitum and predict ahead of time where we are going to put element 245 without doing complicated calculations. But so what? We have already gotten a long way in just mapping out the eighth period, and I don't think anyone alive today will live to see the opening of the ninth. Future generations can simply keep applying the principle of placing elements based on their known or expected chemistry (though the former would override the latter, the latter would be permissible when the former is unknown). Double sharp (talk) 04:45, 18 February 2019 (UTC)

P.S. I think the idea of the table is that it is really a 50-column Aufbau-based table running on Seaborg's first extrapolation, putting Og as eka-Rn and E168 as dvi-Rn, and extending it further with E218 as tri-Rn. However, the aspect ratio of such a thing would be ridiculous, so footnotes upon footnotes have been enlisted to solve this problem. As such, if the gluings are indicated clearly, it does not really matter if the end result is not shown explicitly, and it does not matter where the gluings are if the same result would be obtained if you actually did glue them. Double sharp (talk) 04:51, 18 February 2019 (UTC)

Forthcoming item by Leal and Restrepo

Restrepo is the chemist who concluded that Lu is more similar to the Ln than to the TM, while La shares similarities with Ln and TM ("…therefore La must be the element located at the beginning of the third row of transition metals"). He based this conclusion on a study of the composition of 4,700 binary compounds of 94 elements, and their stoichiometries.

In this open access article (p. 17) Leal and Restrepo include a periodic table instead shaded according to bond polarity (which is derived from electronegativity and bond length). The last 13 pages of the article list the data sets used, which I gather encompass the same 4,700 binary compounds.

They go on to say that "Results on the periodic system of chemical elements based on [n-ary] compounds gathered in Reaxys from 1800 up to date are the subject of a forthcoming publication."

Reaxys encompasses 105 million organic, inorganic and organometallic compounds.

I'm looking forward to this study. Sandbh (talk) 23:32, 28 February 2019 (UTC)

Replaceability

See here.

This paper has a periodic table shaded according to the replaceability of one element in a binary compound with another periodic table element, on the basis of comparable structures, drawing on data for 20,500 materials (p. 3).

The authors write:

"The highest replaceabilities are found for the lanthanides and actinides, with ratios above 60% for most elements; substitutions are most frequently observed among elements in the same series, in agreement with the chemical similarity observed in these series. On the other hand, the lowest ratios are observed for hydrogen and the first-rowp elements. This finding is in agreement with the so-called ‘first-row anomaly’…

La has a replaceability of 46.5% based on 1,317 compounds. Lu is 75.3% based on 417 compounds. The replaceability of most of the Ln falls within the range of 58 to 86%.

This is consistent with my oft repeated quote that, "Since 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."

Ce has the next lowest replaceability index, at 58.1%.

This is consistent with Restrepo’s observation that "Within lanthanoids, Ce is the most different element…"

Chemically, La should go under Y.

OTOH, Sc-Y-Lu (and HeBe) better illustrates the idealised tetrahedral symmetry underlying the periodic table.

Winners all round. Sandbh (talk) 22:17, 1 March 2019 (UTC)

R8R comments

Since you have added a quote, I suppose we are to think within what this quote has for us.

It mentions the concept of the block membership being defined by the differentiating electron in its idealized electron configuration. However, I don't know anything else. Is minimizing the number of exceptions really going to be the criterion? What about other considerations, such as the electron configurations of the lanthanides? I remember there was once a good discussion here, too, in which you produced a couple of good arguments for both -La-Ac and -Lu-Lr that uniquely differentiate an option from the other, so it would be a shame to stop just there.

Also, thinking about your table, we see that the difference between -La-Ac and -Lu-Lr that plays in the favor of the former is that lawrencium's differentiating electron is 7p. Personally, I think this is so much an exception (can't be taken as related to the actual problem at hand, f vs. d) that I don't think it will actually turn out to weaken the case for -Lu-Lr (maybe something else will, but not this).

I vaguely recall (I'm eager to stand corrected if I am mistaken) that chemistry of lanthanum shows some interference of the 4f character of its 57th electron. This seems more important to me than the idealized configs. According to Scerri, "anomalies should not challenge our attempts to establish the overall structure of the periodic table in terms of sequences of blocks in the periodic table," so I doubt they were going to play a big role anyway. I'm not saying which form should be chosen because I don't remember your arguments that I mentioned above and thus can't make a pronounced decision at this very moment.

To wrap it up, I don't know what IUPAC's criterion is/will be so I can't say whether your argument is a deal breaker or not. But I think that IUPAC's criterion won't be this and I think that this argument is built on a somewhat shaky ground, so to me, it's probably not a deal breaker.--R8R (talk) 11:03, 26 December 2018 (UTC)

Thanks for another interesting perspective.

Yes, minimising the number of exceptions is the criterion, since it is quantitative and applies to the whole of the table. None of the other arguments one way or the other can be said to be quantitatively conclusive, even when aggregated. Scerri and Parsons tried to do the same thing i.e. they were looking for a completely general and conclusive argument. This is as opposed to arguments based on individual physical or chemical properties, or electron configurations, such as those put forward by Jensen, and which Scerri and Parsons found to be inconclusive.

The criterion is not concerned with human perceptions of degrees of exceptionality, nor is it concerned with this or that kind of electron (other than in determining if there is a differentiating electron mismatch).

Yes, there may be some marginal f character in La and this is also likely to be the case with Lu. Again, this is another inconclusive argument. Scerri was right about anomalies not challenging our attempts to establish the overall structure of the table. That said, minimising the number of anomalies reduces the challenge, and brings out the block nature of the table in its purest form.

My view is that they would prefer to find a completely general and conclusive argument. Failing that I expect they will have to weigh up all the microscopic individual property-based arguments supporting either La-Ac or Lu-Lr, and make a judgement-based call. Sandbh (talk) 08:16, 27 December 2018 (UTC)

May I ask you, how do you know this is the criterion? I recall you know Scerri; did he tell you this? Or did you read that anywhere maybe?

If this is the reason why group 3 will be -La-Ac, then I'm disappointed. Lawrencium's 103th electron is 7p, or 7p_1/2 even. Rather than showing how Lr is not the candidate for the period 7, group 3 spot in the periodic table, it rather shows us the element this heavy is heavily influenced by the relativistic effects, which distort periodicity and become stronger as you go down the periodic table. They are the reason why periodicity does not work that well for period 7 in general (even leaving aside the curiosities of elements 112, 114, and 118, the vertical periodic trends, as I recall, are effectively reversed by the 6d elements). This is also why the element that is said to continue the -La-Ac group 3, element 121, is also predicted to have its differentiating electron being 8p_1/2.

While I'm still rooting for -Lu-Lr, I remember being surprised after you've produced pro-La-Ac arguments that I found valid and good. Probably I wouldn't be disappointed if those were the reasons for group 3 being -La-Ac (take this with a pinch of salt, however, as I don't remember what the arguments were): after all, this is the more common version of the periodic table, so it makes some sense if it gets chosen eventually. But if the basis for that decision is effectively that the relativistic effects influence lawrencium stronger than actinium, then I certainly won't consider that decision well-thought-out.--R8R (talk) 10:55, 27 December 2018 (UTC)

I don't know if this is the criterion. Scerri did not tell me. I didn't read it anywhere. The idea came to me after I was thinking about what is meant by the term "periodic table block", and discussing the question with some other folks. The "aha" moment occurred when I re-read Scerri and Parsons' paper, and their reference to considering block membership as a global property, based on the predominant differentiating electron. This prompted to me wonder which periodic table format best showed differentiating electron predominance across its blocks.

Per my response to Double sharp, Scerri is of the view that the group 3 question cannot be resolved by recourse to physical and chemical property arguments, as presented by numerous authors over the years. In his paper with Parsons he is looking for the sorting equivalent of atomic number. He seeks to use the 1st and 2nd quantum numbers of the differentiating electrons in question, and how these relate to the Madelung "rule". As the paper notes, this is not a conclusive argument. That is because the Madelung Rule has no first principles origin; it is simply an arbitrary approximation, equivalent to saying pi = 22/7.

My differentiating electron suggestion relies on a basic principle of classification science i.e. a set of items is more representative of its label the more the individual items in it match the label.

As far as I know, while there has been some speculation as to the demise of the periodic law among the super-heavies, so far it seems to be holding up well-enough (not yet sure about the status of Og). Sandbh (talk) 07:55, 30 December 2018 (UTC)

Oh, I see.

I have been reading your discussion with Double sharp as it progresses and I must say, I completely agree with the idea there is no equivalent to the atomic number. While the sorting by atomic number is very natural (ba dum tssss), it is still not a periodic table, as the periodic table has not only the ordering, but also connections throughout the numbers, like 3-11-19-37-55-87. The sorting by atomic number alone does not allow to have that. Equally, while I'd love to have Scerri try and have myself proven wrong (more on that later), I'm absolutely positive he won't find an underneath natural obvious law because else we would've already had it. I actually think this is not all that impressive of a thought and doesn't take that much thinking as I was able to conclude that before I read that from DS (maybe it's that geniuses think alike, but I'll refrain from awarding myself that status).

My thinking has been that what the group 3 question relies on a more general question: what is the periodic table and what kind of relationship do we seek to emphasize. I am of the opinion that both -La-Ac and -Lu-Lr are good. Wouldn't make all that great of a difference one way or another, really. There is no killing argument for either option. Whatever the decisive argument will be, it will be an arbitrary decision (again, I'd love to have Scerri prove me wrong and again, I'm certain he won't). DS now says the good rectangles are the starting point and the -La-Ac arguments don't really account for losing that. While I sort of agree (because this has been initially the, and later a, reason why I liked -Lu-Lr better all that time), I started to avoid this argument because if we were really to have the problem decisively solved, we should not have a starting point to begin with. Then again, this argument can be worded in such a manner as if we had no starting point and just unexpectedly encountered the rectangle thing with -Lu-Lr (who would've guessed) and then decided that what the pro-La-Ac arguments offered was cumulatively less than what the pro-Lu-Lr arguments offered. Group 3 does not exist, we made it up, so here's the argument to have it that way. This would be an arbitrary decision, but then again, I don't expect anything else in the end.

DS says that at least lanthanum is lanthanum. I beg to differ. We also made that up. While it is a convenient invention to have ¹³⁸₅₇ and ¹³⁹₅₇ grouped together, it is still an invention. (By the way, as unlikely as it is, this could actually matter if, say, ²⁹¹₁₂₁ is one day measured to be [Og]8s²8p¹ in its ground state but the difference in energy levels between that and, say, [Og]8s²5f¹ are so low that a heavier isotope actually pulls that last electron closer to the nucleus, into the 5f shell due to a slightly higher gravitation between the nucleus and the last electron. How would that affect the block concept?) What I'm hinting at is that given that, even if the concept of a chemical element is an invention, then it becomes crystal clear that whatever definition of a block Scerri comes up with, it will be an invention just as well. It just depends on whether his definition will be widely accepted. There is no truth to be found. A few hours ago, I read an article in which he called the periodic system a "profound truth." I disagree. It is very convenient, and had a different scientist invented it, they would've had something similar---but it is an invention nonetheless. To quote Niels Bohr, "It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature." (Do you understand the difference between the two, by the way? I first encountered this quote a week ago in a comment to a translation of a chapter of a new book written by Stephen Hawking, and back then, I didn't understand the difference. Now I do.) So when I say that I hope that Scerri comes up with a good definition, that only means a definition everyone could agree on not even on its own, but at least if you add the authority of IUPAC to it. (I see that not everyone agrees on the IUPAC definition of a transition metal; more than that, everyone actually ignores it, since it includes thorium.) I still think such a definition is not within reach. I still hope to be proven wrong.--R8R (talk) 11:03, 8 January 2019 (UTC)

I think I am going to refrain from awarding myself that status too, as I also thought it was pretty obvious. ^_^

I don't think there is a killing argument either. To quote myself, 'I simultaneously accept that "in some sense" putting La in the d-block is not wrong and in some instances may be more illuminating; as the difference is smaller, so too are the differences between the areas where the different tables may be useful.' Now, in hindsight I really should have phrased it more explicitly, but I don't think either Sc-Y-La or Sc-Y-Lu is "wrong". They are both of about equal merit, and I agree with your sentiment that "Group 3 does not exist, we made it up, so here's the argument to have it that way." And, well, when it gets down to the 8th row, drawing all the delayed collapses is just impossible, which is why I am persuaded to draw nice rectangles instead – by drawing a table, we are forced to prioritise some sort of workable coordinate system where you have exactly one cell in one row and one column, so we're more or less forced to put periods and groups on a pedestal: we can do it that way, it looks good and isn't too wrong, but we must remember that the periodic law has many corrections upon corrections and what we can show explicitly in a table is just the surface. But I think increasingly that it is wrong-headed to demand there to be absolutely one form of the periodic table for all purposes. Even if you think Sc-Y-La is better, or if you think Sc-Y-Lu is better, the other side has some good points, and I think we lose more by ironing out all the inconsistencies. It would be ideal if it didn't puzzle students as it does in Scerri and Parsons' experience, and instead made them realise that nature is not so clear-cut and simple as those man-made little boxes make it look like it is. It is difficult to make something simple enough in science to be a definition. And once one does it, it becomes too simple to actually be used.

Yes, grouping ¹³⁸57 and ¹³⁹57 is absolutely also an invention. Z and N, being a count of actually existing objects, do have more reality than groups; but to decide to prioritise moving along the Z-axis instead of the N-axis is a choice we make in how to organise our description of nature, if an obvious one if our organisation is going to help us understand things. That must have motivated Mendeleev too, since his organisation was for writing a textbook. And it should motivate us, too. ^_^ Double sharp (talk) 15:27, 8 January 2019 (UTC)

YBG comments

Group 3 may be debatable, but IMHO, a PT that does not put He above Ne would be pretty useless. It occurs to me that maybe the thing that determines the PT placement is not the distinguishing electron, but the next distinguishing election. For He, the next distinguishing electron is 2s¹, and for Ne, the next distinguishing electron is 3s¹. But this is just the ramblings of an amateur, and nothing more. YBG (talk) 01:44, 31 December 2018 (UTC)

@YBG: By that argument, however, Be and Mg must go over Zn, since for Ca/Sr/Ba/Ra the next differentiating electron is in a d-orbital but for Be/Mg/Zn/Cd/Hg/Cn it is in a p-orbital. Double sharp (talk) 09:11, 11 January 2019 (UTC)

ComplexRational's 2¢

As per YBG, I oppose the placement of He above Be because it would not correctly represent the chemical properties of He. One could also argue that 1s² is the sole technical exception to the octet rule, but chemical inertness following from the stability of the closed-shell configuration akin to that of the noble gases should lead to He placed where it currently is. The PT was originally structured based on chemical properties and periodicity, and technical differences in electron configuration do not alter the chemistry (or lack thereof) of He. ComplexRational (talk) 00:00, 3 January 2019 (UTC)

DePiep comments

I see in Block (periodic table), Sandbh has changed this A image into this B one (put in top). I understand this is an outcome of this thread. Am I right that it is suposed to be like this? I'd prefer such a 32-column form, and also use the later block-colors. OK (create)? -DePiep (talk) 13:57, 6 January 2019 (UTC)

Yes; as I understand it, the 32-column table with Sc-Y-Lu-Lr is more correct for the block concept (ignoring exceptions such as Cu, Pd, La) by itself. ComplexRational (talk) 14:13, 6 January 2019 (UTC)

Sandbh, why do you use that old (as in: oiutdated) image? It is ambiguous or wrong wrt group 3. Were would I have to inject the f-block in the main table? (IMO, this was the group 3 "description" we firmly left). -DePiep (talk) 11:33, 7 January 2019 (UTC)

DePiep, the 32 column-table you have linked to is not right. The 32-column table later on in the article is correct, as it matches with the most commonly used 18-column table, with group 3 as Sc-Y-La-Ac.

I replaced the image at the top of the lead, since having a 32-column table there, with a split d-block, is too complicated for the lead. If you'd like to update the colours for that image, that's be good.

The article needs a lot more work, including adding an explanation for what happens to the 18-column form, when it's opened up into the 32-column form, with a split d-block. I haven't had time to do this yet. ComplexRational, I note your confusion about this, and can see how you could interpret it that way you did. Sandbh (talk) 07:05, 8 January 2019 (UTC)

sandbh, I have removed that table from Block (periodic table). It is plain wrong in that it does not accomodate the f-bock in the main graph at all (no placeholders like asterisks). Also, it is needlessly complicated by splitting the single table in two images without need (except that serious people keep arguing "18-colomn is so often used so let's use that one", thereby continuing the compromises and misrepresentation). The scientist should draw the periodic table in 32-column form to prevent self-delusion (hiding unsolved or conflicting points).

BTW, I see Van Spronsen has the setup (plus the He repositioning) as we had (the "A" image). -DePiep (talk) 22:23, 13 January 2019 (UTC)

OK by me. Sandbh (talk) 06:03, 14 January 2019 (UTC)

Every 18-column periodic table referred to in this thread is bogus. You are a scientist? A scholar? Draw it in a 32-column periodic table. Test yourself (that 18-column one will take care of itself anyway). -DePiep (talk) 22:58, 18 January 2019 (UTC)

I agree the IUPAC table is unhelpfully ambiguous since you can't render it satisfactorily in 32-column format. Sandbh (talk) 02:20, 19 January 2019 (UTC)

Can someone write an introductionary overview of this thread? Don't know where to start reading, and which subthreads are more relevant. Doesn't have to be perfectly neutral. (New subthread at bottom?). -DePiep (talk) 09:44, 8 February 2019 (UTC)

@DePiep: Are you looking for an introductory overview of the entire "A conclusive argument for group 3, and He above Be?" thread? Sandbh (talk) 06:35, 13 February 2019 (UTC)

Well, yes... will it be in your book? ;-) I am looking for angles of approach to understand. Like the main lines or new conclusions. Looks like we have new views on the PT in here. -DePiep (talk) 09:59, 13 February 2019 (UTC)

Sandbh comments

Iteration 1
I've tried writing my suggestion in the form of a deductive argument, as follows:

Premise 1: A periodic table block is named according to the predominant differentiating electron among its members.
Premise 2: A set of items is more representative of its label the more the individual items in it match the label.
Conclusion: A periodic table with HeBe and LaAc is the single best solution to the group 3 question.
Observation: The existence of a single best solution doesn’t extinguish the existence or utility of next best solutions, e.g. He over Ne.

-- Sandbh (talk) 03:54, 21 January 2019 (UTC)

Iteration 2

Premise 1: A periodic table block is named according to the predominant differentiating electron among its members.
Premise 2: A set of items is more representative of its label the more the individual items in it match the label.
Conclusion: A periodic table with HeBe and LaAc has four optimally representative blocks.

-- Sandbh (talk) 10:10, 15 February 2019 (UTC)

The problem is that I don't accept premise 1. As I've been saying, I don't see why we should be choosing differentiating electrons of all possible criteria – not when it is this easy to think of hypothetical scenarios that would render it unable to make a decision, and not when its influence on the properties governed by the periodic law is surely not a monopoly. Double sharp (talk) 05:07, 18 February 2019 (UTC)

How else do you define a block? Sandbh (talk) 10:28, 18 February 2019 (UTC)

I'd simply define them approximately as sets of elements whose chemistry is significantly driven by electrons in their eponymous subshells. Since I would like a table built on actual chemistry rather than formal concepts, I have no problem simply being vague about it like that when it's not the reason I'm placing elements. I'd place He over Ne primarily because both have similar noble-gas chemistry; the electron configurations are in turn the cause of that, but I see no reason for that to be the direct reason for the placement. I'd place Be and Mg over Ca, even though the trends for Be-Mg-Zn are also defensible, primarily because Ca-Sr-Ba does not show secondary periodicity while Zn-Cd-Hg does. Since the Ti through Cu groups can be obviously assigned by chemistry and show this secondary periodicity, I would expect the same for any peripheral "short" groups, whence group 12 starts at Zn and group 3 includes Lu. We can then explain this secondary periodicity by means of inner shell insertions, which neatly explains why only groups 1 and 2 lack it as none of their electrons beyond the last noble gas (those which define the periods) share the same principal quantum number as the previous noble gas core. We can then draw the rectangles as guiding principles afterwards while not forgetting that they are approximations. So I have no problem saying that H and He are s-block elements formally but act more like p-block elements, that group 3 is a d-block group that acts quite like the s-block groups, and that group 12 is a d-block group that acts quite like the p-block groups, because for me all the block assignments are just formal to help us understand the chemistry. We can draw the table without them and only later colour them in by looking at how well they fit the filling of subshells. In the 6th and 7th periods, the mixing is starting to be great enough that the concept is weakening, so I have no problem with simply denying firm boundaries of blocks in the 8th period and just not making assignments for what Droog Andrey calls the "ultransition" elements from E121 to E156. 5g, 6f, they'll both mix a lot just like 4f/5d and 5f/6d do with all the delayed collapses, and that's completely fine. We can draw two rows with E121 atop E139 like he has done to mimic the Ln and An; we can keep sticking to a formal rectangular table to highlight the radial-nodes effect that affects 5g and not 6f; both make sense and we would need more information to decide which is better. But I'd rather let the chemistry come first and define the table, and let the blocks simply show up as interesting features on the table that results, rather than vice versa. Double sharp (talk) 11:17, 18 February 2019 (UTC)

Wow! I'll have to think carefully about this one. You seem to have honed in on something close to the heart of the issue. More to follow. Sandbh (talk) 03:10, 19 February 2019 (UTC)

Off the top of my head. You're taking a more chemistry first based approach to the question, which will get you to Lu-Lr and its 13 d/e discrepancies. I seem to be taking a physics first based approach, which gets me to 11 discrepancies. My IUPAC-recommended version, with 12 discrepancies, then becomes La-Ac as it results in He over Ne rather than Be. The current IUPAC version is even deeper into the chemistry end, with La–Lu in the f-block, and 14 discrepancies. Interesting. Sandbh (talk) 03:20, 19 February 2019 (UTC)

While I agree that I am taking a more chemistry-first approach, I am not sure if it makes sense to gauge a table that results from such an approach by counting differentiating electron anomalies, because it's not really trying to control their number at all. I could just as well note that putting He over Be results in one more chemical anomaly. ^_^ Now, I'd say my preferred Sc-Y-Lu form is still a compromise, but it's a compromise between different bulk-property periodicities. We may relevantly criticise it as such, but not so much by criteria it's not actually considering in its compromise. (I guess an uncompromising chemistry-based table would look like Rayner-Canham's table on steroids. I will not attempt to draw one as it would probably become some sort of fractal nightmare. ^_-☆) Double sharp (talk) 03:59, 19 February 2019 (UTC)

I think your line of reasoning falters when you say, "Since the Ti through Cu groups can be obviously assigned by chemistry and show this secondary periodicity, I would expect the same for any peripheral "short" groups, whence group 12 starts at Zn and group 3 includes Lu." The falter happens when you expect the same for group 3. An absence of secondary periodicity in group 3 is equally easily explained. And we know that cause of the secondary periodicity in period 6 is on account of the Ln contraction, which runs from Ce³⁺ and finishes in Lu³⁺.

I’m travelling for a few days and will post more next week, including on double periodicity. Sandbh (talk) 22:55, 21 February 2019 (UTC)

I addressed this in the next sentence: "We can then explain this secondary periodicity by means of inner shell insertions, which neatly explains why only groups 1 and 2 lack it as none of their electrons beyond the last noble gas (those which define the periods) share the same principal quantum number as the previous noble gas core." The distinguishing property the "schoolbook main groups" 1, 2, and 12–18 have that differentiates them from the transition groups is that (forgetting Cn for a moment) all their chemically active electrons are in orbitals with the highest principal quantum number. This is something that is not true for group 3 as they are giving up an inner d-electron, and the difference shows because the (n−1)d-electrons do not extend enough radially out of the core ended off by (n−1)s and (n−1)p, so they have the characteristic non-ideal overlap with ligands that transition elements have. Group 3 coordination chemistry is similar enough to that of group 4 elements in the +4 state that I continue to consider it a mistake to consider group 3 only main-group just because their transition character is weak (it is more defensible for group 12, but even then you run into some difficulties). Only for groups 1 and 2, also, is there no effect at all of incomplete screening because the s-orbitals fill too early and they are the only orbitals. Already in group 3 the d-electron is partly screening the outer s-electrons. Lastly I disagree that the Ln contraction should be considered as Ce to Lu only. If you look at ions with the same charge across the entire table you will see contractions from left to right (this is literally school chemistry), and La fits the trend just as well at the beginning. The 4f and later 5f orbitals do not suddenly drop down at one element; especially for 5f the collapse is a lot slower, which is why Pa and U still have both 5f and 6d occupation in the ground state as they are nearly degenerate there. This, combined with the typical delay of these collapses as we get further in the table (6d collapses below 7p only at Rf), is why I now consider it a mistake to consider Ce the start of the f-block just because it is the first element with a 4f electron in the ground state. The collapses happen gradually and draggingly, getting more so as relativity asserts itself, and as a result splitting blocks purely to follow collapses rather than to follow similarities in properties is focusing on a criterion that is already not quite well-defined. So once collapses are disregarded, there is not really a good reason to put La below Y, or else we would have to put Lr below Tl as well because of the delayed 6d collapse (in exact parallel to the delayed 4f collapse at La). If we follow similarities in properties, then it is precisely the fact that the Ln contraction makes Lu so much smaller than La that makes it a much better fit extrapolating from the relationship of Zr to Hf. It's chemically very obvious that Lu is a better fit with the other nine 5d metals than La; just compare any properties you like. Of course Lu is even closer to the other Ln, but so is Y. Double sharp (talk) 04:08, 22 February 2019 (UTC)

UtopianPoyzin comments

Utopian makes his uneventful return after an unprecedented wikibreak for a month and a half without telling anybody about it before hand

Hi! I'm back. And this was a way to do it I guess. I realized that if I wanted to actually finish the semester focused with a decent work ethic, I would have to take a break from doing non-school work things, so I just left for a while without saying anything. Now that that's all wrapped up, I should be good to go. Now, give me time to read 158,390 characters, or 27854 words from Double sharp alone (according to a quick copy and paste into a word counter). Hey, I deserved nothing less; that's what taking breaks from Wikipedia will do to you.

Give me a day and I'm back on chromium. — Preceding unsigned comment added by UtopianPoyzin (talk • contribs) 13:31, 22 January 2019 (UTC)

And I'm so bad I can't even sig my responses. Come on, me. Gotta get back in the habit UtopianPoyzin (talk) 02:37, 23 January 2019 (UTC)

UtopianPoyzin - I understand your enthousiam here, I recognise. With this, my question is: does your #Sitrep: Chemical & Engineering News post really belong here in this big thread? Please take an extra look at the TOC, and consider moving your "Sitrep:" post a separate, higher, "=="-level position. Thanks. -DePiep (talk) 22:57, 24 January 2019 (UTC)

This section is for discussing whether Helium should be placed above Be or Ne, as well as whether La or Lu are shown in the d block rather than in the lanthanide section, is it not? I never actually finished reading everything that double sharp had to say (which is what I was referring to), but I personally would rather keep He over Be. Bluntly, the similarities of helium to the noble gases is far more important to be represented than it's similarities to the s-block elements, specifically the alkaline earth metals. As for whether lanthanum or lutetium should be placed in the lanthanide section beneath the bulk of the periodic table, I haven't yet formulated a strong opinion for either. However, besides all of this, there is a good chance that I'm lost in the talk section here. Did I place my comments in the wrong part of the section? I planned on having general thoughts here, but I also wanted to read what everybody had to say first (per my comment). Sorry if I'm disoriented at the moment.UtopianPoyzin (talk) 03:59, 26 January 2019 (UTC)

Droog Andrey comments

Ground electron configuration of a neutral atom says too little about its chemistry (unless we have a noble gas). Chemical bonds are about 1 to 10 eV, so that's the scale we need to take into account when talking about chemistry. For many elements, especially for f- and d-block ones, ground state is one among dozens of states within a few eV. Neutral atoms are rarely encountered in compounds, so we probably need to look at dications or smth else. The participation of subshells throughout the forest of excited states depends on that electric charge. So, my opinion is that no "conclusive argument" could be based only on ground state configurations of neutral atoms. Droog Andrey (talk) 15:01, 15 February 2019 (UTC)

Based on my reading of the literature, the issue is that the ground state electron configurations of the neutral atoms say enough to make the useful generalisations that characterise chemistry. Of course, there is sometimes more to the story than that and it is here where chemistry becomes really interesting. I recall @Double sharp: made a similar comment i.e. that you need to know enough of the basics to be able to discern and appreciate the nuances.

To date, as far as I can tell, the differentiating electron argument remains conclusive at least within its own parameters.

As Double sharp and I have discussed, another issue is the "a little bit of this and a little bit of that" phenomenon that characterise arguments based on physical or chemical properties. For each chemical or physical argument in favour on one option there appears to be a counter argument in favour of the other option. That is why Scerri is looking for something more "fundamental".

Are you able to generalise your dication suggestion? Sandbh (talk) 23:21, 16 February 2019 (UTC)

What is there to generalise about using dications? OK, you cannot apply them to H and He for obvious reasons, but those are easily assigned into the s-block, albeit rather degenerately (which is part of why we don't quibble that they act so differently from Li and Be and their heavier congeners). After that, we just follow the filling order. For the transition elements, which use inner-shell electrons, this is perfect as it simply ionises away the outer s-electrons, and we can easily see what orbitals are filling; for the main-group elements, just restore two electrons to the outer ns, np, and possibly (n+1)s shells. And using dications gets rid of many of the d- and f-block anomalies: at the very least, once a shell is filled at d¹⁰ or f¹⁴, it is full for all the following elements and is not breached. And, in the end, it does not really matter if the configurations don't quite match; we are by drawing a table necessarily doing an approximation that we can keep adding "and wait! there's more!" statements to.

Anyway, I still insist that the periodic table is here to describe chemistry, not the electron configurations. As you say, they are only one part of the story. So are excited-state configurations, so are ionised configurations, and so on and so forth. If we are trying to describe chemistry, which is based on significant contributions from all of these, then I think we should try and compromise between them, instead of insisting on one and only one of them. And, in the case of helium, compromise between them and common sense telling us that if we are describing chemistry, moving helium from a group of largely chemically inactive gases to a group of increasingly more ignoble metals is not an improvement. Double sharp (talk) 15:19, 17 February 2019 (UTC)

Oh, I was referring to where I said, "the issue is that the ground state electron configurations of the neutral atoms say enough to make the useful generalisations that characterise chemistry." So, how can dictations be used to make the useful generalisations that characterise chemistry? You've alluded to this in your first paragraph but this is rather convoluted. Sandbh (talk) 23:50, 17 February 2019 (UTC)

Sure you can, you just use them as one guide among many. Dications work perfectly for the d-, f-, and g-blocks because they tend to remove the covering ns subshell that fills too early and let the defining block speak more or less alone for itself, and also because these elements are usually positively charged in compounds. With the main-group elements, we may indeed want to prioritise something different as a guide; the noble gases for sure can use neutral atoms as the main guide, whereas oxygen, the halogens and some more nonmetals would be better suited to looking at anions. For sure, we must look at fistfuls of excited-state configurations at chemically relevant energy scales, too. Does that mean we are no longer looking at one and only one criterion for each element? Yes, it does. But we are still applying every criterion to every element, while recognising that the elements are different and hence some criteria are more relevant to some elements, and while simultaneously recognising that these differences are higher-order corrections that we should try our best to average out to create a table near the mean of all possible ideals. And even then: dications work for main-group elements, too, even if not as ideally as I would like. You know it's main-group if electrons are preferentially removed from a block-defining subshell, and whether it's s-block or p-block should be very straightforward to decide from which electrons those are. Double sharp (talk) 05:00, 18 February 2019 (UTC)

OK. My position now is that chemistry can't be used to unambiguously decide between La or Lu. Jensen had a go in 1982 (citing as far back as 1921), and 37 years later the question still hasn't been resolved. As I see it, you're arguing that it can be resolved chemically. My position is that differentiating electrons can be used, quite simply, to resolve the question. Your position is that if we pile up the Sc-Y-La and Sc-Y-Lu chemistry based arguments, using multiple criteria—some of which will vary in their relevance to different sets of elements—the balance will lean in favour of Lu. Have I expressed this fairly? Sandbh (talk) 02:32, 19 February 2019 (UTC)

The balance will entirely spank down on Lu. Droog Andrey (talk) 08:50, 19 February 2019 (UTC)

@Sandbh: Yes, that is a fair summary of my current position. Double sharp (talk) 14:16, 19 February 2019 (UTC)