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Group 3 observations

I have split these subsections from the header "Professor Poliakoff on group 3" at the suggestion of DePiep, as they open a new topic. Double sharp (talk) 14:57, 25 February 2018 (UTC)

Split f-block?

I am unsure about a split f-block when (please, not if!) elements beyond 120 materialise. Remember that there is expected to be so much mixing of the 5g, 6f, 7d, and 8p_1/2 orbitals in the region starting at element 122 that it becomes really difficult to say which have opened where, and if this has any chemical relevance at all, especially since there is likely no second row of the g-block. I would instead draw an analogy in which this extremely long transition series starts something like a "superlanthanide" series in the 120s and 130s where oxidation states are small and the elements are even closer than twins, before they become more like a "superactinide" series, with high oxidation states (reminiscent of uranium) around the 140s before all the inner subshells rush into the core (reminiscent of nobelium) around the 150s. I would not go quite so far as File:Pt172.png and actually draw elements 122–139 to go directly above 140–157 (in my Sc-Y-La-Ac localisation), like Ce–Lu go over Th–Lr, but the analogy is compelling and I would keep it in the back of my head even while explaining that this is because 5g (the early superactinides) is analogous to 3d and especially 4f in having no radial nodes while 6f (the late superactinides) should act as an enhanced version of 5f just like the 5d metals are close to and yet chemically even weaker than the 4f metals. This, combined with yet a third contraction in the 7d series should result in extremely interesting chemical behaviour there and in the closing 8p (=9p_1/2+8p_3/2) series, especially in how after all the relativistic craziness this final subshell mimics the non-relativistic 3p subshell! It really does seem that the eighth period is going to serve as a wonderful recapitulation of the entire structure, bidding each chemical stereotype a fond farewell. So while I would analogously put element 121 as eka-actinium, I think that there may not be any really good reason to split the f-block. Double sharp (talk) 11:08, 20 February 2018 (UTC)

I suspect incidentally that Fricke and Pyykkö's odd placement of the late members of the 8th period is due to trying to draw analogies with the more relativistic 6d and 7p elements instead of with the less relativistic ones that the 7d and 8p shells seem to be imitating. More details later... Double sharp (talk) 11:22, 20 February 2018 (UTC)

OK, here we go. Let me begin by noting that the sd bloc is very distinct in behaviour from all the other blocks; elements here tend to be pretty much universally stuck in one oxidation state, and for the most part their interactions can be explained simply as being electrostatic. (Even the strong nonmetals in the 2p row and halogen column, while stuck in one oxidation state in their ionic chemistry, can certainly bond to each other with impunity in compounds such as NO₂.) Thus it is not surprising that the chemistries of elements 119, 120, and 121 are not in serious dispute and all indications are that they act as eka-Fr, eka-Ra, and eka-Ac.

Now, what of the 5g block? Well, Fricke et al.'s calculations have the 5g and 8p_1/2 subshells filled up in Z = 121–143. There does not seem to be very much distinct chemistry arising from the 8p_1/2 orbital, which mostly acts like an additional set of s-electrons (remember that the 7p_1/2 spinor pretty much behaves like an extra inert pair in the 7p elements on top of the really inert 7s pair); we can simply assume that these are, like the s-electrons, just some outer electrons that usually participate along with the block-determining electrons. So we have the opportunity to give up 8s (at first), 8p_1/2, and maybe some of those 6f and 7d electrons that "hang up" just like the omnipresent 5d in the lanthanides; the 5g electrons aren't expected to participate, and hence the valence across the row should remain quite constant or only change slowly as 8s gets drowned into the core. After all, Pyykkö says in his paper: "We repeat that we do not mind if other orbitals, such as 8p*, 7d, or 6f ones could be occupied in some early members of a row, or in low oxidation states of these elements. They are nevertheless counted as members of the 5g series." So I don't see why we need to shove E139 and E140 away from them simply to keep what looks like the g-block nice and tidy with eighteen columns. By the time we reach the 6f block, 8s has been drowned into the core, and 8p_1/2 has taken over its role completely; it too will be drowned into the core by the time the block finishes.

Since neither 8s nor 8p_1/2 is chemically active by the time we reach the elements in the 150s and 160s, it makes sense to not count them as part of the valence electrons; then E164 with its predicted valence 7d¹⁰ configuration seems most analogous to Pd with [Kr]4d¹⁰, and the occupancy of the 9s subshell in some of these elements (E159–E163) seems to indicate that it is now low enough that it takes the s-subshell role instead of 8s now. As Pyykkö writes about the 9p_1/2–8p_3/2 situation: "Note that the SO splittings are so large that they are making two SO split suborbitals with different n nearly degenerate."; I reckon the same thing has gone on with 9s, only more so. This would seem to make E157–E166 act surprisingly not so relativistically, as relativity has made the otherwise "correct" homologues move so far away that the strictly "incorrect" homologues act as you would expect from the "less relativistic" rows of the table (and, in fact, I think the lessened usefulness of calling E164 eka-copernicium is because the relativistic effects have gone too far and make something else a better homologue, namely E166). While Pyykkö calls out E166²⁺ being 7d¹⁰9s⁰ (rather than 7d⁹9s¹ or 7d⁸8s²), it is true that it's not much like what we would expect from Cn (where the 6d electrons should be ionised before the 7s ones), but it is pretty much exactly what we get from Zn, Cd, and Hg. The underlying 7d¹⁰ core would seem to make E165 and E166 more like group IB and IIB elements than group IA and IIA elements. A similar cancellation of relativistic effects seems to have happened for E167 through E172. Double sharp (talk) 15:16, 20 February 2018 (UTC)

I suppose the predictions of compound series analogous to (E125)F₆ suggests indeed something like an idealised 6f²8s²8p_1/2² valence shell for the 5g elements, something like this for dications (although past element 122 these may not really be the ground states per Droog Andrey at Talk:Extended periodic table, at least they should be close, though I'd appreciate seeing the original sources for this table!). Then I'd think that a split f-block makes sense, along the lines of how the already-filled 5d¹6s² is pretty much maintained as the valence shell across the 4f series. Condensed-phase configurations would be even more interesting but I unfortunately doubt we'll be able to get them in the literature. T_T Double sharp (talk) 00:15, 21 February 2018 (UTC)

The tyranny and limitations of blocks

At the end of the day, arguments about where the f-block starts or finishes are often used to try and sort out the group 3 question. I call these microscopic arguments because they are focused on electron configurations. They are often used to advocate Sc-Y-Lu-Lr.

The counter to the microscopic arguments are the chemistry-based arguments. I call these macroscopic arguments. They are mostly used to advocate Sc-Y-La-Ac.

Some comments in the literature prompted me to try combining macroscopic and microscopic approaches.

The first comment is, "By their nature, rectangular tables encourage one to see the elements in rigidly separate 'blocks' the basis of which, in differentiating electrons, is of dubious validity." Stewart PJ 2004, "A new image of the periodic table", Education in Chemistry, November, pp. 156–158 (156). Stewart cited Scerri (1997) in this paper: "The Periodic Table and the Electron: Although electronic configurations are traditionally invoked to explain the periodic system, their explanatory power remains only approximate", American Scientist, vol. 85, no. 6 pp. 546–553.

If there are doubts about the validity of blocks then I'm not sure how the Janet Left Step table can be relied on to sort out the group 3 question.

Later, Stewart (2008) claimed that arguments about the composition of group 3 are proof that, "it is a mistake to break the [periodic] system into sharply delimited blocks": "The flyleaf table: An alternative", Journal of Chemical Education, vol. 85, no. 11, p. 1490.

Jeff Moran, the designer of this table, takes a somewhat similar approach. He is happy to split blocks in order to better bring out macroscopic properties. He calls them blocs rather than blocks to emphasise that he is taking a more holistic approach, rather than being dictated by strict electron configuration blocks.

And there was Jensen (2009) who said that classification of an element in the periodic table depended on, amongst other things, "Verification of the validity of the resulting block and group assignments through the establishment of consistent patterns in overall block, group, and period property trends.": "Misapplying the periodic law", Journal of Chemical Education, vol. 86, no. 10, p. 1186. Here I am relying on the fact that group 3 behave like trivalent group 1–2 metals, hence periodic property trends support La and Ac under Y.

So, rather than a simplistic Janet-like distinction between s, p, d, and f blocks, I argue for a combined block- and chemistry-based distinction. Not block-based; not chemistry-based: both-based.

The resulting blocs then look like this:

• sd bloc: H, and groups 1–3 (the latter is Sc-Y-La-Ac, with their d electrons)
• sp bloc: groups 12–18 (the s belongs to He, and to group 12)
• ds bloc: groups 4–11 (the s belongs to Mn, Tc, and Re)
• fdp bloc: Ce–Lu; Th–Lr (the d belongs to Gd, Lu, Th, and Cm; the p belongs to Lr).

Again, this results in a 32-column table with a split d-block but, as prominent writers have said, holistic single-letter blocks are of dubious validity.

I think this is a more sophisticated approach to relying on either microscopic or macroscopic properties to settle the group 3 question. In retrospect I'm a little surprised that the cookie-cutter approach of supposedly sharply-defined s, p, d, and f blocks has lasted for so long. It's like the simplicity of single-letter blocks has caused chemists and physicists to no longer see the periodic wood for the spdfgh trees.

And I didn't think of it myself, noting the four articles that precipitated the idea.

But this has no place in our Wikipedia since it appears to be OR, so I'll have to publish an article on it. Sandbh (talk) 09:04, 5 January 2018 (UTC)

This is not far from my own thoughts based on King's main group vs. transition divide through the table, accepting a division between s-block-like "electropositive main group elements" and p-block-like "not-so-electropositive main group elements", and noting that hydrogen is weird. There really are essentially these four narratives on the periodic table that give you a useful second-order correction to the coarse first-order "pure spdf blocks" explanation, and these four describe pretty much every element but the true weirdos (Cn is just strange).

If you're curious, here's a non-exhaustive list of some third-order fuzziness that can be added off the top of my head. In its most common +1 state Ag is rather more like the sp bloc than the ds block, and the lanthanides are so close to being sd block members that I mentally "annex" them as such (agreeing that some of this is a bit diluted in the second half of the series by decreasing atomic size, but it never drops below Sc's qualifications as a main group metal). Mind you I'd also annex Al to the sd block. The sd-fdp distinction is quite fuzzy: I'd be happy to call Ac a main-group element, and likewise Th and Cm, but I think that the situation of {Pa, U, Np, Pu, Am} is rather more fascinating and that's where a distinct fdp character (neither main group nor transitional) asserts itself. Oh and while Rf through Rg could be considered (accepting predictions for Mt, Ds, and Rg) to be rather normal transition metals (we crowned Au as king, after all), I'd add a "superheavy zoo of weirdness" for the last seven elements (Cn, Nh, Fl, Mc, Lv, Ts, Og); these are assuredly not normal main-group elements. Now I guess I should stop tossing out my third-order considerations on the bus and get this more organised. ^_-☆ Double sharp (talk) 10:06, 5 January 2018 (UTC)

@Sandbh: How long is that article likely to be – something like yours on the metalloids, or maybe a bit longer? Because if it's the latter, I'd be very interested in working together with you to get some of these things we've been talking about for a year crystallised under the nucleation site of your impeccable scholarship, and I think R8R at least would be likewise interested. ^_^ Double sharp (talk) 10:13, 5 January 2018 (UTC)

@Double sharp: I don't have any preconceptions about the length of the article. The most important thing is the structure. Once I have a draft of that I start to fill things out. I'd be delighted to have some coauthors. I tend to think Foundations of Chemistry. Thank you! I expect I'll post some more thoughts here. Sandbh (talk) 07:37, 7 January 2018 (UTC)

I think three or four orders would cover all the elements:

1st	s block	p block	d block	f block
2nd	sd bloc	ps bloc	ds bloc	fdp bloc
3rd	H	-- Al -- Hg -- reluctant pair effect -- Cn, Nh, Fl, Mc, Lv, Ts, Og	Ag Au?	-- solid state configurations of Ln and An -- f-orbital involvement seen in early An

…or something like that? Sandbh (talk) 08:56, 7 January 2018 (UTC)

Here is some more about trying to combine macroscopic and microscopic approaches.

In this article on the philosophy of chemistry Philip Ball notes that chemistry is positioned between the physics-like exact, quantified, deductive disciplines, and the natural-historical, descriptive, classificatory disciplines like geology and biology.

In this vein it seems to me that neither the microscopic nor the macroscopic perspective in isolation will do and that chemistry is the richer for trying to reconcile the two views rather than emphasising either one.

I am borrowing this approach from Charles Hampden-Turner who has written extensively, in management theory, on reconciling dilemmas.

As Ball further notes, Roald Hoffmann has stated that chemistry is full of fuzzy concepts that can't be precisely defined in reductionist terms, to which I say, indeed! Sandbh (talk) 09:38, 7 January 2018 (UTC)

Hear, hear. -DePiep (talk) 10:25, 8 January 2018 (UTC)

(Do not archive post) -DePiep (talk) 21:40, 2 February 2018 (UTC)

Group 3 arguments

Part 1

At the end of the day, arguments about where the f-block starts or finishes are often used to try and sort out the group 3 question. I call these microscopic arguments because they are focused on electron configurations. They are often used to advocate Sc-Y-Lu-Lr. The counter to the microscopic arguments are the chemistry-based arguments. I call these macroscopic arguments. They are mostly used to advocate Sc-Y-La-Ac.

I'm sorry, but that sounds bullshit for me. To my knowledge, electron configurations are taken as the main argument for Sc-Y-La-Ac, while periodic trends in chemical behaviour are taken as the main argument for Sc-Y-Lu-Lr.

I strongly support the position of William Jensen. The trends Sc-Y-La-Ac and Sc-Y-Lu-Lr are very similar to the trends B-Al-Sc-Y and B-Al-Ga-In, respectively. The f-contraction effects for Lu and Lr correspond to the d-contraction effects for Ga and In. As for so-called double periodicity, it definitely supports Sc-Y-Lu-Lr. Draw any property against the atomic number, and you'll see that Eu and Yb fall out of trend for 4f family, while Am and No fall out of trend for 5f family, just like Mn and Zn do for 3d family.

Lutetium and lawrencium has their f subshells drowned deeper than, say, 5d subshell for thallium or 3d subshell for zinc. You see, the excitation energies of Lu³⁺, Tl³⁺ and Zn²⁺ are 11.2 eV, 9,3 eV and 9.7 eV respectively. At the same time, the promotion 5d → 4f for La²⁺ takes only 0.9 eV.

Droog Andrey (talk) 12:04, 24 February 2018 (UTC)

@Droog Andrey: I think Sandbh is simplifying things here, but both electron configurations and chemical behaviour have been used to argue on both sides. Back in 2016 Sandbh and I collected arguments from the literature in a submission to IUPAC (which you can read here, where many of the sources for the summary here are), but I'll try to summarise things more quickly (and also explain my viewpoint, which is in favour of Sc-Y-La-Ac).

First of all, gas-phase electron configurations are inconclusive. Both the pairs -La-Ac and -Lu-Lr have a ds² valence electron configuration in the ground state. This is not the case for B-Al-Sc vs B-Al-Ga, where the inconsistent ds² configuration of Sc immediately decides the matter. So we need to look at the chemistry.

Now it is true that Sc-Y-La presents a trend that is like B-Al-Sc, Be-Mg-Ca, and Ca-Sr-Ba, while Sc-Y-Lu presents a trend that is like B-Al-Ga, Be-Mg-Zn, and Ti-Zr-Hf. On the face of it it would seem that Sc-Y-Lu is a shoo-in because it gives us a trend that is more like those of the other d-block groups, and provide a correspondence of an f-block and a d-block contraction. But the group 3 metals do not behave very much like transition metals. Instead they behave like trivalent main group metals, and the same is true of lanthanide chemistry. Aluminium likewise behaves like an s-block metal in its high electropositivity and highly negative electrode potential. The decisive break in chemical behaviour does not happen between groups 2 and 3; instead it happens between groups 3 and 4, as Ti is surely a transition metal. Even with the larger Zr and Hf, the high +4 charge is unsupportable in a simple ion; there is no "Zr⁴⁺ (aq)" except at the very lowest of concentrations and the very most acidic conditions, because the charge density is too high. So, at least, the question is raised if a trend like Ti-Zr-Hf and V-Nb-Ta is really desirable for group 3, given that it is chemically allied with K-Rb-Cs and Ca-Sr-Ba instead. (After all, why do we not support Be-Mg-Zn over Be-Mg-Ca, even though the former would create similar analogies? It seems to me that the situation is similar because both Zn and Lu add an electron past a complete d- or f-shell.)

I will also note that Jensen's trend arguments in his famous 1982 article are unsupportable, because they likewise demand similarity in behaviour that is not found anywhere on the periodic table. If we were to apply his criteria to the alkali metals, we would immediately run into the problem that NaCl and CsCl have different structures (and this is the model example of great group trends, as I've mentioned before). If we go to the alkaline earth halides, we find that not a single choice of alkaline earth metal or halogen results in a consistent set of MX₂ structures, simply because of size differences. What is common in the periodic table is increasing size and basicity as one descends a group, which is exactly what we get for the pre-transition metals of group 1 and 2; given that group 3 also exhibits this sort of chemical behaviour, it makes sense to treat it the same way.

We also need to look at why Eu and Yb fall out of the trend line. (With the actinides it is more complicated because the f-electrons are much less drowned into the core in the first half of the series). In the condensed phase, the lanthanides all have an f^xds² configuration, with the 5d and 6s electrons in the conduction band, except for Eu and Yb which have an f^x+1s² configuration and contribute only the two 6s electrons. They are divalent metals while the rest of the lanthanides are trivalent metals. (Given the drowning of the 4f electrons into the core, this is particularly gratifying as it is otherwise difficult to explain why +3 and not +2 is the dominant oxidation state across the lanthanide series. Indeed, in the late actinides, when the f^x+1s² configuration does win out in the condensed phase for Es through No, we do indeed have +2 gaining in importance.) If we go by condensed-phase configurations, since that is the phase that determines most of the chemistry we see, we have one d-electron, then the filling of the f-orbitals, then the other nine d-electrons: that filling order determines the normative trend we see across the f-block. Eu and Yb are the outliers. (Ce is also a little bit of an outlier because of the partial involvement of the 4f electron in bonding.) This, to me, creates a pretty strong case for Sc-Y-La. It should also be noted that this regularity is only seen for processes in which the electron configuration is unaltered. The comparison to the d-block is weakened by the facts that Re does not fall out of the trend, and that Tc falls out significantly less than Mn.

In the article "The Full Story of the Electron Configurations of the Transition Metals" by W. H. Eugen Schwarz (the doi is 10.1021/ed8001286) it is noted that the (n−1)d shell only collapses below ns after group 2, and the (n−2)f shell only collapses below (n−1)d after group 3 (it is clear that he means a Sc-Y-La group 3, because Greenwood and Earnshaw 2nd edition p. 1232 says the same thing, referencing a "sudden contraction and reduction in energy of the 4f orbitals immediately after La"). This collapse is why the d-block filling starts "late", even though one would have expected 3d < 4s (and indeed, the only reason why 4s is occupied at all in the first-row transition metals – same for the others – is because inter-electron repulsion due to the compactness of the 3d subshell is sufficient to make it favourable to bump some of them up into 4s in free atoms; but in a chemical context, the radial extent of the 4s orbital means that it is destabilised by the occupied cores of the peripheral bonding atoms, so that even in the neutral oxidation state the d^xs⁰ configuration is dominant; that is incidentally why I was convinced by your argument for the 7d elements). This corroborates the trend line above.

Another effect of this collapse is that there is a near-total lack of f-orbital involvement from La and Ac in chemistry. One effect is a near-total lack of 5f involvement in Ac. Because of relativistic effects, even the small-radius non-hydrogenic f-orbital that La has is denied to Ac and given to Th. The 6d→5f transition for Th happens at 7790 cm⁻¹, compared to its first IP at 50867. The 5d→4f transition for La is more energetic (15196 cm⁻¹ compared to an IP of 44981). For Ac, the 6d→5f transition occurs at ~30000 cm⁻¹ (pleading measurement uncertainty due to its high radioactivity), while ionisation happens at 41700. Theoretical calculations of the collapse of the 5f wave function place it for the most part at Th, not at Ac; and metallurgically, Th acts as the first actinide (this is why it has an fcc crystal structure, not hcp like Ti, Zr, and Hf, as would have been expected if 5f were above the Fermi level). This means that if we put La and Ac in the f-block, we are putting there two elements which have no f-electrons in either their gas- or condensed-phase configurations, and one of which does not even have any appreciable 5f involvement. And while La shows some incipient involvement of its 4f bands, the same is true for the d-bands in Ca, Sr, and Ba, which precede the d-block.

On these grounds I consider Sc-Y-La-Ac to be preferable. On WP, of course, the reason is not so much this but the fact that it is more common in the literature. Double sharp (talk) 16:59, 24 February 2018 (UTC)

@Double sharp:First of all, thanks for the link to the deep analysis of the topic. I should read it carefully, so just a few remarks now.

But the group 3 metals do not behave very much like transition metals. Instead they behave like trivalent main group metals, and the same is true of lanthanide chemistry. Aluminium likewise behaves like an s-block metal in its high electropositivity and highly negative electrode potential.

The similarity of lanthanides to aluminium suggests to place them outside the d-block. :) BTW, aluminium is not very electropositive; e.g., it collects negative charge in NiAl phase. Its "too negative" standard potential is due to strong bonds with oxygen (remember the hardness of Al₂O₃) because of small 1s²2s²2p⁶ electron core; the same thing occurs for beryllium.

The decisive break in chemical behaviour does not happen between groups 2 and 3; instead it happens between groups 3 and 4, as Ti is surely a transition metal.

The point is not to decide whether Lu and Lr behave like transition metals, but to decide whether they are d-elements. As for breaks in chemical behaviour, we could find a few of them, e.g. between groups 11 and 12.

After all, why do we not support Be-Mg-Zn over Be-Mg-Ca, even though the former would create similar analogies? It seems to me that the situation is similar because both Zn and Lu add an electron past a complete d- or f-shell.

That's because ns² is filled before (n-1)d¹⁰, not after it.

If we were to apply his criteria to the alkali metals, we would immediately run into the problem that NaCl and CsCl have different structures

The cations of IA group elements have very different sizes. If you take lithium or hydrogen, there will be even more problems :) 4f and 5f elements have closer atomic/ionic radii.

What is common in the periodic table is increasing size and basicity as one descends a group

Things are not that simple. Ga(OH)₃ is more acidic than Al(OH)₃, GeO₂ is nearly as acidic as SiO₂, while H₃PO₄ is more acidic than H₃AsO₄. And we have the same for 3-5 groups: Lu(OH)₃ is less basic than Y(OH)₃; HfO₂ is nearly as acidic as ZrO₂; Nb₂O₅ is more acidic than Ta₂O₅.

Eu and Yb are the outliers.

Yes, and that's natural, because they end 7-element subfamilies La-Eu and Gd-Yb which have some correlations across. If one take Ce-Lu as 4f family, then Eu and Yb will be penultimate members of subfamilies which is just weird.

The comparison to the d-block is weakened by the facts that Re does not fall out of the trend, and that Tc falls out significantly less than Mn.

That's also pretty normal: the higher is (n-l), the weaker is the double periodicity. A common example is that ionization energy for nitrogen is higher than for oxygen; that difference quickly decays for P-S and As-Se, disappearing for Sb-Te.

This means that if we put La and Ac in the f-block, we are putting there two elements which have no f-electrons in either their gas- or condensed-phase configurations, and one of which does not even have any appreciable 5f involvement. And while La shows some incipient involvement of its 4f bands, the same is true for the d-bands in Ca, Sr, and Ba, which precede the d-block.

Here I'd partially agree for Ac. Indeed, 5f is somewhat weakly involved for it; the promotion 7s → 5f for Ac²⁺ takes 2.9 eV (remember that in real chemical context both La and Ac are positively charged). But, hey, the promotion 4f → 5d for Yb²⁺ takes 4.1 eV, have we any doubts that 5d is involved for Yb?

On these grounds I consider Sc-Y-La-Ac to be preferable. On WP, of course, the reason is not so much this but the fact that it is more common in the literature.

Unfortunately, the literature is very inert. Most of the authors just copy-and-paste the backgrounds like PT. Few of them make a deep analysis like Jensen. So, we'll have Sc-Y-La-Ac still for years and maybe decades. I guess the origin comes from older times when thorium and uranium were IVB and VIB group members, respectively. Then the electronic structure of the atoms was discovered, and the ground state electronic configurations became a panacea. Now computational quantum chemistry is developed, and we see that changes are to be made. So it is up to the future.

Droog Andrey (talk) 18:58, 24 February 2018 (UTC)

@Droog Andrey: thank you very much for your timely and fresh thinking in this space. I will go back and read your comments with renewed interest. Sandbh (talk) 07:19, 25 February 2018 (UTC)

Reading this review, I noticed that the trend Sc-Y-La-Ac is preferred mostly because of its similarity to Ca-Sr-Ba-Ra. But that's unjustified, because Sc-Y-Lu-Lr does not have to follow such a trend. If we judge B-Al-Sc-Y vs. B-Al-Ga-In with these rules, the former will definitely win. Serious changes happen from 13 to 14 group (Si, Ge and even α-Sn are non-metals), and so on. That's so sad I'm too late to put my 2 cents in that submission to IUPAC. Droog Andrey (talk) 08:33, 25 February 2018 (UTC)

As for the property not much affected by f-contraction, that's the energy of ns²np¹ state (eV):

Sc	Y	Lu	Lr
2.3	1.3	0.5	0.0

Lanthanum has 2.0 eV, no data for Ac (theoretical value is about 1 eV). Droog Andrey (talk) 08:53, 25 February 2018 (UTC)

@Droog Andrey: Yes, but it's not just that Sc-Y-La-Ac has a trend similar to Ca-Sr-Ba-Ra. The point in our review we are making by comparing Sc-Y-La to Ca-Sr-Ba is that choosing La as eka-yttrium results in a trend like groups 1 and 2, whereas choosing Lu results in a trend like groups 4 and 5. In other words, arguments that say that Lu must be placed below Y because it produces a d-block-like trend are incomplete without justifying why group 3 should show such a trend. In other words, we need to ask ourselves:

1. Is group 3 really a normal d-block group?
2. The reason why the d-block group trends look like that is because of the 4f contraction; so where does that start? Does it precede or succeed group 3?

(And in fact, we do write this in our submission under "1965: Similarity of Lu with Sc and Y": "In advancing their positions, we think these authors fail to demonstrate why similarity in properties (aside from valency) necessarily connotes group membership. In some other parts of the periodic table, most germanely in groups 1 and 2, we see a continuation of trends upon descending a group (such as increasing atomic radius, basicity and electropositivity), rather than a convergence of such properties. Either pattern could apply to the eka-yttrium position. That is to say, if group 3 were treated as early main group elements we would expect more of a linear trend going down the group. On the other hand, if group 3 was treated as a transition metal group, it would be reasonable to expect more of a convergence properties on going from period 5 to period 6, as a result of the lanthanide contraction. We discuss the behaviour of the group 3 elements later in this submission.")

To answer the first question, the chemistry of Sc, Y, and the lanthanides is pretty much that of trivalent highly electropositive metals that dissolve in water to form Sc³⁺, Y³⁺, and Ln³⁺, just like you would expect for trivalent versions of the s-block metals, and very different from the variable oxidation states of the transition metals proper from groups 4–11. (Yes, I agree that there is another break in chemical behaviour between groups 11 and 12, which is why I'd consider Zn, Cd, and Hg to be main group elements. But just like how the 3d-shell can be chemically breached in d¹⁰s Cu but not d¹⁰s² Zn, the 4f-shell can be chemically breached in f¹⁴s² Yb but not f¹⁴ds² Lu.) This supports a linear trend down the group.

As for the second question, the collapse of a d or f subshell below its corresponding s subshell is a good measure for when it becomes chemically active. But then we notice that the collapse of 3d, 4d, 5d, and 6d below 4s, 5s, 6s, and 7s respectively happens with Sc, Y, La, and Ac, which strongly suggests that these are the elements that begin each row of the d-block. Instead the collapse of 4f and 5f below 6s and 7s is delayed to Ce and Th, which suggests that the f-block begins only there. This implies that the 5d block has been interrupted by the 4f block between La and Hf. But that also means that while Hf through Hg come after the lanthanide contraction, La comes before it, and so there is no reason why Sc-Y-La should show a trend that implies the involvement of the lanthanide contraction. (And indeed, the examples you give where basicity doesn't increase down the table are all cases where the 3d or 4f contractions make the elements of the following series smaller and more acidic than expected.)

Oh, and I'd mostly stick to what can be done with chemical reagents. I'd think that La²⁺ and Ac²⁺ are not very important for a real chemical context; La³⁺ and Ac³⁺ are the species to look at. Double sharp (talk) 13:41, 25 February 2018 (UTC)

P.S. Droog Andrey, I must likewise echo Sandbh's thanks for your dropping in with your timely reflexions on this subject! Forcing us to think about and reexamine the conclusions we drew over a year ago can only be a good thing. I regret that Sandbh is currently according to his talk page busy in IRL and may not be able to respond very quickly, but I'm certainly around and will try not to keep you waiting for longer than a day. ^_^ Double sharp (talk) 13:51, 25 February 2018 (UTC)

Minor idea: may I suggest to add a top-level section title (==) right above #Split f-block? ("Group 3 observations"?), with a short introduction about this split. I think this new approach deserves header. - DePiep (talk) 14:23, 25 February 2018 (UTC)

 Done (and since this has become a new topic, I've also moved it to the bottom of the page for clarity.) Double sharp (talk) 14:57, 25 February 2018 (UTC)

@Double sharp:, thank you for the detailed reply. Well, I'm just confused with the question "Is group 3 really a normal d-block group?". What does it mean "normal"? There are different groups in d-block. Is group 13 "normal" for p-block?

Again, don't see any problem with water-soluble Y³⁺ and Ln³⁺. That's just the small hard core with just triple charge. The fact that the charge density becomes critical for tetracations has nothing to do with classification of elements as f- or d-. And, you know, Th⁴⁺ is big enough to be stable in water solutions; is there a reason for Ce and Th to belong to group 4? Nope.

Concerning the collapse of (n-1)d and (n-2)f below ns, it's just a matter of atomic charge. You are confused with La²⁺ and Ac²⁺, - ok, take it this way: the attachment of the electron to 5d subshell of La³⁺ is only 0.9 eV more profitable than to 4f subshell. BTW, the atomic charges of trications in real chemical context are closer to +2 than to +3. But if you prefer +3, then here we are: the first excited state for La³⁺ is 5p⁵4f¹, while 5p⁵5d¹ is 1.6 eV higher.

Anyway, Lu and Lr has nothing to do with f-elements, since their f-electrons are buried deep down. Yes, that reminds group 12, but in fact 3d-subshell in Zn²⁺ is measurably involved in chemical bonding because it outspreads far away from 3s3p core. That's not the case for Lu³⁺ where 4f doesn't bulge much from 5s5p. Looking down the group 12, we see that the energy of (n-1)d subshell rises, but Lu-Lr-157 has an opposite trend for (n-2)f energy to go deeper, so the analogy is quite vague here. Droog Andrey (talk) 21:53, 25 February 2018 (UTC)

@Droog Andrey:, I think we're looking at blocks a little differently. If we take the spdf names at face value, then of course, we have to classify the elements based on which subshells are being filled, which generally works very well. But sometimes there's a significant disconnect between that and the chemistry that results. Although the d-block spans ten columns from group 3 to group 12, it's only in groups 4–11 that we see transition-metal behaviour. Helium, although clearly an s-block element with its 1s² configuration, is almost a complete stranger to beryllium, and sits most naturally at the top of the p-block noble gases. And the early actinides do not act at all like their lanthanide congeners, except when in the highly reducing +3 oxidation state, but rather like d-block elements (hence the old placement of Th and U in groups IVA and VIA respectively).

In this sense, I would think that group 3 is not a normal d-block group. If anything it acts more like the s-block groups in about the same way group 12 acts more like the p-block groups. I don't think Ce⁴⁺ and Th⁴⁺ support putting Ce and Th in group 4; I think they support considering Ce and Th to be main-group elements (since their chemistries are basically those of hard cations with noble-gas or quasi-noble gas configurations, which is pretty similar to groups 1 and 2). I don't see why the main-group vs. transition distinction has to perfectly match the s- and p-block vs. d- and f-block distinction, and indeed it doesn't; and I think that it is more reasonable to draw the table to suggest the former than the latter (it's supposed to be a foundation for chemistry, after all). That is to say, we can still have those nice rectangles, but helium has already shown us that we can break them apart if we need to, and I think the main-group vs. transition distinction is a good enough reason to at least think about doing so.

Group 13, OTOH, is rather "normal" for a p-block group, apart from Al due to its anomalously high electrode potential; unlike the others, Al³⁺ is a strong class A cation. Ga, In, and Tl are rather more amphoteric and softer; they mostly bond covalently in their trivalent compounds (the increasing ionicity of Tl⁺ is a consequence of the inert pair effect; Tl^III isn't like that) and readily form Zintl phases (and even Al does all this). Increasingly down the group the formation of oxyanions happens more easily, as it also does when we go rightwards; the triads Ge/Sn/Pb and As/Sb/Bi are not too different from Ga/In/Tl or Zn/Cd/Hg, as after all the increasing nonmetallic character is already incipient in most of groups 12 and 13, and Sn and Pb at least can reasonably be called metals (I'm a bit sceptical about Bi and would rather call it a metalloid). There isn't a very sharp discontinuity like there is between groups 3 and 4, 11 and 12, or 18 and 1.

Thanks for explaining your point about La²⁺, though I still have questions about it. According to the NIST database, it only takes 0.6 eV to excite the 6s electron of Ba⁺ to 5d, less than the 0.9 eV it takes to excite the 5d electron of La²⁺ to 4f, but no one is calling Ba a d-block element because of it. (The figures for Sr and Ca respectively are 1.8 eV and 1.7 eV.) Indeed Ca, Sr, and Ba have been called "incipient transition metals", because the d-bands are close enough to influence spectroscopic properties, and indeed have been invoked as contributing to their chemistry. That seems to make the analogy of Ca–Zn with La–Lu more potent (this is also noted in our submission under User:Sandbh/Group 3#1967: f-character of La). Under the same section you can also find some findings indicating that 4f is not as inert in Lu as might have been thought. The non-ideal c/a ratios of the hcp structures of Zn and Cd have been attributed to d-orbital hybridisation with the conduction band (which incidentally also display p-character near the Fermi energy, at least for Zn and probably for Cd as well, just like for the group 2 elements), and there are also some indications that the 4f electrons in Lu are contributing at least to hybridisation (also on that page with sources). Double sharp (talk) 15:17, 26 February 2018 (UTC)

@Double sharp: the "being filled" criterion is not a good idea for classification I think. Here I proposed to use the valence (HO or LU) subshell with highest angular momentum. Yes, that has some troubles with barium and zinc, but here the whole pattern helps to keep the ordering. Helium is indeed abnormal because of first period, but down there at periods 5-6 things become less jumpy.

The early actinides for my liking are totally different from d-elements. Does ThO₂ really remind ZrO₂ or HfO₂? Does uranium(VI) have something in common with tungstates or molybdates? I'm totally all abroad trying to compare the coordination chemistry of rhenium and neptunium.

You say that group 3 is similar to s-block, while group 12 is similar to p-block. But that's normal when near-border groups reflect some features of adjoining blocks. We just can't demand the blocks to unify the same-type groups. Why to consider Ce and Th as main-group elements? Does they have anything in common with tin, for example? Yes, they inherit some features from groups 1 and 2, but that's just the way things go in the PT.

I'm rather skeptical about the role of hybridisation in the metallic phase. The real chemistry is shown in the compounds. The equilibrum internuclear distance in ZnCl₂ molecule is 2.07Å, suggesting that chlorine atom penetrates quite deep into the 3d subshell of zinc; the corresponding value for LuCl₃ is 2.4Å, but 4f subshell in lutetium is smaller than 3d subshell in zinc.

Anyway, the goal of PT is to explain the trends and to give a predictive power. I don't see any troubles with it in the Sc-Y-Lu-Lr variant just using the same principles along the whole table. Switching to Sc-Y-La-Ac, one have to explain the rupture in the d-block and to answer some occasional questions. Yes, the same happens for helium, but all is perfectly clear with it, we understand its unique situation (along with the hydrogen BTW), bla-bla-bla. However, Sc-Y-La-Ac implores Occam's razor. Droog Andrey (talk) 21:29, 26 February 2018 (UTC)

@Droog Andrey: I'll write a response later today, but in the meantime, 10.1134/S1066362207050025 is an interesting article about how the lanthanides and actinides are related to other elements in the periodic table, covering in particular the similarity between the early 5f elements and the 3d elements. Double sharp (talk) 01:51, 27 February 2018 (UTC)

Thanks for it. I guess they look at the fact that 3d as well as 5f readily forms multiple bonds with 2p atoms such as oxygen.

P.S. Nope. They only account double periodicity and oxidation states. BTW, oxidation state +3 dominates for 3d family until Mn(+2); that suggests not to consider +3 as an argument for displacing the 4f family from La-Yb to Ce-Lu :) Droog Andrey (talk) 10:57, 27 February 2018 (UTC)

@Droog Andrey: I'd consider Ti to have +4 as the main oxidation state (Ti^III is readily oxidised), as for V (V^III and V^II are strongly oxidising, while V^V usually occurs in derivatives of the fluoride, oxohalides, and pentoxide, counting the isopolyvanadates as coming from V₂O₅). In general I'd follow Greenwood and Earnshaw that the most stable oxidation states in the transition metals are Ti/Zr/Hf +4/+4/+4; V/Nb/Ta +4/+5/+5; Cr/Mo/W +3/+6/+6; Mn/Tc/Re +2/(hard to say, converts too easily)/+7; Fe/Ru/Os (+2 and +3)/+3/+4; Co/Rh/Ir (+2 and +3, latter mostly in complexes)/+3/(+3 and +4); Ni/Pd/Pt +2/+2/(+2 and +4); Cu/Ag/Au +2/+1/+3. I'd say that +2 tends to dominate from Mn onwards, with some competition with +3 for Fe and to a lesser extent Co, while before that we have a small rise to +4 with Ti and V before going back down. I'm afraid I've been somewhat too busy today and will write a more detailed response hopefully by tomorrow. m(_ _)m Double sharp (talk) 15:34, 27 February 2018 (UTC)

Sorry, I've been thinking about aqueous solutions of the cations when talking about +3 and should specify that. As for the most stable oxidation states at all, I'd mostly agree with you. There's a front page of the table we publish for many years (atomic weights are to be adjusted for the next edition). Droog Andrey (talk) 18:38, 27 February 2018 (UTC)

@Droog Andrey: Could you please let me know what the first three heading lines of your periodic table are in English? Thank you. Sandbh (talk) 22:43, 3 March 2018 (UTC)

@Sandbh: yes, that's the title and the statement of Periodic law:

D. I. Mendeleev's periodic system of chemical elements

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

Droog Andrey (talk) 05:25, 4 March 2018 (UTC)

@Droog Andrey: OK, but I'm still concerned that using aqueous cations as a criterion is unfair to higher oxidation states, because until you get to the size of Ce⁴⁺ and Th⁴⁺ there are no aqueous cations with such high charges because hydrolysis has led to oxocations or oxoanions (and even for Th⁴⁺ hydrolysis is almost as real as it is for Fe³⁺, for which the colour we are told to recognise in school is already for hydrolysed species). And many of the 4d and 5d metals (I'd expect the same from the 6d series) do not even form aqua cations (e.g. W), or form them very reluctantly and happily ditch water for better ligands as soon as they are present (e.g. Pd), so we can't even start this comparison for those series because Zr^III and Hf^III reduce water and Zr^IV and Hf^IV only exist as hydrolysed species. In other words, the trouble with using this comparison for the d-series is that many of the elements involved have no simple cationic chemistry in water in their favoured oxidation states (in this sense, the first-row transition elements we learn about in school are the oddballs), unlike the elements from La to Lu which are quite happy to form +3 and sometimes +2 (Sm, Eu, Yb) and +4 (Ce) cations. I'd think that the only d-block elements that might be considered on the electropositive side (perhaps being a bit permissive) would be groups 3 and 4 plus the whole of the first row. Double sharp (talk) 06:06, 28 February 2018 (UTC)

@Double sharp:I'm comparing 3d vs. 4f here. First rows are always "oddballs" because of a single maximum on the radial electronic density distribution. Just look at 2p or, heh, 1s :)

Group 13, OTOH, is rather "normal" for a p-block group, apart from Al due to its anomalously high electrode potential; unlike the others, Al3+ is a strong class A cation.

What about boron then? Well, I'd say Al looks the same in the Al-Ga-In context as Y looks in the Y-Lu-Lr context. Droog Andrey (talk) 11:54, 28 February 2018 (UTC)

I agree (and here's a good paper about the first-row anomalies you mention). Indeed, that is also partially why the 3d elements for the most part are unhappy to be in their highest oxidation state, because the 3d subshell is small and doesn't overlap well with the substituents. But Sc, Ti, and V are fine with it, unlike Cr and Mn which are strong oxidisers in their group oxidation states. If we look at those, then I'd still think that Ti^IV and at least V^IV species should be considered, rather than Ti³⁺ and V³⁺, and then we don't have much of a dominance of the +3 state at all, and certainly nothing like the continued upholding of +3 across the whole lanthanide series.

As for boron, I think you might well think of it as a forcibly nonmetallised version of aluminium. It's too small to really be a metal and form B³⁺, but its chemistry is closer to Al than anything else (kind of like how I think of H vs. Li). Greenwood (10.1039/B103917M) called metals "honorary boron atoms", and certainly the fact that B is hypoelectronic means that its solutions tend to be similar to metals (borane adducts with their coordinate bonds are a bit like coordination complexes; 3c–2e and other hypoelectronic bonds taken to the limit approach the delocalisation of metallic bonding, as indeed we see comparing covalent BH₃ to metallic ScH₂). I've written more about this here, justifying boron's classification as a metalloid rather than as a nonmetal.

I don't dispute the analogy with Al, but I also don't think it's complete. After all, Mg–Zn–Cd gives a similar trend to Y–Lu–Lr, while Mg–Ca–Sr gives a similar trend to Y–La–Ac. And perhaps this analogy is better, because B and Al are s²p while Sc and Y are s²d, while the group 2 and 12 elements (except Cn) all add an s electron to the preceding element. I agree that if you look at atomic properties, the trend B–Al–Sc–Y–La–Ac (e.g. electronegativity and ionisation energies) is a smooth decline, while that of B–Al–Ga–In–Tl–(Nh) has multiple kinks in it due to the influence of the filled 3d¹⁰ and 4f¹⁴ shells. But likewise we can go the other way: the trends of melting and boiling points are rather smoother for B–Al–Ga–In–Tl than for B–Al–Sc–Y–La (or Lu), where the latter has a mighty big kink at Sc, because the d-electrons form more localised bonds than the p-electrons (they are inner subshells, after all). In other words, this depends on what trends you look at, and ignores that the primarily difficulty in deciding on La vs. Lu is that both of them are s²d, whereas for Sc vs. Ga one is s²d and one is s²p. If lanthanum had the configuration [Xe]4f¹6s², we wouldn't be having this conversation, and Sc–Y–Lu–Lr would have long since become a standard.

I also find myself with a bit of time, so I'll make an attempt to answer your previous points. Firstly, I'm not convinced by sweeping things like Ba and Zn under the rug (not to mention Ne for which no electrons are chemically active at all). If we can say that Ba is an exception and it shouldn't be a d-block element, then why can't we make a similar exception for La and say that it isn't an f-block element? Further, why can't we declare a split d-block that runs Ba, then Lu–Au, along the same lines as how a Sc-Y-Lu table declares an f-block that runs from La to Yb? Just as Ba uses 5d as a lowest unoccupied valence subshell, so La uses 4f; just as Hg hasn't got uncontroversial evidence of 5d being chemically active, Lu hasn't got much of such evidence for 4f either. Even Ca and Sr have shown d-involvement in their chemistry, while Zn and Cd have not, so what such a table would do in practice is move Be and Mg over Zn, where many have remarked they fit rather well due to their small size. So what is allowing us to say that La is using 4f as a lowest unoccupied valence subshell of highest angular momentum, while denying this to Ca, Sr, Ba, and probably Ra using 3d, 4d, 5d, and 6d respectively? And then what are we to make of the condensed-phase configurations of the group 2 metals being sp rather than s² (although it does nicely explain why group 2, unlike the other groups that end blocks, still can breach the newly completed subshell)? But judging from the condensed-phase Ln configurations it seems like f^xds² is the norm and Eu and Yb are just exceptions paralleling Cr and Cu in the 3d row to get the half-filled subshell, and then having a d-electron fill before the f-block as in the Sc-Y-La-Ac table seems to be a simple enough explanation and predicts things reasonably well.

About 4f involvement in Lu, I agree that I cannot find much conclusive evidence for it in compounds (our submission cites some papers for and against 4f involvement in LuF₃). Still, it's not as if He or Ne use the complete 1s or 2p shells for chemistry either, and not only is 4f in Lu smaller than 3d in Zn, but it's also stuck under 5s and 5p as well as 6s (while 3d is only stuck under 4s). ^_^ And while 3d might be strengthening the bonding for Zn, they certainly don't manage to bond in a way they could in Cu; Zn never gets higher than the +2 state.

I'll respond to the points about main-group elements and the amount of resemblance the actinides really have to d-elements later. Double sharp (talk) 15:31, 28 February 2018 (UTC)

Part 2

@Double sharp: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. 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. Droog Andrey (talk) 20:27, 28 February 2018 (UTC)

P.S. Thanks for the paper! Quite sensible indeed. Droog Andrey (talk) 20:50, 28 February 2018 (UTC)

P.P.S. Just noticed that 5f in Lr³⁺ lies lower than 6p in La³⁺ :) Droog Andrey (talk) 21:29, 28 February 2018 (UTC)

@Droog Andrey: Apologies for this incomplete reply; I ran out of time to write it. I hope it at least tries to respond to more than half of your points. ^_^

I agree that 4f is less active than 3d (the latter at least has a more effective overlap); but I'm not convinced about significant 5d involvement for Hg, because independent matrix-isolation studies (admittedly using solid Ar rather than solid Ne as in the original experiment) failed to find HgF₄ and, as Jensen mentioned in his paper about it, there was neither experimental compositional nor structural data supporting the purported detection of HgF₄, but only a "single match between a weak infrared absorption peak and the value of one of the calculated stretching modes for a hypothetical square-planar HgF₄ molecule" as he put it. I am similarly doubtful about Cn, given that some other calculations expect that CnF₄ is unbound. And even if they do exist, it seems to me that 4f and 5f are most usefully compared to 3d and 4d (the latter also in the way that 4d rapidly retreats into the core with Ag preferring +1 just like how No in the 5f series prefers +2), and neither Zn nor Cd shows oxidation states past +2; thus we should then only expect some 6f involvement in eka-Lr (E157).

Again, the idea behind our rejection stems from the following line in our submission, addressing the argument that Lu is more similar to Y and therefore should go under it instead of La (here): "In advancing their positions, we think these authors fail to demonstrate why similarity in properties (aside from valency) necessarily connotes group membership. In some other parts of the periodic table, most germanely in groups 1 and 2, we see a continuation of trends upon descending a group (such as increasing atomic radius, basicity and electropositivity), rather than a convergence of such properties. Either pattern could apply to the eka-yttrium position. That is to say, if group 3 were treated as early main group elements we would expect more of a linear trend going down the group. On the other hand, if group 3 was treated as a transition metal group, it would be reasonable to expect more of a convergence properties on going from period 5 to period 6, as a result of the lanthanide contraction. We discuss the behaviour of the group 3 elements later in this submission." It's not that we want a group-2-like trend because it looks nicer, but because the chemical behaviour of group 3 is a lot more like that of group 2 than like group 4. The characteristic transition element properties (variable oxidation state, coloured compounds, paramagnetism) only start in group 4. (With group 12 this is also true – these properties disappear after group 11 – although Cu, Ag, and Au in the +1 oxidation state do act like post-transition metals, and for Ag this is even the main oxidation state, making it a little bit fuzzier.) Part of this is also exacerbated by the high oxidation states needed (so KCl, CaCl₂, and ScCl₃ are ionic solids, while TiCl₄ is a covalent liquid). But regardless of the cause, there does seem to be a preemptive "covering" of the s²d electrons which usually get lost throughout the 4f elements, just like the s² electrons usually get lost throughout the d-elements leaving idealised d⁰ to d¹⁰ electron configurations for their complexes (so much so that even in oxidation states below +2, Fe, Ru, and Os are d⁷ through d¹⁰, and the same is true for the other transition metals; the only time the s-orbitals get filled is for things like [Au(NH₃)_n]⁻, which is d¹⁰s² because the d-orbitals can only hold 10 electrons). Only in the post-transition elements are the s- and p-electrons really running the show (in the pre-transition elements they usually just get lost as well). I'll address the 5f elements later together with their similarities to the 3d and 4d elements. Double sharp (talk) 15:22, 1 March 2018 (UTC)

@Double sharp: if I were a copernicium atom, I'd never show an affinity to fluorine. Something like [CnCl₆]^2- or maybe even [CnCl₄]^- looks much better. As for 5d: the promotion 5d→6p in Hg takes less energy than 6s→6p in Pb [10.1103/PhysRevA.36.425], while the Hg-C bond length in mercury cyanide is just 2.0Å.

The characteristic transition element properties (variable oxidation state, coloured compounds, paramagnetism) only start in group 4.

Don't see any problem with this. The leftmost group 3 reminds s-block, the rightmost group 12 reminds p-block, groups 4 to 11 being classical transition groups. Why do we cry for certainly "pure group-2-like" or certainly "pure group-4-like" behaviour of group 3? It is between them, so let's just leave it alone with water-soluble cations but convergent trends, that's just natural here. Droog Andrey (talk) 18:52, 1 March 2018 (UTC)

@Droog Andrey: Of course group 3 is intermediate, but the charge difference leads to dramatic differences like ScCl₃ vs. TiCl₄, and in the later periods this is pushed even later (Zr and Hf can better support the +4 charge, and Rf probably can really be Rf⁴⁺ like Th⁴⁺ could; and while Zr and Hf have a reducing +3 state, this is likely to be very unstable for Rf due to the destabilisation of the 6d orbitals), so annexing group 3 as a main group seems to have a real point (noting that this delay is common with the transition metals; generally, when a change happens in the 3d elements, it will happen in the next group for the 4d and 5d elements).

Our case for -La-Ac mostly proceeds from two angles. One is the above argument that group 3 acts rather like a main group (even if you put Lu and Lr in it), so that an exceptional s-block-like trend can at least be considered. Since the electron configurations that result are consistent (always ds² for -La-Ac), this doesn't run into the obvious problem with things like B-Al-Sc (3d doesn't match as it's the first d-subshell) or Ti-Zr-Ce (4f doesn't match as it's the first f-subshell, and anyway Ce is only half-heartedly tetravalent). That implies to me that trends can be consistent with either -La-Ac or -Lu-Lr and that something else is needed to settle the question.

The second angle is that the electron configurations shown by the elements in their chemistry strongly suggests an order in which one 5d electron "hangs up" above the filling of the 4f shell, and 5d6s² then acts like an easily removed outer covering shell like 4s² does for the 3d metals. The 3d metals almost always show oxidation states +2 and above, where the 4s shell is completely ionised away; even Cu⁺ isn't really an exception, because it is [Ar]3d¹⁰. And even in complexes where they are in oxidation states under +2 the extra electrons enter the 3d shell instead of the 4s unless it's really full. Similarly, the 4f metals almost always show oxidation states +3 and above, where the 5d6s² shells of their condensed-phase configurations are ionised away, and then Eu and Yb moving the 5d electron to 4f to get the half-full or full subshell look like Cr and Cu moving the 4s electron to 3d for the same reasons, with the typical +3 oxidation state of the 4f elements being recovered at the end of each half (Gd and Lu) in a double periodicity reminiscent of the typical +2 oxidation state of the later 3d elements being recovered at Mn and Zn. Of course, 4f and 5d both being inner shells and the hold on the 4f electrons increasing with oxidation state, looking at the Ln²⁺ ions is not as clear-cut, but most are [Xe]4fⁿ5d (10.1021/acs.organomet.7b00498), with the exceptions being the usual suspects (Sm, Eu, Tm, and Yb), and Nd and Dy changing their minds depending on the ligands. And in itself the ready removal of that third electron is easier to predict from the periodic table if we suppose that it has usually been promoted from 4f to 5d (which it mostly has), implying a split d-block, with Ac³⁺ to Lr³⁺ as [Rn]5f⁰ to [Rn]5f¹⁴ resembling Sr²⁺ to Cd²⁺ as [Kr]4d⁰ to [Kr]4d¹⁰ and similarly for La to Lu paralleling Ca to Zn. The first element coming before each series gives us the "default" +2 or +3 oxidation state that becomes the norm once the inner shell electrons start being unhappy to participate.

One could then draw an analogy comparing the more chaotic anomalous configurations in the 4d elements with those of the 5f elements. Also, the at first stronger involvement of 4d (so that only with Ru is the group oxidation state no longer the most stable, unlike in 3d with Cr) and then quick sinking of it into the core (Pd prefers +2 just like Ni, and Ag has to be "convinced" by fluorine to willingly bring out the 4d electrons and acts like it is part of the next series for the most part). That looks to me like how the oxidation state corresponding to reaching the [Rn] core is still one of the most stable until U in 5f (compare Ce in 4f), while it quickly sinks into the core later (Cf onwards are quite unhappy to be oxidised beyond +3, even to +4, and No famously prefers the +2 state). This also creates a double periodicity in the 5f elements in which Cm is the last one that can show the +6 state that has no parallels among the lanthanides, and then Bk through Lr look like the later 4d elements, especially Md-No-Lr resembling Pd-Ag-Cd. (Of course it is not exact, but neither is the 4f/3d relationship, and matching seven elements to five will hardly allow for a complete match. I do admit that the matches are fuzzy in the middle, but again, splits at the half-filled shell look less obvious for shells with radial nodes. I also admit that I have not considered whether this analogy extends to 6f/5d. ^_^) Double sharp (talk) 03:53, 7 March 2018 (UTC)

@Droog Andrey: This was meant to be just a try for 6f/5d and the 8th period. The tale grew in the telling, as I think Tolkien would say.

I think one good way of considering the 8th row is to say that it really was going to be the Madelung-style approximation with E168 as eka-Og (and it is almost disappointing how the Madelung order of "8s, 5g, 6f, 7d, 8p" is still correct in a broad-brushstrokes sort of way), but that all those inert pair effects have pushed things further back, so much so that the "knight's move" pseudohomologues (cf. Ag, Cd, In paralleling Tl, Pb, Bi) have become better than the purely formal real homologues (cf. In, Sn, Sb when those still had significant meaning). Just like Tl and Pb act to some extent like groups IA and IIA when in the +1 and +2 oxidation states, and just like how the group oxidation state is unlikely to show up for the 7p elements (Nh to Mc should be happy in +1 through +3, unless 6d isn't drowned deeply enough yet for Nh; and similarly Mc through Og should be happy in +1 through +4, since now both 7s and 7p_1/2 are spherical or spherical-ish inert pairs). So if you look at E164, for instance, it does have the 7d¹⁰8s² configuration you would expect for eka-Cn; only the inert pair effect has been hammering away at the 8s electrons for 46 elements ever since they first came in at E119 (eka-Fr), and so they are really core electrons. Meanwhile 9s has fallen down far enough that it instead gets used as the sink for extra d-electrons, and so E164 ends up acting more like eka-Ds (tri-Pd); 9s has usurped the role of 8s because the huge contraction over all those extra 5g and 6f elements has compensated for the increased principal quantum number of 9 instead of 8. Furthermore, one would have originally expected E162 to be eka-Cn (it really ends up being eka-Hs), and this is because 8p_1/2 has also acted as an extra inert pair and is later usurped analogously by 9p_1/2. Your observation that Ts and Og should be analogous to Ga and Sn seems to thus bear fruit in the placement of E167 and E168, which would theoretically have been eka-Ts and eka-Og under the naïve extrapolation, as the heaviest members of groups IIIB and IVB (which Ga and Sn are indeed in). The appearance of 6g in E173 after 9s and 9p_1/2, and the incursion of 7f and 8d by E184, is then completely according to expectations; while 6g should be more active than 5g because of the radial nodes, relativity should, I imagine, create another similar contraction where 9s and 9p_1/2 are usurped by 10s and 10p_1/2. That would seem to indicate a new noble gas at E222 (E172 + 6g + 7f + 8d + 9p_3/2 + 10s + 10s_1/2), with 6h then following to start a tenth period and bring us to E244. This would pose hell for drawing a table since the eighth and ninth rows wouldn't match, unless you resignedly put E168 and E218 in group VIIIB (0) as eka- and dvi-Og and just take the "inert quartet effect" as a given. (I should also remark that the remarks on elements beyond 184 are just my OR running wild after a brief throwaway comment from Burkhard Fricke! If you like, it is just a speculation on what happens for the early supercritical elements until yet a third subshell dives into the negative continuum around E245.)

This actually also does illuminate a point about Sc-Y-Lu-Lr as the Madelung rule version and Sc-Y-La-Ac as a deviation from it. What's the other famous deviation in the PT? Well, He being in group 0 because it has a full shell; this is once again because the normal rule of "start with an s-shell and end with a p-shell" is broken, this time because there is no 1p shell. In other words, we break the strict Madelung rule placement when the electron-filling order consistently results in chemistry that doesn't follow it. Is He a big enough difference to reflect for general purposes? I would say yes. Is La? I suppose we differ here, but the general presence of 5d6s² as a covering shell for the 4f elements suggests to me that it makes some sense and helps to explain the consistent oxidation state of +3 across the Ln. Similarly, the relatively consistent presence of 6f²8s²8p_1/2² as a covering shell for the 5g elements suggests that they might be taken to form an "eka-uranide" series starting after E124, with a consistent +6 oxidation state. This would end after 18 elements at E142 (exactly where we need it to), before the 6f series resumes at E143 and takes us to E154. Here the oxidation states would initially zoom up like the actinides (Pyykkö's proposal of +12 for E148 might be the maximum, wildly surpassing Ce in the 4f row and Np in the 5f row), but then drop downwards as 6f, 8s, and 8p_1/2 all drop down into the core and create a quasi-closed shell at E154 (similar to Cn and Fl). Then we can assign 7d as a covering shell for E155 and E156 to fill (allowing then to act like eka-Md and eka-No, and not just like some calculations expected eka-Lr to act in the case of E155 with the possibility of a +1 state), and continue with E164 (or we can assign E121 formally to 7d as the LU shell and swap it with E155, with the 8p_1/2 stabilisation just making it the first excited state instead, and the overlapping g-, f-, and d-blocks illustrating the chaos going on here; this is even worse than all the 5f and 6d hybridisation in the early actinides). Then we can put the covering 9s shell onto E165 and E166 (since these are likely to prove the adage that transition chemistry is d-block chemistry, with no covering s-electrons in complexes), and finally have the hybrid 9p_1/2+8p_3/2 subshell to complete the row with E167 through E172. And, after all, the breaking of the pattern to shove in 9s and 9p_1/2 is another sacrifice of the Madelung rule to reflect expected chemistry, is it not? We can of course go the other -Lu-Lr-like route writ large by putting E168 and E218 as eka-Og and dvi-Og respectively, following Og's tendency to be in the +2 and +4 states and its almost-but-maybe-not-quite metallic behaviour, even when E172 should be a better noble gas than Og (in fact, perhaps as good as Xe; let's also not forget the possibility of Cn, Fl, and E154 becoming "pseudo" noble gases as the real ones bow out). When we contemplate what is likely to happen past E120, we might reflect that compared to the magnitude of those adjustments (and the He adjustment), the -La-Ac vs -Lu-Lr dispute is small potatoes.

I realise that I have gone on and on mentioning everything but a hypothetical 6f/5d analogy. Perhaps one might be found in the fact that 5d is the only other place on the periodic table to E172, besides 6f, where oxidation states beyond +8 can be obtained (Ir^IX is known and Pt^X is expected), and in how E154 at the end of the 6f block would then mimic Hg at the end of the 5d block in being a very noble closed-shell metal (also similarly to Cn and Fl). But I think that this tale has not only grown in the telling, but steered us down very different paths, and the main point is in the two preceding paragraphs. ^_-☆ Double sharp (talk) 06:11, 7 March 2018 (UTC)

P.S. I shall incidentally also say that I think your original illustration of the 8th period, with 121–138 and 139–156 footnoted as two rows (121 above 139 and so on till 138 above 156) is almost certainly the best way to deal with these elements, leaving aside for the moment the group 3 argument. Yes, it breaks the block structure, and it means that the table cannot be expanded without causing an awful mess, but at this point the block structure means hardly anything and the real chemical considerations make the Ln/An analogy better. We are drawing the table for chemistry first and foremost, after all; and if you try to draw period 9 (is my OR idea of it right?) underneath, it can easily be accommodated by another "ultransition" series even though it seems to be four elements shorter than period 8 (whatever it actually is, they're probably not the same length). Maybe you should publish a journal article suggesting it and if it happens to be right, get an element named after you like Seaborg. ^_-☆ Double sharp (talk) 10:21, 7 March 2018 (UTC)

P.P.S. I have tried to draw my "formal" block assignments below. As everyone probably could have expected, it is a frightful mess.

The 8th period then goes: 8s², 8p_1/2², and 6f² first as covering shells; then a fairly constant +6 oxidation state for the "eka-uranides". By the time E143 is reached 6f gets progressively filled up, so that oxidation states rise again and reach the maximum for "eka-Pu" as expected, and then quickly fall down to end the "subperiod" at the noble metal at E154 (yes, I'm not sure there is a good way to draw this). A second beginning starts at E155 until we reach the noble metal at E164 and noble gas at E172. Double sharp (talk) 15:32, 7 March 2018 (UTC)

P.S. Old 1969 calculations (10.1063/1.1672054) indeed suggest that E121, E122, E123, and E124 should be eka-Ac-like, eka-Th-like, eka-Pa-like, and eka-U-like in their chemistry, and that E125–E132 should indeed form the start of an "eka-uranide" series with similar chemical properties to E124. These elements would likely have many oxidation states and have quite complicated chemistries, a situation reminiscent of the early actinides. Double sharp (talk) 06:51, 13 March 2018 (UTC)

Part 3

@Double sharp: thanks for the detailed reply. Then a few notes from me.

About the "second angle": you compare diactions with trications, so that's not a surprise you obtain analogies like Ca-Zn vs. La-Lu and Sr-Cd vs. Ac-Lr. So that's just an old "+3 state" argument. My point is that we should use equal terms for such a comparison. You say that outer ns² are almost always ionized, - that's the reason why namely the third ionization potential is the best suit.

Just imagine how ugly this picture would become if we shifted the boundaries.

On the 5d¹ for Ln²⁺ complexes: I bet that if we make a CAS-SCF calculation, then the weight of such a configuration will be far from 100%. And we know that np-subshell is involved in the same complexes of d-elements, but that doesn't make them p-elements.

About the analogy 5f vs. 4d: that's just the radial nodes, yes. But, again, you manually shift the boundaries: the (+1) state is most likely to be found in Md, not No. So Pd-Ag-Cd correspond to Fm-Md-No.

As for the 8th period: I think there will be no strict boundaries, and drawing them explicitly is just arbitrariness. BTW, E154 definitely shouldn't be Hg-like, I think it should be a common f-element like Er, but with both +3 (6f¹²8p¹ or 6f¹³8p⁰) and +4 (6f¹²8p⁰) oxidation states possible. Droog Andrey (talk) 22:10, 7 March 2018 (UTC)

@Droog Andrey: I'm making analogies between different oxidation states to reflect how they fall above or below the "baseline". When I compare No²⁺ with Ag⁺, I mean it in the sense that both of them are the more stable oxidation state near the end of the block corresponding to a full-shell configuration, which can nevertheless be breached to form No³⁺ and Ag²⁺ in the presence of strong oxidising agents. Then Lr³⁺ and Cd²⁺ look analogous (neither can be oxidised or reduced except directly to the metal) and Pd being happy with 0 looks like the possibility of Md having +1. I got the prediction of a noble E154 with no outer shells outside the core from Fricke's 1971 paper. I admit that the third IP is a convincing argument for -Lu-Lr (what a pity you weren't active when we were scouring the literature for arguments for the IUPAC submission) and it makes me suspect that already by the sixth period breaking the table strictly into blocks is a mistake, and that the -La-Ac vs -Lu-Lr choice is partly a reflexion of what properties you consider more important in assigning elements a position in the periodic system. I'll write something more detailed later. Double sharp (talk) 00:33, 8 March 2018 (UTC)

@Double sharp: 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), especially in the blurred 7th and 8th periods. That's why I simply marked the whole bunch of 121-156 as "ultransition" elements :) Droog Andrey (talk) 01:31, 8 March 2018 (UTC)

@Droog Andrey: Well, like I said, it depends what you're looking for. I think we'd agree that the differences betwwen He and Be are enough to justify rupturing the s-block; I think we'd agree that the blurring that happens in the 8th period is enough to not follow the Madelung rule and put E168 in group VIIIB against all chemistry, even if it would nicely follow Og's half-metallicity and "inert quartet". So clearly we can agree that in some situations, rupturing the blocks is justified, and that it is a mistake to take the blocks too seriously. We're just discussing whether or not the situation going on in group 3 is enough to justify the rupture. ^_^ In general, I'd expect properties of gaseous atoms (e.g. ionisation energies) to support -Lu-Lr (because there fⁿ⁺¹s² is the normal configuration), and properties of condensed-phase atoms to support -La-Ac (because there fⁿds² is normal). So you can find double periodicities that look like La-Eu and Gd-Yb form pairs, and I can also find some that look like Ce-Gd and Tb-Lu form pairs, and both have similarities with the Sc-Mn and Fe-Zn pairs. I am mostly swayed by La's f⁰ position (same for Ac) making me uncomfortable putting it in the f-block, combined with the increased chemical relevance of condensed-phase configurations and the 4f- and 5f-collapses only happening at Ce and Th; and given the precedents of He and Ne, I can better stomach a finally completed shell at Lu and Lr that chemically does nothing than one at Yb and No which can still get ionised. (I still think Lu is more usefully compared to Zn; even if 3d strengthens the bond for Zn compounds, it is not ionisable, and if we have to wait for Cn for 6d to be destabilised, then the f-block can wait. In fact, given how the "knight's move" relationships have become the real ones that make us redraw the 8th row, then we might never see this happen to the f-block.)

I am aware that this regularity gives way to a complete mess after eka-Ra and that breaking the blocks for similar reasons is hence an unsustainable solution; even if I am tempted to draw an analogy of E125 and the following elements to "eka-uranides" following likely hexavalent E124, things get ugly when the series starts adding 6f electrons again at E143. But I'm not sure these elements should dictate what we do for the elements we know and love. In the end I'd probably draw 122-157 as my "ultransition" elements in two rows of 122-139 and 140-157, even if the resemblances like 130-148 are unlikely to be all that great; I don't think it's very much worse than 121-138 and 139-156 since the oxidation states are expected to be arrested at at most +6 (6f²8s²8p²) for 125 to 142, which matches neither. I'd say that we're not really breaking blocks there, because strict blocks have ceased to exist beyond element 120. ^_^ Double sharp (talk) 03:08, 8 March 2018 (UTC)

P.S. About the p-electrons for d-complexes; if we're talking about Pauling's hybridisation scheme, the p-orbital contribution is minor, and there are serious doubts whether there is any significant contribution at all. It may be a bit more real than the d-orbital contribution to main-group hypervalent molecules and perhaps contribute to the resonance, but (1) 12-electron structures involving only the d- and s-orbitals explain things well enough, and (2) if they have a real involvement I wonder if this might be explained by the fact that the condensed-phase configurations of the group 2 and 12 metals appear to be sp rather than s². Double sharp (talk) 03:20, 8 March 2018 (UTC)

@Double sharp: I guess you mean E168 in VIIIA, not in VIIIB. But E172 fits VIIIA much better (blurring is observed mostly before E157), so there's not a complete anarchy :)

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

p-Subshell in d-elements contributes mostly in the low-oxidation-state complexes like Fe(CO)₄^-, Vaska's complex, etc. Droog Andrey (talk) 10:23, 8 March 2018 (UTC)

@Droog Andrey: Ah, sorry about that. There were two completely contradictory systems on what the A and B letters mean, described in Group (periodic table). One way is as you have it (IA–IIA, IIIB–VIIIB, IB–IIB, IIIA–VIIIA) on your beautiful table; the other way has A at the start and B at the end (IA–VIIIA, IB–VIIB, with the last group being either 0 or VIIIB). I learned it the second way (where the Sc group we are discussing is IIIA rather than IIIB) and write it by default (although I've seen enough stuff using the other convention that I may slip), but this is obviously a prime recipe for confusion, so I'll stick to the 1–18 numbering for now.

I mean that the usual structure of the solid Ln metals has three electrons in the 5d6s conduction band (again, Eu and Yb are exceptions). For the early An there is a lot of 5f-6d hybridisation and so one cannot really pin down the precise 6d occupancy, but 6d is occupied for Ac–Cf and Lr (which is probably ds² in the condensed phase even though it is s²p in the gas phase). And for example in the lanthanide sesquioxides (source) the Ln–O bonding is primarily between the 5d orbitals of the Ln atoms and the 2p orbitals of the O atoms, although "changes in the energy and occupancy of the 4f orbitals can impact Ln 5d and O 2p mixing". In general, 4f is deeply buried and is more of a reserves area for one electron (or two in the cases of Ce and Tb) to be promoted to 5d and only then participate in chemistry. The situation for the early An is different since there the 5f orbitals are more valence-like, whence the complexity of elements like Pu, and the more extensive coordination chemistry (more transition-metal-like) and greater crystal field effects, but for the late An the 5f orbitals of course sink into the core even more deeply than for the Ln (so that by the time we get to No it's difficult to convince any 5f electrons to be promoted to 6d). I'm out of time now and will look up the p-orbital involvement in low oxidation state complexes in the d-elements later (or do you have some links? ^_^). Double sharp (talk) 15:05, 8 March 2018 (UTC)

@Double sharp: you've just catched a beautiful idea: 4f-electrons is more of a reserves area, so they are indirectly valent (prevail in non-bonding MOs), while 5d6s (and sometimes 6p) are directly valent (prevail in bonding MOs), but both are significant for chemistry because of electron correlation between the subshells. Such a situation is observed mostly from La to Yb, so that's another fruit in my bin :P

As for solid metals, I think their structure is better considered in metalloids vs. metals context than in 4f vs. 5d context. Droog Andrey (talk) 20:53, 8 March 2018 (UTC)

P.S. About p-involvement for d-complexes: I have no links, but I thought that was deducible from general principles (and could be confirmed with quantum-chemical calculations of course). Droog Andrey (talk) 20:59, 8 March 2018 (UTC)

Part 4

(This section used to have the title "Third IP chart", but since it continues on the previous discussion I have retitled it "Part 4".) Double sharp (talk) 14:55, 11 March 2018 (UTC)

Hi @Droog Andrey: You wrote above, "Just imagine how ugly this picture would become if we shifted the boundaries."

There is no reason why the boundaries could not be shifted to show the f block as Ce to Lu, and Th to Lr. Periodicity in the IE's would still be observed. The double periodicity discussed in the IUPAC paper would become more visible instead of being hidden due to the inclusion of Lu in the d-block. The trend in third IP going down Sc-Y-La is more like that of the group 1 and 2 metals, which is as expected given the chemical behaviour of the group 3 metals as (effectively) trivalent group 1 or 2 metals. The appearance of a downward spike going from Eu to Gd, and from Yb to Lu, would not be unusual. Comparable valleys occur in the series C-N-O, Si-P-S, Ge-As-Se, Sn-Sb-Te, and Tl-Pb-Bi. Sandbh (talk) 10:48, 10 March 2018 (UTC)

@Sandbh: Hmm, which ionisation potentials are we looking at? C-N-O shows a peak at N for the 1st IP, but a smooth trend for the 2nd, and a dip at N for the 3rd. We must also consider similarities in electron configurations. As we all learnt in high-school chemistry ^_^, the electron being removed from an O atom is paired while that being removed from an N atom is unpaired, and the increased repulsion means that O has a lower first ionisation energy despite its valence electrons experiencing a higher effective nuclear charge. We have the same story going down group VIB for S, Se, and Te. When we get to the sixth period, the subshell splitting between 6p_1/2 and 6p_3/2 is now quite large, so the 6p_3/2 electron being removed from Bi is not only farther from the nucleus in general but is also partially screened by the 6p_1/2 electrons, an effect which is not present in Pb. The effect is quite small here but gets significantly greater in the 7th period, where there is expected to be a much larger drop in IP between Fl and Mc. If we look at what happens going from Eu to Gd, and from Yb to Lu, it is essentially the same situation; the extra electron is added to a higher-energy subshell, and is thus easier to remove. This is also true for the third IP's in the lanthanides: Eu²⁺ [Xe]4f⁷, Gd²⁺ [Xe]4f⁷5d; Yb²⁺ [Xe]4f¹⁴, Lu²⁺ [Xe]4f¹⁴6s. For the actinides, the paired-electron explanation is operative for the Am-Cm pair: Am²⁺ [Rn]5f⁷, Cm²⁺ [Rn]5f⁸; No²⁺ [Rn]5f¹⁴, Lr²⁺ [Rn]5f¹⁴7s. All this is naturally in accordance with the elements' atomic gas phase configurations, and the argument stands if we accept that as a basis. So it seems to me that the most effective counter we have to it is simply questioning whether gas- or condensed-phase configurations are more relevant. Double sharp (talk) 16:51, 10 March 2018 (UTC)

Oh, the 3rd IP in all instances. The 1st IP of the elements is regularly used to examine periodic trends, never mind the differentiating electron. On this basis, the same approach is valid for the 3rd IP. Sandbh (talk) 05:42, 11 March 2018 (UTC)

Of course, but the differentiating electron does explain the small bumps and dips that happen along the way. For C-N-O, the dip at N happens because we are removing a 2p electron from N²⁺ and O²⁺ but a 2s electron from C²⁺. For Tl-Pb-Bi, there is a peak at Pb and a dip at Bi; presumably Pb-Bi-Po would have given us the trend we needed, except that the 3rd IP of polonium is not listed at Molar ionisation energies of the elements. Similar considerations explain the dips at Gd/Cm and Lu/Lr. Double sharp (talk) 06:16, 11 March 2018 (UTC)

@Droog Andrey:

Lu is obviously closer to the remainder of the 5d transition metals than La, just look at the trends La-Hf-Ta-...-Hg and Lu-Hf-Ta-...-Hg.

Ugh. Try to draw the plots and you'll see all the stuff.

@Droog Andrey: Thanks, I did not draw the plots I just looked at the numbers. There is no major change, apart from introducing two dips in the middle and end of each series of f block elements. Sandbh (talk) 05:42, 11 March 2018 (UTC)

@Droog Andrey: Comparable valleys occur in the series C-N-O, Si-P-S, Ge-As-Se, Sn-Sb-Te, and Tl-Pb-Bi.

They are not comparable, because the number of outer-shell electrons increases with group number for main groups, while we are talking about groups 3 to 12 where the number of outer-shell electrons is nearly constant (namely, two electrons, that's why the third IP).

@Droog Andrey: I am only saying that valleys are not novel. Sandbh (talk) 05:42, 11 March 2018 (UTC)

You explained the peaks for Eu, Yb etc. right, but that's not the point we discuss here. The point is the position of that peak along f-block, compared to the same situation along d-block.

@Droog Andrey: 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) 05:42, 11 March 2018 (UTC)

Third IP has nothing to do with gas-phase or condensed-phase configurations of neutral atoms. Droog Andrey (talk) 18:46, 10 March 2018 (UTC)

@Droog Andrey: No, but it has to do with gas-phase configurations of dications. I mean, the definition of the 3rd IP is the amount of energy required to remove an electron from a gaseous dication, after all. ^_^ In groups 3 to 12 taking the 3rd IP indeed usually gets rid of the s² electron pair outside that is almost always lost chemically anyway and irons out most of the anomalies, so of course you will see Eu and Yb corresponding to Mn and Zn there. Chemically speaking the 3rd electron is usually promoted, creating a consistent ds² valence configuration that makes Eu and Yb correspond to Cr and Cu instead. So, while Gd and Lu seem to be anomalously low when we consider the 3rd IP of each element (where they are the ones that have the anomalous configurations fⁿds² and almost all the others are fⁿ⁺¹s²), it is Eu and Yb which seem to be anomalously low when we consider the melting point of each element (where they are the ones that have the anomalous configurations fⁿ⁺¹s² and almost all the others have fⁿds²).

If we are in a situation where some other lanthanides have different configurations, then you will see a different trend, which actually happens for the boiling points. This is the only source I have found explaining that (which intriguingly posits mostly fⁿd^1.5sp^0.5 or fⁿdsp configurations for the solid metals, similar to how the group 2 and 12 metals are usually sp instead of s² in the condensed phase); for the Ln₂ gaseous molecules it is Sm as well as Eu that is anomalously mostly divalent instead of trivalent, and it also gets a low boiling point. There is a switch in configuration from fⁿd²s to fⁿ⁺¹sp at Dy and the resulting divalence also corresponds to a drop of boiling point, although I admit that the precipitous drop at the end of the series to Tm and Yb is left unexplained (given that these two can without so much difficulty drop down to the +2 oxidation state, though, the location of the anomaly there is not too surprising). I'll give the electron configurations posited for the Ln below:

Element	Ln atom	Ln2	Ln metal
La	ds2	d2s	d1.5sp0.5
Ce	fds2	fd2s	fd1.5sp0.5
Pr	f3s2	f2d2s	f2d1.5sp0.5
Nd	f4s2	f3d2s	f3d1.5sp0.5
Pm	f5s2	f4d2s	f4d1.5sp0.5
Sm	f6s2	f6d0.5sp0.5	f5d1.5sp0.5
Eu	f7s2	f7d0.5sp0.5	f7d0.5sp0.5
Gd	f7ds2	f7d2s	f7d1.5sp0.5
Tb	f9s2	f8d2s	f8d1.5sp0.5
Dy	f10s2	f10sp	f9d1.5sp0.5
Ho	f11s2	f11sp	f10d1.5sp0.5
Er	f12s2	f12sp	f11dsp
Tm	f13s2	f13sp	f12dsp
Yb	f14s2	f14sp	f14d0.5sp0.5
Lu	f14ds2	f14dsp	f14dsp

I must add of course that other authors (e.g. Johansson and Rosengren) give fⁿds² for all the Ln metals except Eu and Yb which are fⁿ⁺¹s². But I think my main point that it is only 5d, 6s, and 6p which contribute to the bonding for the most part, and that there are three electrons in total in those valence bands in the elemental metals except for Eu and Yb, is pretty sound.

So, what is to be done? Some trends look better in the Sc-Y-La table and some trends look better in the Sc-Y-Lu table. But the trends that look better in the Sc-Y-La table tend to be those involving condensed-phase configurations (e.g. melting points), whereas those that look better in the Sc-Y-Lu table tend to be those involving gas-phase configurations (e.g. ionisation potentials). When neither set of configurations is active (e.g. boiling points), a completely new trend asserts itself that conforms to the actual configurations at work in that new situation. In other words, this is an extension of the argument over the relative merits of gas-phase and condensed-phase configurations, the first of which supports Sc-Y-Lu and the second of which supports Sc-Y-La. Given the increased chemical relevance of the latter, corroborated by the consistently delayed collapse of the f-orbitals, I am inclined to say that the strong points of Sc-Y-La outweigh its weak points. But it is true that this depends on the premise that condensed-phase configurations should be the basis for drawing the table, as reasonable as it sounds to me and Sandbh. Double sharp (talk) 04:04, 11 March 2018 (UTC)

I have made a few expansions to the above comment for clarity. In the meantime, I've been considering the ubiquity of sp hybridisation messing with the s- and p-blocks for the condensed phases of the main group elements (agreeing for the moment to stop at Lr, because calculations have not extended beyond that, beyond noting that Rf and Db are tetravalent and pentavalent metals in the condensed phase as would have been expected). The group 2 and 12 metals are approximately sp instead of s² in the condensed phase (with Hg beginning to have some 5d involvement); group 13 and 14 appear to be split with B, Al, and Ga sp² but In and Tl s²p, and C, Si, Ge, and α-Sn sp³ but β-Sn and Pb s²p². Given the "pre-transition" character of Al³⁺, Zn²⁺, Tl⁺, and Pb²⁺, I am inclined to say that it may be reasonable to forego the s- vs. p-block distinction (which also sweeps the He issue under the rug), as there is not really that much relativistic splitting in the shells for the main-group elements we know and love; it is still quite possible to get Tl, Pb, and Bi into their group oxidation states with weakly electronegative, usually organic ligands, and the paucity of evidence on Po^VI and At^VII is probably just a reflexion of their strong radioactivity making experimentation difficult (similarly for Cm^VI); the same should explain why no one has seen Rn^VIII (or indeed why the characterisation of Rn^IV and Rn^VI is so spotty), even though it is theoretically expected to be quite possible in perradonates (paralleling perxenates). In other words, even in the presence of the strong 6s-6p splitting, the octet rule is still functional; things only go bonkers in the last main group elements Cn through Og (after the surprisingly normal 6d elements; Cn has one foot in each camp). This is similar to the functionality of the duodecet rule in the d-elements (the outer p-shell has much less importance than the valence s- and d-shells), and I've alluded to the "reserve" status of the f-electrons in the Ln and late An (Th through Cm have a different story). In other words, I think that perhaps a better "bloc" classification, inspired by R. Bruce King considering the Ln and An to be main-group elements:

• Main group elements, where the octet (sp) rule holds: groups 1–3, Lu and Lr, and 12–18.
• Transition elements, where the duodecet (sd) rule holds: groups 4–11. These form a transition between the first (2) and second (12) divalent main groups.
• Incipient transition elements, where the octet rule still holds, but with the f-electrons ranging from quiescent but cohesive for metallic bonding (e.g. something like samarium) to active (e.g. something like plutonium). These form a transition between the first (3 with -La-Ac) and second (Lu-Lr) trivalent main groups. These can be considered to be a subset of the main-group elements for the most part.

The 7p series, of course, starts to show serious cracks in the periodic table thanks to the octet rule being quickly supplanted with a sextet and then a quartet rule, so much so that the metallicity of Og is something that is not obviously false (it does appear to have significant similarities with Sn, as Droog Andrey mentions). As a result I would tend to want to stop this classification at copernicium, as after that it isn't particularly useful with the mess of the 8th period looming. Double sharp (talk) 06:45, 11 March 2018 (UTC)

@Sandbh: @Double sharp: the appearance of dips at penultimate members of subfamilies is weird. And that's not about the configurations, that's about chemistry. The comparison of d-block with f-block is valid simply because of the same number of outer-shell electrons.

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

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

At boiling point temperatures there are no Ln₂ molecules, the gas is mostly monoatomic.

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

<off-topic>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.</off-topic>

As for the stabilization of Pb(IV) and Bi(V) with organic ligands like PbEt₄ and BiPh₄⁺: in these molecules 6s² orbital almost entirely transforms to the non-bonding MO, while almost all the bonding is done by 6p subshell. Generally, the concept of sp-hybridization doesn't work very well even for carbon (look at the photoelectron spectrum of CH₄ for example), and down the group 14 it works much worse, as well as to the right of the group. It has still some sense for Be/Mg and B/Al because of high energy of ns- and np-subshells (therefore a small gap between them), but also gets worse down the groups.

Pulling group 3 outside the d-block and making it "main group" is bordering on fantasy. The real chemistry is not black and white; groups 3 and 12 are just on the edge of the block, that's why they are a bit different. We have discussed this already. Droog Andrey (talk) 11:15, 11 March 2018 (UTC)

@Droog Andrey: I think I need to clarify that I'm convinced by your 3rd IP argument, even if Sandbh isn't. I think it is a good argument for Sc-Y-Lu. I'm just not entirely sure it is outweighed by the delayed collapse of the 4f and 5f orbitals. What I'm trying to say by mentioning the "anomalies" (which I agree was a poor choice of words) is that the reason why things break into La–Eu and Gd–Yb here is that at Gd, we are removing a 5d electron instead of a 4f electron, which is easier and so there is a drop (just like the high school explanation of why the IP trends don't just go straight up across the period as effective nuclear charge grows). Similarly, at Lu, we are removing a 6s electron instead of a 4f electron. At Cm we are removing a paired 5f rather than an unpaired 5f electron (it would explain things, even though the splitting into 5f_5/2 and 5f_7/2 may start to be vaguely noticeable), and at Lr we are removing a 7s rather than a 5f electron, and all of these explain why they are the elements at which the 3rd IP drops. Electron configurations surely are here to explain periodicity and chemical properties, and we shouldn't put the cart before the horse. But indeed, the half-filled subshell at Eu/Am and the fully-filled subshell at Yb/No is why they have this position, combined to some extent with their configurations being different from those of the surrounding elements (notice that for the late actinides, we don't see a dip at the predicted melting point for No, which is the same as that for also divalent Md). These are arguments that support La-Yb and Ac-No as the f-block (and once again let me say that I wish you had been around to give us such good arguments back in 2016 when we were preparing our IUPAC submission; it would have improved it greatly).

Against this we still have to consider what I think is the strongest -La-Ac argument. The f-orbitals of Ac are not very relevant chemically (they are quite high up), and for La and Ac they appear to be rather like the "pre-d" (to use Pyykkö's term) 3d, 4d, and 5d involvement of Ca, Sr, and Ba. You've mentioned that Hg is closer to the 6p elements than Ba (which makes a nice pair with Cs for 6s), but whether La or Lu is closer to the remainder of the 5d transition metals is rather harder to say. ^_^ All of the lanthanides are fairly similar and I am doubtful if such a comparison would really give statistically significant results. (Nonethless, Restrepo has done some work indicating that La may be more similar to the transition metals than Lu is.) This is also an illustration of how the collapse of the f-orbitals is delayed to Ce and Th, suggesting that the f-block begins there; and the 5d6s² involvement as a "covering shell" suggesting that it may be interrupting the d-block.

Regarding the "main group" vs "transition" divide; I'd also note that unlike Jensen, I'm not trying to say that group 12 is not a d-block group, and I am likewise not trying to say the same for group 3. They are d-block groups, as each d-subshell can hold ten electrons and hence the series must span ten columns. I (and I imagine most authors that consider group 12 a main group) am instead considering "main group" and "transition" to be labels of descriptive chemistry rather than strictly following an sp vs. df block divide. (I wonder if there is a cultural gap here: how do Russian texts usually use the terms? The way I learnt it from English-language texts, mostly from the UK, Zn was a d-block element but not a transition metal because its d-electrons weren't valence electrons.)

I think it is not unfair to say that group 12 lacks both the chemical and physical properties characteristic of the transition metals (because of the filled d¹⁰ shell sinking into the core and not even being present as a "reserve" – incidentally Jensen also mentions that idea in the context of the d-elements, as the non-bonding d-electrons are not stereochemically active as are the non-bonding p-electrons in main-group compounds), and that while group 3 has the physical properties of transition metals it lacks the chemical properties. I think Jensen's article I linked to on group 12 does get the crux of what is going in the group 3 situation by applying it to the group II situation (the Roman numeral is deliberate):

In general, if one plots a given property for the members of group II, the group trend will parallel that shown by the alkali metals in group I if, after Mg, one follows the Ca–Ra subgroup or branch, but will parallel the pattern shown by groups III–VIII if one follows the Zn–Hg subgroup or branch. This is illustrated in Figure 4 for group trends in electronegativity. In summary, both the chemical and spectroscopic evidence clearly place the Zn group in group II of the main-block elements and lead to the irresistible conclusion that, following Be and Mg, there is a fundamental bifurcation of this group into a Ca–Ra branch and a Zn–Hg branch.

I would say much the same on the La-Ac vs Lu-Lr dispute. In general, if you plot properties for group 3, the trend follows groups 1 and 2 if you take the Sc-Y-La branch, but it follows groups 4 and 5 if you follow the Sc-Y-Lu branch. Of course, this is because of the d- and f-block insertions before Zn-Cd-Hg which are not present in the Ca-Sr-Ba branch, and similarly because of the f-block insertion before Lu-Lr that is not present in the La-Ac branch. Since the f-orbitals are mostly inactive in La-Ac and Lu-Lr, just like the d-orbitals in Ca-Sr-Ba and Zn-Cd-Hg, we have about the same sort of situation. It would make sense to consider both Be-Mg-Ca and Be-Mg-Zn to be branches of group II on an equal footing, as Jensen suggests, and to do the same for Sc-Y-La and Sc-Y-Lu as I might suggest. 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).

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. Double sharp (talk) 14:48, 11 March 2018 (UTC)

@Droog Andrey: P.S. Do you have some newer sources than mine on the lanthanide metal vapours? The source I linked to alludes to "gaseous Ln₂ species" but is admittedly from 1982 and I am really sorry if I've based some of my arguments on false premises. Similarly, I got my comments about the higher oxidation states about the main-group elements from Kaupp's paper on radial nodes that I linked here a while back:

Pyykkö pointed out that the nodeless 2p orbital has a similar radial extent as the 2s orbital (which has one radial node). This idea was extended by Kutzelnigg, who introduced the concept of hybridization defects. Because of the similar radial extents of the 2s and 2p shells, these are particularly well suited for hybridization. The resulting hydrides are close to orthogonal at the central atom and are thus able to form good and strong bonds with other bonding partners. This good isovalent hybridization is a typical feature of organic chemistry and therefore deeply rooted in chemistry teaching. In contrast, the 3p orbitals (with one radial node) are already appreciably larger than the 3s orbitals (with two radial nodes), because of an additional centrifugal contribution to the repulsive potential exerted by the 2p core shell. Therefore, the concept of orthogonal hydrides starts to fail. Hybridization may only be used for the heavier main group elements, when nonorthogonal hydrides are accepted.

...

Electronegative substituents increase the size differences between valence s and p-orbitals at the central atoms. Hybridization defects are thereby enhanced, and the resulting covalent bonds are weakened. This explains for example, why organoelement compounds of the heavier p-block elements in their highest oxidation states are actually often quite stable (sometimes the lower oxidation states are even unknown or postulated only as reactive intermediates), whereas substitution of organic groups by more electronegative elements destabilizes the higher oxidation states. As a good example, we may note the relative stability of organolead(IV) compounds compared with the instability of typical inorganic lead(IV) species.

Like Thayer (10.1021/ed082p1721), I suspect that this is why Po^VI is so spottily documented (just PoF₆ and PoO₃, and both only in minute tracer quantities): it would be more stable in organopolonium compounds like Ph₄PoF₂, but then radiolysis starts to become a real problem. Anyway, I think it's still worth noting that the octet rule "works": you can still expect the group oxidation state to exist for Tl–Rn, but it's less stable than it was for In–Xe (and more destabilised than it was for Ga–Kr, of which As–Br are reluctant to reach the group oxidation state after the 3d¹⁰ contraction and Kr has never been convinced to go higher than +2). On the contrary, the group oxidation state is very much not likely to happen for Nh–Og (except maybe for Nh if the 6d expansion is still active there). Double sharp (talk) 15:10, 11 March 2018 (UTC)

@Double sharp: thanks for your consistent response.

You say that the strongest -La-Ac argument is small f-subshell involvement. Well, that can be calculated: just look at the electron correlation impact on some chemical reaction (say, XCl₃ = XCl₂⁺ + Cl^-) with and without f-orbitals accounting for X = La, Lu, Ac, Lr. I bet for La and Ac f-subshell neglecting will produce larger error than for Lu and Lr, respectively. On the other hand, the same kind of calculation could be done for Ca/Sr and Zn/Cd, and we could check the error from d-subshell neglecting here (I think it would be larger for Zn and Cd). Again, if we compare divalent Ba/Ra vs. Yb/No, the f-subshell neglection will produce larger errors for the latter.

Lu is obviously closer to the remainder of the 5d transition metals than La, just look at the trends La-Hf-Ta-...-Hg and Lu-Hf-Ta-...-Hg. The difference is yet larger for Ac vs. Lr (although there are mostly predictions here).

In Russian-language literature the term "d-element" is used wider than "transition metal". I don't support the idea of placing Zn-Hg in the same group as Be-Mg, unless we consider a short variant of the PT with 8 groups, where Cu-Au was also in the same group as alkali metals.

My appeal to Occam's razor was not against the analogy. I just take another analogy: Ca/Sr vs. Zn/Cd and Ba/Ra vs. Yb/No. All are divalent, equal terms are maintained.

On the metal vapours: that's just thermodynamics. The bond energies for La₂, Ce₂, Pr₂, Nd₂, Eu₂, Gd₂, Tb₂, Ho₂, Yb₂, Lu₂ are 2.3, 1.7, 1.2, 1.7, 0.3, 1.4, 1.5, 0.8, 0.1, 1.4 eV respectively, so (accounting typical entropy change of about 1 eV/1000K) only La₂ could present in significant concentrations above the boiling point temperatures. BTW, bond energies of diatomic species also support Sc-Y-Lu-Lr trend :) Droog Andrey (talk) 16:39, 11 March 2018 (UTC)

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

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

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

@Droog Andrey: Hmm, it appears this has been tested for La vs. Lu: "All the valence electrons were correlated, but experiments were also performed to investigate the error introduced by not correlating the subvalence electrons. For lutetium we performed calculations to test the effect of not correlating the 14 inner-valence 4 f-electrons as well." (The article is a study of the Ln and An contractions, which entails studying analogous La and Lu compounds for the lanthanides and analogous Ac and Lr compounds for the actinides). It appears that 4f does play a significant role in Lu bonding: "It does appear that including the 4f-electrons in the inactive core removes that flexibility of the 4f-shell to relax upon correlation giving a significant underestimation of the correlation effect on the bonding." The error seems to be about the same size if we neglect 4f in La or in Lu: for lanthanum the authors write "If the four inner f-functions are excluded from the basis set the bond lengths expand by as much as 0.03 Å for some of the lanthanum compounds. This is an indication that the 4f orbitals are involved in the bonding in these systems", but for lutetium they write "Our results in Table I indicate that for LuH and LuH₃ only about 50% of the bond contraction due to correlation is obtained if the 4f-electrons are not correlated. For LuF the effect is even more dramatic giving a small bond expansion upon correlation, and only when the 4 f-electrons are correlated, the more correct contraction of 0.03 Å is obtained." It seems that they only ran the calculations with 5f correlation for Lr and without it for Ac, which apparently resulted with agreement with independently calculated data, as I would expect given the delayed collapse for the 7th- and 8th-period elements. 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. So while the condensed-phase argument has problems (such as making the d-block end at group 10, which is not what we want), it seems to me that the "delayed collapse" argument and the toss-up between including relatively inactive f⁰ or f¹⁴ still has some force. (I should note that I have not had the time to find a similar study of Ca/Sr/Ba/Ra vs. Zn/Cd/Hg/Cn, but certainly including the 3d¹⁰ electrons of Zn has an effect on predictions. The 7th-period case of strong 6d involvement in copernicium is something like the relativistic further delay in the 7th row, in that not only is Cn a transition metal in the sense that it forms ions with an incomplete 6d subshell, it is questionable if Rf is. Unlike the later 6d metals, the dication Rf²⁺ is already d⁰, and the probable lack of a stable +3 state for Rf matches the lack of a stable +2 state for yttrium while the beginning of an unstable reducing Db^IV seems to match Zr^III and Hf^III well, so that the transition metals proper of the 6d row are probably Db–Cn instead of Rf–Rg. That would seem to skew things even further to including group 12 as a d-block group.) Double sharp (talk) 15:05, 15 March 2018 (UTC)

@Double sharp: 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.

Condensed-phase configurations appeal for B-Al-Sc-Y because of p-subshell occupancy in d-metals, so I'd be cautious with them. Droog Andrey (talk) 17:31, 15 March 2018 (UTC)

@Droog Andrey: Looking forward to seeing the results of that! ^_^ I think that the "delayed collapse" of 5f should result in Ac showing much less than Lr regardless. It would also be interesting to similarly measure d-involvement for Ca-Sr-Ba-Ra vs. Zn-Cd-Hg-Cn. I agree that condensed-phase configurations can be quite troublesome sometimes; I'll write a more detailed response on that later. Double sharp (talk) 23:40, 15 March 2018 (UTC)

Part 5

@Droog Andrey:

Lu is obviously closer to the remainder of the 5d transition metals than La, just look at the trends La-Hf-Ta-...-Hg and Lu-Hf-Ta-...-Hg.

Do you have any citations in support of this? Here is a quote from Restrepo’s paper (Restrepo G 2017, "Building classes of similar chemical elements from binary compounds and their stoichiometries", in MA Benvenuto and T Williamson (eds), Elements old and new: Discoveries, developments, challenges, and environmental implications, American Chemical Society, Washington, DC, pp. 95–110):

Scerri has discussed about the element at the beginning of the third row of the transition elements, which in some tables is La and in others Lu (9). Schwarz and Rich have stated that Lu cannot be considered a lanthanoid, for it does not fill f orbitals as they are already filled; and have suggested that Lu should be regarded as a transition metal (33). According to our results, La appears in between two clusters, one of 11 lanthanoids and another of transition metals, namely {Y,Sc}. Lu is part of the clusters of 11 lanthanoids and the smallest cluster containing it is {Ho,Er,Lu}, which shows that Lu is more similar to lanthanoids than to transition metals, while La share similarities with lanthanoids and with transition metals. Therefore La must be the element located at the beginning of the third row of transition metals if chemical resemblances is what it is to be emphasized.

Sandbh (talk) 10:28, 12 March 2018 (UTC)

I think that this does not quite answer the same question that Droog Andrey and I are bringing up. We are not comparing La and Lu to Sc and Y, but to Hf through Hg (which we both agree form the rest of the 5d series). These intraperiod resemblances are naturally swamped by the closer intragroup resemblances; but periodicity is based on trends, not just similarities. Double sharp (talk) 14:31, 12 March 2018 (UTC)

@Droog Andrey:

You compare Eu and Yb with Cr and Cu, but that's just ridiculous. Look at the densities, phase transition temperatures, standard potentials, electronegativity, etc. along the atomic number, and you will see that.

I was only comparing the pattern of electron configurations, nothing more. Sandbh (talk) 10:33, 12 March 2018 (UTC)

@Sandbh: Well, yes, Eu and Yb "promote" a reserve inner electron to the outer valence core in comparison to the condensed-phase configurations of the other Ln, like Cr and Cu do in the gas-phase configurations of the 3d metals. But clearly this is not comparing like with like. If you take condensed-phase configurations in the 3d metals, the anomalies do not appear at Cr and Cu.

More importantly, the effects that the half- and fully-filled shells are purported to explain do not happen at Gd/Lu and Cr/Cu, but at Eu/Yb and Mn/Zn. This implies that Eu and Yb are taking analogous positions in the 4f series as Mn and Zn do in the 3d series. After all, I recall that one reason we were going for condensed-phase configurations and Sc-Y-La is to explain the trivalence of the Ln; the configurations are there to explain chemical and physical properties that are the subject matter of periodicity. In other words, I think we should treat them as a means to an end rather than an end. I find this a convincing argument for Sc-Y-Lu that would have been excellent to have had in our submission. Of course, we must consider it against the Sc-Y-La arguments, but I think the case for Sc-Y-Lu is growing on me; I have to think about it a little more, though. Double sharp (talk) 10:46, 12 March 2018 (UTC)

Could we please back up here. I was only commenting on gas phase configurations. I said, " 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 [from the pov of what's going on with the inner shell configurations, in deciding where to split the d block and the f block into two tranches each]." That is all I said. Sandbh (talk) 11:16, 12 March 2018 (UTC)

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. Double sharp (talk) 12:17, 12 March 2018 (UTC)

@Droog Andrey:

The comparison of d-block with f-block is valid simply because of the same number of outer-shell electrons.

That's true. I am however concerned that what's going on with the inner shell electrons is inconsistent. All TMs have inner shell d electrons. Of the f block elements, La and Ac don't have inner shell f electrons, whereas Ce to Lu do. We can argue the toss on Th, in the series Th to Lr, since Th formally has no f electron. But we know that Th has a low-lying f-orbital, that 5f orbitals demonstrably contribute in metallic thorium (being hybridised with the 6d and 7s levels), and resulting in its FCC structure, and that the electron configuration of the Th³⁺ ion is [Rn]5f¹. Sandbh (talk) 11:04, 12 March 2018 (UTC)

@Sandbh: I haven't looked for citations on La vs. Lu similarity to transition metals, but just look at the trends I mentioned, starting from corny densities and melting points and finishing with coordination chemistry.

On the validity of the d-block vs. f-block comparison: we just look at the trend for inner shells no matter which subshells are in them and which configurations they have in each particular case. That simply works for all the groups from 2 to 13. Droog Andrey (talk) 13:07, 12 March 2018 (UTC)

We need a data page for electronic configurations of stable phases of chemical elements.

Electronic configurations of the standard or stable phases can be different from standard phase of elements. 

Element	Ln atom	Ln2	Ln metal
La	ds2	d2s	d1.5sp0.5
Ce	fds2	fd2s	fd1.5sp0.5
Pr	f3s2	f2d2s	f2d1.5sp0.5
Nd	f4s2	f3d2s	f3d1.5sp0.5
Pm	f5s2	f4d2s	f4d1.5sp0.5
Sm	f6s2	f6d0.5sp0.5	f5d1.5sp0.5
Eu	f7s2	f7d0.5sp0.5	f7d0.5sp0.5
Gd	f7ds2	f7d2s	f7d1.5sp0.5
Tb	f9s2	f8d2s	f8d1.5sp0.5
Dy	f10s2	f10sp	f9d1.5sp0.5
Ho	f11s2	f11sp	f10d1.5sp0.5
Er	f12s2	f12sp	f11dsp
Tm	f13s2	f13sp	f12dsp
Yb	f14s2	f14sp	f14d0.5sp0.5
Lu	f14ds2	f14dsp	f14dsp

For example, electronic configurations of each carbon atom at standard phase of carbon (graphite) is s¹p³. Why don't we make those data page? --Sharouser (talk) 13:08, 12 March 2018 (UTC)

It would indeed be very interesting and I support the idea, though we'd need to go and take information from a lot of sources (not all of which agree). There is also the problem of overlapping bands making exact numbers hard to pin down for some elements. Double sharp (talk) 13:23, 12 March 2018 (UTC)

Would it be useful if I created a template that does the formatting: {{elconfig|NG=|linkNG=|f=14|d=0.5|s=1|p=1}} → f¹⁴ d^0.5 sp (plus some smarter options)? -DePiep (talk) 14:53, 12 March 2018 (UTC)

To some extent what you see above is shorthand; the source should really be saying [Xe]5d6s² or indeed [Xe]5d¹6s² for gaseous La atoms, but since the context is the lanthanides it is clear that "f, d, s, p" mean "4f, 5d, 6s, 6p" respectively and that the [Xe] core is implied. So while a template may be a good idea, it would have to be a good deal more complicated to deal with all possible uses. Double sharp (talk) 02:54, 14 March 2018 (UTC)

OK then. Only if it helps. We'd first have to be clear even about spacing ;-) -DePiep (talk) 01:39, 18 March 2018 (UTC)