User:Sandbh/Group 3

The following is an exact copy of the submission as was originally done in 2017.

On 5 April 2020, one of the two authors (Double sharp), having learnt more about chemistry and periodicity from Droog Andrey, withdrew his support for the article and what he has written. He now supports Sc-Y-Lu per Jensen's argument of chemically active f-orbitals in La and Ac which are absent from Lu and Lr. Double sharp (talk) 13:44, 2 April 2021 (UTC)

Cover sheet

11 January 2017

Eric Scerri
IUPAC Task Group Chair
The Constitution of Group 3 of the Periodic Table

SUBMISSION TO TASK GROUP

1. I refer to your request for comments on this project, as advertised in Chemistry International, March–April 2016.

2. Please find attached our submission in support of -La-Ac. It comprises:

♦  arguments supporting -Lu-Lr, followed by arguments supporting -La-Ac;

♦  our analysis of each argument and its validity;

♦  a comparison of the overall case for the two options; and

♦  an explanation of our support for -La-Ac.

3. Many of the arguments have been made in the literature; others arose in the course of our deliberations or from contributions by colleagues. While we strived to make each of our analyses self-contained, the systemic nature of the elements and their properties obliged us to occasionally reiterate some of our earlier thinking.

4. On the literature in particular, we note an abundance of arguments pro -Lu-Lr and a dearth pro -La-Ac. Combined with our desire to otherwise limit redundancy and to not re-present counterarguments made in one section as arguments in another section this may give an impression that our submission is unbalanced. Be that as it may, we have attempted to judge each argument and option on its overall merits.

5. We thank Wikipedia editor R8R Gtrs* for extensive, thought-provoking and insightful comments provided upon reviewing the first draft of our submission. One of us (Sandbh) thanks you for your help over the years in reading the e-mails they sent you on this topic and sharing your insights. We further record our appreciation for the series of papers authored by Professor Jensen on this question.

6. We emphasize that this is not a Wikipedia submission. Rather, it is a submission made by two Wikipedia editors acting in our personal capacities.

Thank you for the opportunity to contribute to your project.

Sandbh	Double sharp
Wikipedia editor   WikiProject Elements	Wikipedia editor WikiProject Elements

__________

*also a member of WikiProject Elements

Abstract

Drawing on the literature, arguments in support of -Lu-Lr are reviewed and analysed for their validity. Most of these arguments are based either on group trends compared with other members of the d block, or similarities between Lu and Sc and Y. The same process is then applied to -La-Ac arguments dealing with basicity, condensed phase electron configurations, and the behaviour of group 3 as pre-transition metals. Comparing the two sets of arguments, we conclude that those supporting -La-Ac are stronger.

Lu-Lr arguments

1958: Electron configurations

Landau and Lifshitz (1958, pp. 256–257) argue for group 3 membership of Lu on the basis of its complete 4f shell. They write:

The filling up of the 3d, 4d, and 5d shells…[has] a characteristic feature…[of] the "competition" between the s and d states…The filling up of the 4f shell also occurs in a slightly irregular manner characterized by the competition between 4f, 5d, and 6s states…In books of chemistry, lutetium is usually placed in the rare-earth elements. This, however, is incorrect, since the 4f shell is complete in lutetium; it must therefore be placed in the platinum group… [They refer to Sc–Ni as the Iron group; Y–Pd as the Palladium group; and La+Lu–Pt as the Platinum group.]

Scerri (2015, pers. comm., 9 December) referred to this as "one of the oldest categorical statements in favor of Sc Y Lu Lr".

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

1965: Similarity of Lu with Sc and Y

A number of authors have argued that because Lu is more similar to group 3 than is La, it follows that Lu should be moved into group 3. For example:

• "In a widely-used version of the periodic table, lanthanum is classed in the same column with scandium and yttrium. However, in a number of respects lutetium resembles scandium and yttrium more closely than lanthanum does. Hence the periodic table should be modified so that scandium, yttrium, and lutetium are in the same column." (Hamilton 1965)

• Jensen (1982), as discussed later in this submission, partly relies on greater similarities in the properties of Sc-Y-Lu, than is apparently the case for Sc-Y-La.

• McCaw (2015), in a comment to an Eric Scerri blog, opined that "the chemistry of Lu is more like the other nine 5d metals than is the chemistry of La" and added that he based this comment "on what I read in the Jensen paper…[1982]. Apparently the methods of separating Lu from rare earths are the same as for Sc and Y but La is different - this is referenced to S I Levi's "The Rare Earths". The greater chemical similarity of Lu than La to the trends of that group and period is also referenced to T Moeller in "The Rare Earths", ed. F H Spedding & A H Daane." (McCaw 2015)

Analysis: 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.

We comment on Moeller's "The Rare Earths" later in this submission, in the Separation groups section.

1967: f-character of La

Speculation as to 4f electrons influencing the properties of the lanthanides and their compounds dates back as far as 1965 (Gschneidner 1971, p. 405).

For lanthanum, the earliest reference we could find was Matthias et al. (1967) who attributed its melting point, which is seemingly lower than would be expected from its periodic table position, to the presence of some f character, "in the hybridised wave functions describing the band structure for the valence electrons."

Subsequently, Gschneidner (1971; 1980; 1993; 2006; 2016) may have been the most enduring advocate for the presence of 4f character in lanthanum. Whilst he acknowledged that La nominally has no 4f electrons he also said that the 4f levels lie just above the Fermi energy, "and could easily be occupied at least to a small extent, but sufficient to account for the observed effect(s)." These effects largely encompassed thermodynamic properties, and the stability constants of rare earth EDTA complexes. While we found evidence for the former effects to be plausible, the latter effect appeared to us to be inconclusive (see Gschneidner 1993, passim; p. 8). It could be attributed to varying ionic radii, within error limits, rather than to 4f influence.

A few other authors have suggested the presence of some 4f character in lanthanum: Kmetko and Hill 1976; Glotzel 1978; Welling 1978; Smith 1980; Dolg and Stoll 1996; Xu et al. 2013.

For lutetium, Ratto, Coqblin and d'Agliano (1969, pp. 498, 509) suggested that its lack of superconductivity might be attributable to a small 4f character. We look closer at the question of Lu superconductivity later in this submission.

A few other authors have referred to some of the properties of Lu being influenced by the presence of its filled 4f shell: Langley 1981; Tibbetts and Harmon 1982; Clavaguéra, Dognon and Pyykkö 2006; Xu et al. 2013; Ji et al. 2015. The most surprising of these is likely to have been Clavaguéra and colleagues, who reported a pronounced 4f hybridisation in LuF₃ on the basis of three different relativistic calculations. Their findings were questioned by Roos et al. (2008) and Ramakrishnan, Matveev and Rösch (2009).

An analogous situation certainly occurs at the end of the d-block, in group 12. Zinc and cadmium have HCP crystal structures with c/a ratios of 1.856 and 1.886, much higher than the ideal value (of 1.633). These deviations have been attributed to covalent bonding contributions arising from hybridisation of the filled d band with the conduction band (Steurer & Dshemuchadse 2016, p. 207). We note that condensed mercury has a distorted structure, and mixed metallic-covalent bonding (Steurer & Dshemuchadse 2016, p. 207; Russell & Lee 2005, p. 354).

Analysis: We think it plausible that the low-lying 4f levels in La may influence some of its properties. It is also conceivable that the filled 4f shell of Lu may influence some its properties but, if so, the scope of this influence is likely to be smaller and more obscure.

Overall, we think the presence of any 4f influence, as a relatively low-order phenomenon, would only be a "tipping point" argument. That is to say, if the merits of -La-Ac and -Lu-Lr are otherwise similar in terms of which one is placed under Y a case could then be made for -Lu-Lr.

1982: Separation groups

Jensen (1982, p. 634) writes, "For quite some time it has been known that Y, and, to a lesser degree, Sc are closer in their chemical properties to Lu and the other heavy rare earths than they are to lanthanum (1,2) and on this basis alone a number of chemists in the 1920's and 1930's assigned Lu rather than La to group IIIB (3)." Jensen's three notes read as follows:

(1) In the classical chemical methods for separating the rare earths Sc, Y, and Lu occur together in what is called the Y group, whereas La and Ac occur together in what is called the Ce group. See, for example, Levi, S.I.,"The Rare Earths," Longmans, Green and Co, London, 1915, Chap. IX.

(2) Moeller, T., "The Rare Earths", Spedding, F. H., and Daane, A. H., (Editors), Wiley, New York. 1961. Chap. 2.

(3) See, for example, Shemyakin, F. M., Zh. Obshch. Khim., 2, 62 (1932) and Bury, C. R., J. Amer. Chem. Soc., 43, 1602 (1921). Further examples can be found in reference (14): Mazurs, E. G., "Graphic Representations of the Periodic System During One Hundred Years" Univ. Alabama Press, University, Alabama, 1974

Analysis: The fact that Sc, Y and Lu occur in the so called yttrium group, and that La and Ac occur in the "cerium" group does not imply anything particularly significant; it is simply a reflection of the increasing basicity of these elements as atomic radius increases. Taking the alkaline earth metals as another example, Mg (less basic) belongs in the "soluble group" and Ca, Sr and Ba (more basic) occur in the "ammonium carbonate group" (Moeller et al. 1989, pp. 955–956, 958). Making an argument that Lu should go under Y because they occur in the same chemical separation group fails to consider separation group patterns elsewhere in the periodic table and, in this context, does not demonstrate why Lu under Y is a superior outcome.

We were not able to find anything in reference (2) that supported Jensen's statement that Y and Sc were closer to Lu, aside from a comment (p. 21) that the chemistry of Sc differs significantly from that of the "rare-earth elements" (La–Lu), something that is to be expected given the differences in radii. Similarly, Li is usually found with Mg and not with the heavier alkali metals Na and K; and Be does not occur together with Mg, Ca, Sr, and Ba. Reference (2) in fact describes Sc, Y, La and Ac, rather than Sc, Y, Lu and 103, as the first members of the four "transition" series.

Of the older periodic tables mentioned in reference (3):

• Bury shows Sc-Y-Lu on the basis of chemical properties, but does not elaborate which properties he had in mind. He draws an analogy to Be and Mg resembling Zn better than Ca. The fact that modern periodic tables generally show Be-Mg-Ca rather than Be-Mg-Zn, despite these resemblances, calls into question the validity of Bury's analogy. At the very least, it suggests that there are other factors at work that can overrule these resemblances, and that these may also apply to the question of group 3.

• One needs to be careful with Mazurs as some of his renderings of tables appearing in the literature are fanciful. He includes plenty of tables with Lu in group 3 as well as La-Ac tables pre-dating, dated during, and post-dating the 20s and 30s. There is no doubting both kinds of tables have been around for quite a while.

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

Furthermore, the historical record does not necessarily flag ongoing relevance. As noted, many old tables from this time period also place Be and Mg in group 12 with Zn, Cd, and Hg, a practice which has since been deprecated.

Irregular electron configurations

Jensen (1982, pp. 634–635) argues for -Lu-Lr on the basis that La and Ac can be regarded as being f-block elements with irregular electron configurations, just like Th. He starts by saying that La and Lu have equal claims to the position under Y, based on their differentiating d electrons. He then asserts that nobody doubts Th is an f-block element with an irregular electron configuration i.e. [Rn]6d²7s² and that this therefore "strongly" supports treating La i.e. [Xe]5d¹6s² and Ac i.e. [Rn]6d¹7s² as f-block elements with irregular electron configurations. Thus Lu i.e. Xe4f¹⁴5d¹6s² and Lr i.e. Rn5f¹⁴7s²7p¹ fit under Y, with the result that each element in periods 6 and 7 of the d block has either a completed 4f¹⁴ or 5f¹⁴ shell.

Analysis: This is a weak argument.

Firstly, it is based on gas phase electron configurations which have limited relevance to the chemistry of the elements. (We discuss gas phase v condensed phase electron configurations later in this submission.)

Secondly, it seems to be only a "tipping point" argument. That is to say, if the merits of -La-Ac and -Lu-Lr are otherwise similar in terms of which one is placed under Y then, of course, -Lu-Lr would be the one given this would result in completed 4f¹⁴ or 5f¹⁴ shells across periods 6 and 7 of the d block.

Thirdly, though nobody doubts that Th is an f-block element, this is probably due to the fact that the 5f orbitals demonstrably contribute in metallic thorium (being hybridised with the 6d and 7s levels), and that the electron configuration of the Th³⁺ ion is [Rn]5f¹, thereby showing that the 5f orbitals are low-lying and available for chemistry. In contrast, we do not think that what evidence there is for f orbital involvement in La is of comparable significance (we return to this question later in our submission). While slight irregularities in electron configuration are of course permissible and occur throughout the d and f blocks, it does not seem right to us that elements with no substantial f orbital involvement should be placed in the f block before elements that do have such involvement. (There are precedents: while neither Ca nor Zn has d orbital involvement, Zn is placed in the d block because it notionally completes the subshell, while Ca has not even started it yet.)

Electron configuration analogy

Jensen (1982 p. 635–636) notes that intraperiod and (Lu–Hg) and intragroup (Sc–Lu) electron configurations favour Lu under Y. That is to say all of the period 6 d bock elements would have a filled f shell and, in going from period 5 to 6 there would be a consistent addition of 32 to the atomic number.

Analysis: Not only does the s-block already break this pattern (going from Sr to Ba does not add 4f electrons, but going from Te to Po does), but the asymmetry in atomic number is already broken in period 1 for chemical reasons: consider H and Li (Z = 1, 3) versus He and Ne (Z = 2, 10). While the differences between the chemistry of La and Lu are obviously not of the same order, it should at least raise the possibility that this argument needs to be assessed in light of other other considerations, as discussed hereafter, and indicates that it is not a primary basis for element placement but rather a secondary one.

Overall, we think a consistent atomic number pattern across the period 5 and 6 elements from group 3 onwards (rather than from group 4 onwards) would only be a "tipping point" argument. That is to say, if the merits of -La-Ac and -Lu-Lr are otherwise similar in terms of which one is placed under Y a case could then be made for -Lu-Lr.

Ionization potentials

Citing the Russian chemist Chistyakov (1968), Jensen (1982, p. 636) argues that the trend in the sum of the first two ionization potentials going down Sc-Y-Lu is similar to that occurring in groups 4 to 8, and unlike that of Sc-Y-La, thereby supporting Sc-Y-Lu.

Analysis: Factually correct but incomplete as an argument, and of questionable relevancy. Why the sum of the first two ionization potentials? In any event, the trend in this case (for Sc-Y-La) is similar to the trend seen in the group 2 and 1 metals, -Ca-Sr-Ba and -K-Rb-Cs. As well, the trend in the sum of the first three ionization energies for Sc-Y-La is a better fit with the trend occurring in groups 2 to 1, whereas Sc-Y-Lu resembles that of groups 4 and 5 (Cowley 2002).

A closer look: Chistyakov compares the atomic radii and sum of the first two ionization energies (IE) for groups 3–8 and 11-12 and finds that Sc-Y-Lu is a better fit than -Y-La. He says this is probably due to the impact of the lanthanide contraction on the period 6 transition metals. For Group 11 he only uses the first IE's. In his conclusion he writes, "The radii of the free atoms, recently calculated from Dirac's equation, and the sums of the first two ionization potentials, i.e., parameters of the external ns-electrons of the d-elements, are periodic functions of the atomic numbers in each side d-subgroup." We thought his reference to "ns-electrons" explained why he was using the sum of the first two IE's rather than the first three (since it was group 3 that was the anomaly) but this does not work since, for example, Nb, Cr and Mo only have one s electron, so he is not really comparing like with like as, to get the sum of the first two IE's for these metals he has to include one d electron each. And comparing the first two IE's of the group 11 metals fails to produce the pattern seen in the other groups, although admittedly doing so involves one s and one d electron for all three. We think this explains why Jensen left out the group 11 and 12 metals in his article.

Atomic radii

Again citing Chistyakov, Jensen argues that the trend in atomic radii going down Sc-Y-Lu is similar to that occurring in groups 4 to 8, and unlike that of Sc-Y-La, thereby supporting Sc-Y-Lu.

Analysis: Factually correct but incomplete as an argument. The trend in atomic radii going down Sc-Y-La is instead similar to the trend seen in the group 2 and 1 metals, -Ca-Sr-Ba- and -K-Rb-Cs-.

Ionic radii

Jensen (1982, p. 636) argues that comparisons in periodic trends favour Sc-Y-Lu.

Analysis: Consulting the literature, the trend going down group 3 appears to be inconclusive. Using ionic radii for coordination number 6 (Aylward & Findlay 2008, pp. 5–13), the trend going down Sc-Y-Lu looks like the trend seen in groups 4–10, where the radii of the period 5 and 6 metals are either similar or the period 6 member is smaller than the period 5 member. On the other hand, the trend of steadily increasing ionic radii going down Sc-Y-La-Ac matches the trend seen in main groups 1 and 2, and 13 to 16 (Wiberg 2001, p. 119).

In contrast to Jensen, a comparison of ionic data by Atkins et al. (2006, p. 34) concludes that Sc-Y-La is preferred over Sc-Y-Lu. Their comparison is expressed as a problem and answer, in the context that ionic radii generally increase down a group (pp. 89–90):

Problem 1.14

At various times the following two sequences have been proposed for the elements to be included in Group 3: (a) Sc, Y, La, Ac; (b) Sc, Y, Lu, Lr. Because ionic radii strongly influence the chemical properties of the metallic elements, it might be thought that ionic radii could be employed as one criterion for the periodic arrangement of the elements. Use this criterion to describe which of the sequences is preferred.

Answer

The common ionic state for the group 3 elements is +3, so the electron configurations for the elements in each sequence are:

Sequence (a)

Sc³⁺: [Ar] Y³⁺: [Kr] La³⁺: [Xe] Ac³⁺: [Rn]

Sequence (b)

Sc³⁺: [Ar] Y³⁺: [Kr] Lu³⁺: [Xe]4f¹⁴ Lr³⁺: [Rn]5f¹⁴

The electron configurations in sequence (a) are all rare gas configurations so the ionic radii should increase slowly as the principal quantum number, n, increases. In sequence (b), Lu3+ and Lr3+ also have filled f subshells. Since f electrons shield the nuclear charge so poorly, Z* is expected to be much larger for Lu³⁺ and Lr³⁺, thereby reducing the ionic radius. Thus, sequence (a) is preferred based on ionic radii. The measured ionic radii bear this conclusion out. For six coordinate radii, the values found are 0.885 Å for Sc³⁺, 1.040 Å for Y³⁺, 1.172 Å for La³⁺, and 1.001 Å for Lu³⁺.

Atkins et al. shed no further light on the group 3 question. The periodic table on the inside cover of their text shows Sc-Y-La-Ac; the general structure of their periodic table on page 10 is Sc-Y-Lu-Lr; the accompanying text says that the f block is divided into the lanthanides (57–71) and actinides (89–103), and thus 15 places wide; the table of atomic radii on page 24 is Sc-Y-Lu; while at the start of their chapter on the f-block metals, they say that the f block runs from Ce to Lu, and Th to Lr, and is thus 14 places wide. Their text therefore contains references to, or alludes to notions of, the three major variants of the periodic table: a 14-place wide f-block starting with either La-Ac or Ce-Th; and a 15-place wide f-block. At best, the notion of ionic radius as a criterion for the arrangement of group 3 appears to have been intended as no more than a conversation starter.

Redox potentials

Jensen (1982, p. 636) argues that comparisons in periodic trends favour Sc-Y-Lu.

Analysis: We had a look at the National Institute of Standards and Technology standard electrode potential data (Bartsch 1989) but were unable to discern any meaningful differences in periodic trends between Sc-Y-La and Sc-Y-Lu, and neither choice results in a trend that is very similar to those of the neighbouring groups.

Electronegativities

Jensen (1982, pp. 635, 636) argues that comparisons in periodic trends for Allred-Rochow electronegativity favour Sc-Y-Lu.

Analysis: Factually correct but incomplete as an argument. The trend in going down Sc-Y-La is instead similar to the trend seen in the group 2 and 1 metals.

Further, the choice of electronegativity scale is a little arbitrary. The Pauling scale, for example, favours Sc-Y-La. Groups 1, 2, 4, and 5 have the period 6 element somewhat more electropositive than the period 5 element; this works with La (1.1) under Y (1.22) but not with Lu (1.27) under Y. In the Mulliken scale (Boeyens 2008, pp. 207–208), the values for La (1.74) and Lu (1.70) are both less than that of Y (1.81).

Melting points

Jensen (1982, pp. 635, 636) argues that the trend in melting points going down Sc-Y-Lu is a better fit with groups 4 to 10 than is the case with Sc-Y-La, thereby supporting Sc-Y-Lu.

Analysis: Factually correct but incomplete as an argument. The trend in melting points going down Sc-Y-La is instead similar to the trend seen in the group 2 and 1 metals, -Ca-Sr-Ba and -K-Rb-Cs.

Crystal structures (elements)

Jensen (1982, p. 636) contends that the most compelling evidence for Sc-Y-Lu comes from the physicists. He says that, as a first example, the crystalline structures for Sc, Y, Lu are all hexagonal close packed (HCP) whereas that of La is double hexagonal close packed.

Analysis: The example given is true, but its relevance is questionable. For example, the structures of the group two metals Be, Mg, Ca, Sr, Ba, and Ra are HCP; HCP; face centred cubic; face centred cubic; body centred cubic; and body centred cubic. Groups 7, 8, 9, and 10 also show inconsistencies in crystalline structures.

Crystal structures (oxides, chlorides, various intermetallics)

Continuing the theme, Jensen (1982, p. 636) further observes that the crystalline structures of the oxides X₂O₃ for Sc, Y and Lu are the same whereas that of La is different, and that the same pattern occurs with the chlorides -Cl₃ and various intermetallic compounds.

Analysis: True, but not relevant for at least oxides and chlorides. Different structures for homologous ionic compounds are unremarkable. Consider, for example, NaCl vs. CsCl (and this is for the alkali metals, the model example of great group trends). NaCl has the sodium chloride (rocksalt) structure; CsCl has a different (primitive) cubic structure, as shared with caesium bromide and caesium iodide, and many binary metallic alloys. When both ions are similar in size (Cs⁺ ionic radius 174 pm for this coordination number, Cl⁻ 181 pm) the CsCl structure is adopted; when they are different (Na⁺ ionic radius 102 pm, Cl⁻ 181 pm) the sodium chloride structure is adopted. When we move even slightly away from the model trends in group 1, to the alkaline earth dihalides, we find that there is not a single choice of alkaline earth metal or halogen that leads to a totally consistent set of structures. This thus strikes us as too harsh a criterion to be possibly used throughout the periodic table.

The reference to intermetallic compounds (Hamilton 1965, p. 637) is inconclusive. The author says, "There are at least several intermetallic compounds where the compound with La has a different crystal structure from the corresponding compounds with Sc, Y, and Lu." Again, this is not entirely unexpected. Given its position in the next row down in the periodic table, lanthanum atoms are larger than scandium or yttrium atoms. It would therefore stand to reason that they should not be able to pack in a crystal structure in quite the same way as the smaller scandium, yttrium, or lutetium atoms.

Excited state spectra

Again citing Hamilton, Jensen argues for Sc-Y-Lu on the basis of commonalities in the excited state spectra of Sc, Y and Lu. He says that the atomic spectra for Sc, Y, and Lu differ from that of La. Specifically, for La, "excited energy levels have been observed which can be attributed to an electron in an f orbit" (Hamilton 1965, p. 637) whereas this is not the case for Sc, Y, or Lu thereby indicating, "that the 4 f wave function in La differs from the 4 f wave function in Sc and Y or the 5 f wave function in Lu; this causes the various line strengths to be different." (Hamilton 1965, p. 637)

Analysis: OK as an ephemeral tipping point argument, at best.

An analogous situation occurs in group 2, when we compare Be and Mg with the heavier alkaline earths (Ca, Sr and Ba). Here, the empty d-bands in the latter lie close enough to influence spectroscopic properties and enter into supervalent hybridisation in CaF₂, SrF₂, SrCl₂ and BaX₂, such that Ca, Sr and Ba have been called "incipient transition metals" (Myers 1997, p. 201–202).

We would regard La as an "incipient inner transition metal" with a similar presence of f-bands. However, just as Ca, Sr, and Ba are not d-block elements and precede the d block, so we argue that La (and Ac by default) are placed quite well in the positions immediately preceding the f block.

Superconductivity

Jensen (1982, p. 636) says Sc, Y, and Lu are not capable of superconductivity in bulk form at normal pressure whereas La is, therefore supporting Sc-Y-Lu on the basis of shared properties.

Analysis: Inconclusive, due to contradictory and incomplete information.

Nikulin, Volkenshtein and Staftsev (1973) reported ambient pressure superconductivity in Lu at 0.10 K. This is the figure given by, for example, Buzea and Robbie (2004).

In contrast, the ASM Metals Handbook (1990, p. 1183) indicates that "bulk lutetium is not superconducting down to 0.03 K at atmospheric pressure; it becomes superconducting at 0.022 and 4.5 GPa."

Probst and Witting (1978, p. 764) shed some light on the discrepancy. They write that "Nikulin et al. (1973) reported a very broad superconducting transition at normal temperature below 0.5 K for a Lu sample of a nominal purity of 99.9%. Another sample containing large amounts of iron was not superconducting...However a T_c as large as 100mK does not appear to be acceptable. Jensen (1965) also observed broad superconducting translations between 0.9 and 0.1 K. He attributed them to precipitations of tantalum which dissolves in Lu during the manufacturing process in Ta-crucibles."

Dougherty (2009?) picks up the thread: "The number of reports of one bar superconductivity for Lu is very limited (Nikulin 1975). We removed Lu from the group of superconducting elements at one bar (Buzea & Robbie 2004) because none of the subsequent investigators of Lu’s superconductivity [no details provided] confirmed it was a superconductor at one bar. Lutetium’s atomic resistivity is an order of magnitude lower than that of lanthanum at ~180 Ω-atom. This makes it even more unlikely that lutetium is in fact a superconductor at one bar pressure (because the band gap for conductivity is quite small, suggesting involvement of 6s electrons in the ground state conduction band) and further justifies our removing it from the list of one bar superconducting elements (Buzea & Robbie 2004)."

Given this background, and without further testing of a high purity sample, the superconductivity status of Lu at ambient pressure appears to be an open question.

Conduction band structures

Citing Merz and Ulmer (1967), Jensen says that Sc, Y and Lu have conductivity bands with a d block like structure whereas La does not, thereby supporting Sc-Y-La on the basis of shared properties.

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

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

1985: Seven properties

In a paper prepared for presentation at the 33rd IUPAC Assembly in Lyon, France, Holden (1985) makes a case for -Lu(Lr) on the basis of:

1. Landau's complete 4f shell argument;
2. average density data for Ca-Ti and Sr-Zr;
3. the crystalline structures of Sc, Y, Lu, La and their sesquioxides
4. melting points
5. superconductivity behaviour
6. shear and Young's moduli; and
7. coefficient of thermal expansion values.

Of these arguments, Holden estimated the strongest to be that of Landau.

Analysis: As a general observation we think Holden fell into the trap of focussing on similarity as a determinant of group membership, to the neglect of periodic trends. We further think that, with the benefit of over 30 years of hindsight, his reliance on Landau to "lead the charge" did not do much for his case.

We now analyse only those of his arguments that we have not already addressed:

Average density data
We do not think the density argument withstands scrutiny, since examples can be found contradicting it across the table. For example, the density of Be is about the average of those of Li and B, and the density of Mg is about the average of those of Na and Al, but due to the insertion of the d-block between groups 2 and 13, the density of Ca is not anywhere near the average of those of K and Ga. Similarly, the argument that the density of a group 4 element should be about the average of that of its group 3 and 5 neighbours does not weaken the case for Sc-Y-La-Ac since an Sc-Y-La-Ac table implies there is an f-block insertion between group 3 and group 4 and hence that the density triad for La-Hf-Ta would be "broken".

We further note that the density of Ba (in group 2) is about the average of the density of Cs (group 1) and that of La (group 3). This relationship is reinforced by analogies seen in period 5 for Rb-Sr-Y, and in period 4 for K-Ca-Sc.

Shear and Young's modulus
Taking our values from Martienssen and Warlimont (2015) for shear modulus, and reading down each group:

• group 1 and 2 values fall
• Sc-Y-La values fall
• Sc-Y-Lu values fall, then rise
• group 4 values fall, then rise
• group 5–9 values rise
• group 10 values fall, then rise
• group 12 values are incomplete.

Taking our values for Young's modulus from the same source, and reading down each group:

• group 1 and 2 values fall
• Sc-Y-La values fall
• Sc-Y-Lu values fall, then rise
• group 4, 5 and 10 values fall, then rise
• group 6–9 values rise
• group 12 values are incomplete.

We consider the net results to be inconclusive.

Thermal expansion
Taking our values from Russell and Lee (2005), and reading down each group:

• group 1 values rise
• group 2 values, from Mg onwards, fall
• Sc-Y-La-Ac values rise
• Sc-Y-Lu values rise, then fall
• group 4 values fall, then plateau
• group 5–11 values fall
• group 12 values fall, then rise.

We consider the net result to be inconclusive.

2005: Physical properties

On the basis of 18 mainly physical properties Horovitz and Sârbu (2005) argue that Sc and Y are rather dissimilar to the lanthanides and that since Lu is similarly an outlier among the lanthanides, it should be assigned to Group 3 as a homologue of Y.

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

2006: Characteristic electron configurations of ions

Wulfsberg (2006, p. 3) advocates teaching chemistry by focusing on the electron configurations of the ions of elements rather than their gas phase configurations and, on this basis, advocates for -Lu-Lr. He writes:

Besides charge, size, and Pauling electronegativity, other parameters such as valence electron configurations of atoms and ions are also important in predicting the periodicity of chemical properties. Since ions are more important than isolated gaseous atoms for nearly all atoms, and important ions have no anomalous electron configurations, there is little reason to worry students with anomalous electron configurations of atoms: we prefer to teach ‘characteristic’ electron configurations without anomalies in the occupancies of d and s orbitals in the transition elements or d, s, and f orbitals in the inner transition elements. Such characteristic electron configurations are most easily arrived at by considering the f-block of elements to begin with La and Ac and end with Yb and No, allowing Lu and Lr to be members of group 3 of the d-block, an adjustment of the periodic table that has been advocated on several chemical and physical grounds.

Analysis: We are puzzled by Wulfsberg's claim. The table to the left compares the electron configurations of the electron configurations of Ln³⁺ ions for the two f-block options (Cotton 2007, p. 150):

	f block
Atom	La–Yb	Ce–Lu
La	[Xe]
Ce	[Xe]4f1	[Xe]4f1
Pr	[Xe]4f2	[Xe]4f2
Nd	[Xe]4f3	[Xe]4f3
Pm	[Xe]4f4	[Xe]4f4
Sm	[Xe]4f5	[Xe]4f5
Eu	[Xe]4f6	[Xe]4f6
Gd	[Xe]4f7	[Xe]4f7
Tb	[Xe]4f8	[Xe]4f8
Dy	[Xe]4f9	[Xe]4f9
Ho	[Xe]4f10	[Xe]4f10
Er	[Xe]4f11	[Xe]4f11
Tm	[Xe]4f12	[Xe]4f12
Yb	[Xe]4f13	[Xe]4f13
Lu		[Xe]4f14

The electron configurations of the corresponding An³⁺ ions are the same but for having an [Rn] core and 5f electrons (Cotton 2007, p. 150).

On this basis, while we agree with the spirit of Wulfsberg's claim namely that that ions are more important than isolated gaseous atoms for nearly all atoms, we find that his support for the f block as La–Yb is misguided, and that his argument in fact (quite strongly and elegantly, to our surprise) supports Ce–Lu, and Th–Lr, with -La-Ac under Y.

2011: Triads

Scerri (2011 p. 135) suggests atomic number triads support Y-Lu-Lr rather than Y-La-Ac.

Analysis: The suggestion is inconsequential since Sc-Y-La form a triad whereas Sc-Y-Lu do not.

2012: Split d block

Scerri (2012) dismisses Sc-Y-La-Ac on the grounds of a symmetry deficit in the 32-column version:

I say "almost entirely" because there does exist a third option, although this can be dismissed on the grounds that it represents a very asymmetrical possibility. As seen in figure 6, the third option requires that the d-block elements should be broken into two very uneven portions consisting of one group, followed by the insertion of the f-block elements and continuing with a block of nine groups that make up the remainder of the d-block elements. Indeed, this form of the periodic table is also sometimes encountered in textbooks and articles, although this fact does not render it any more legitimate.

Wulfsberg (2000, p. 53) likewise invokes symmetry, since he reckons the chemical and electronic properties of La and Lu (and Ac and Lr) are too close to make a call. He cites Jensen's 1982 arguments saying that the "metallurgical" resemblance is much stronger for Lu than La, and has therefore adopted Lu (and by extension, Lr) below Y. More relevantly, he goes on to note that "an important additional advantage is that the periodic table becomes more symmetrical, and it becomes easier to predict electronic configurations."

Analysis: In contrast, Scerri (2015) notes that, "some textbook authors have taken -Lu-Lr up, but the majority seem reluctant." La-Ac is indeed still the most common form although very few authors show it with a split d block. The vast majority use alternative graphical solutions. For example, the Sargent-Welch table shows a single star above the 'a' in La and a double star above the 'c' in Ac, to denote the footnoted lanthanides and actinides.

A desire to keep the d block intact is all fine and well from the perspective of Platonic symmetry, but there is already an established precedent in breaking the s block to prioritise chemistry over Platonic symmetry. Scerri (2015, pers. comm., 21 May) has however questioned the comparability of separating a single element (He) with separating an entire group from other d-block groups. On the other hand, He over Ne involves moving an s-block element over two intervening blocks, into the p block whereas Sc-Y-La-Ac at least maintains its d block identity. Indeed, Hamilton (1965), shows a periodic table extract (groups 1 to 11, plus footnoted Ln and An, showing Ce, Pr…Lu; and Th, Pa…Lw) with a split d block (the gap is between groups 3 and 4) and says that—without any fuss—this is "the periodic table as it is usually presented".

As previously noted, even Jensen (1986) commented on the abuse of symmetry considerations in the construction and interpretation of periodic tables in general. More specifically (2003, pp. 953–954), he noted the triumph of Platonic symmetry over the inconvenient facts of chemistry with respect to the placement of the coinage metals in pre-electronic periodic tables.

Reger, Scott and Ball (2010, p. 295) write that "perhaps" the correct shape of the 32-column periodic table should feature a split d block given the electron configurations of La and Ac, but that "we avoid these structures by splitting the f block from the rest of the periodic table. This also has the advantage of being able to print a legible periodic table on a single piece of paper." (They show La below Y in the rest of their book.)

We support this line of reasoning. The 32-column form of the -La-Ac table may be regarded as being asymmetrical but we do not think this is necessarily significant given other examples of asymmetry in physics. The 18-column form strikes us as representing an elegant synthesis of accuracy and symmetry. Accuracy in capturing the relationships among the elements; symmetry in the maintenance of an intact d block. We think the -Lu-Lr table sacrifices accuracy in the pursuit of symmetry.

In conclusion, are we here to draw a table to reflect Platonic symmetry? Or are we here to draw a table to reflect chemical properties? We firmly advocate the latter.

2013: Carbonyls

Nelson (2013) examines periodicity in carbonyls and on this basis supports Lu in group 3. He argues that the number of outer electrons possessed by an atom, and the number required for it to achieve an inert gas configuration exhibit an almost exact periodicity. Further, these two numbers correlate almost exactly with the highest conventional valency and the highest carbonyl valency exhibited by an element. For example in iron carbonyl, Fe(CO)₅, the carbonyl valency is taken to be 10 whereas Fe has a highest conventional valency of 6. Now, while Y, La and Lu all have a highest conventional valency of 3, Y and Lu require only 15 electrons to achieve an inert gas configuration whereas La would need 29. The latter configuration (Sc-Y-Lu) is therefore preferred.

Analysis: We can see periodicity in carbonyl valencies but the values of the rare earths carbonyl valencies are tentative, incomplete and based on matrix isolation studies. On the lanthanides Nelson says, "The values…for the Ln and An are tentative. These are based on matrix isolation studies. I have adopted the formulae for the highest carbonyls suggested by workers in the field. Errors in these will not significantly affect the argument." This instability is unsurprising given that the 4f shell is very inert and cannot easily participate in pi backbonding.

The issue we see with basing arguments on such unstable species is the many things which can be done that are not representative of the chemistry of the element being considered. We do not think the existence of iridium(IX) is particularly important when countering the generalisation that beyond group 8, the range of oxidation states shrinks. Jensen himself notes that the possible existence of mercury(IV) is just a tiny exception to the far more characteristic main-group chemistry of Zn, Cd, and Hg. Finally, the very existence of the last actinides and the transactinides only occurs under very anomalous conditions: we would not change the name "noble gases" even if oganesson acts like a reactive nonmetal, and already the halogens are often taken to end at iodine instead of the fugitive astatine or tennessine. So while this might be true, we feel it has no more bearing on the placement of La than HgF₄ does on the classification of group 12.

We further query what happens to the s block if one takes this approach. We are not aware of s-block carbonyls, but this would seem to suggest that Mg (which needs 6 electrons to achieve the [Ar] configuration) cannot be placed above Ca (which needs 16 to achieve the [Kr] configuration), and that Sr (which needs 16 to get to [Xe]) cannot be placed above Ba (which needs 30 to get to [Rn]).

2014: Lu as a transition metal

Settouti and Aouragi (2014) conclude that Lu shares many properties and similarities with period six transition metals and, "and can be well described as a transition metal" thereby implying it should occupy the position in the d block below Y. They base this conclusion, using mathematical analysis, on a comparison of the physical and mechanical properties of Lu with those of Cs, Ba, Hf, Ta, W, Re, Os, Ir, Pt, Au, Tl, Pb, and Bi.

Analysis: The authors go too far in saying Lu may well be described as a transition metal since they would also have to show that the properties of Lu in question are closer to e.g. Hf than they are to the other heavy lanthanides, and they did not do that. Other authors have different observations. Spedding and Beadry (1968, p. 377), wrote, "Since metallic lutetium resembles closely erbium and holmium, except that it melts at a slightly higher temperature and is essentially non-magnetic, the details of producing, purifying and fabricating it are almost identical with those described under Holmium." Leal, Restrepo and Bernal (2012) compared 4,700 binary compounds of 94 elements. Sc and Y ended up in their own cluster; Lu ended up in a cluster with Er, Ho and Gd (La landed in its own cluster, as did Ce).

Name matches position

In a comment to an Eric Scerri blog, McCaw (2015) suggests that putting La and Ac in the f block is pleasingly consistent with their names.

Analysis: We consider this argument to be weak and inconclusive. The reason for using convenient trivial names for categories of elements is to describe and simplify the more complex reality that stands before us, not to dictate that reality. The inconsistency between authors on the limits of some of these categories, such as the metalloids, stands as a clear illustration of this.

Placing La and Ac in the f block would visually separates Lu and Lr from the other lanthanides and actinides in the 18-column form, even though their properties are quite similar to those of the late lanthanides. Admittedly the same could be said about placing La and Ac in the d block since this visually separates them from the other lanthanides and actinides. Still, while Lu and Lr are always shown or regarded as lanthanides this is not the case for La and Ac, which are sometimes not regarded as Ln or An. For example: "lanthanide" literally means "like lanthanum" and thus should not include La; and La and Ac have empty and chemically mostly inactive 4f and 5f orbitals unlike the rest of the lanthanides and actinides respectively.

In any event we consider that this argument is almost too weak to bother with.

2015: Dimer spectroscopy

Jensen (2015) cites Fang et al. (2000) who, in discussing the spectra of Sc, Y La and Lu X₂ dimers, and those of some other period 6 transition metals, conclude that lutetium is more like the other transition metals and is therefore a better fit under Y than is the case for La.

Analysis: Factually correct but incomplete as an argument since Fang et al. do not say anything about the spectra of the group 2 or 1 metals, or the other lanthanides.

Relativistic contraction of 6s shell

Jensen further cites Fang et al. who note that the relativistic contraction of the 6s shell falls on the same trend line as that applying to the period 6 transition metals Hf to Ir whereas the contraction for La is more consistent with the trend line for Ce to Yb, therefore suggesting Lu is a better fit under Y.

Analysis: Correct, but this is mainly due to the differing degree of relativistic effects on d electrons as opposed to f electrons. La, Ce, and Gd similarly have fⁿd¹s² gas-phase configurations and also fall significantly off the lanthanide trend line just like Lu does. We also question the relevance of these small differences given that Pt and Au are even further away from the Hf–Ir trend line than Lu is from the Pr–Yb trend line. It seems to us that if such an argument is not relevant to the d block assignment of Pt and Au, then it similarly cannot be relevant to the f block assignment of Lu.

Aluminide dimers

Jensen cites Ouyang et al. (2008) who note that the "AlLa dimer has a different chemical bond compared with its congeners AlSc, AlY and AlLu. This discrepancy raises the question as to whether it would be more suitable to replace La with Lu in the periodic table."

Analysis: Fine, but to our knowledge no one has ever argued for the splitting of group 16 even as the dioxides range from molecular polar covalent SO₂, through polymeric SeO₂ and TeO₂, to ionic PoO₂. This thus strikes us a dubious argument for placing elements in the periodic table, at least when presented alone: at the most it might be valuable only as a "tipping point".

Heat of vapourisation

Jensen refers to "trends in the [heat] of vaporization for the alternative group sequences Sc-Y-La versus Sc-Y-Lu" and goes on to say, "the latter, rather than the former, corresponds most closely to the group tends observed for this property for the other elements in the early part of the d block", therefore supporting group 3 as Sc-Y-Lu.

Analysis: Unclear. The values for La (402 kJ/mol) and Lu (415) are quite close and in comparing these to values for other nearby elements we were unable to discern anything favouring the placement of either La or Lu under Y.

Ionization energy of Lr

Jensen (2015a) discusses, as reported in the 9 April 2015 edition of Nature, the experimental confirmation of the ionization energy (IE) of Lr and the implications of this for the composition of group 3. The latter question dominated all subsequent news stories on the Nature paper. He finds that no conclusions can be drawn on this question.

Analysis: We agree with Jensen that this finding is inconclusive.

La-Ac arguments

1970: Six properties

Trifonov (1970) compares La and Lu across (a) electronic structure; (b) atomic volume, radius, ionisation energy, and density; and (c) basicity; and, having regard to the last of these, places Lu in group 3. We have grouped, renumbered and translated Trifonov's observations into five specific arguments, as follows:

1. Electronically he says Sc (2, 8, 9, 2), Y (2, 8, 18, 9, 2) and Lu (2, 8, 18, 32, 9, 2) each have only two incomplete shells and that this pattern holds true for the rest of the transition metals proper for periods 4 to 6, whereas La (2, 8, 18, 18, 9, 2) has three incomplete shells.
   
2. Placing Lu in group 3 also means there is a consistent difference in atomic numbers of 32 between the period 5 and 6 transition metals, whereas this is not the case for La in group 3.
   
3. He further notes (c) that, "…in the spectrum of La the configuration levels containing 4f-electrons are extremely deep—already there is a tendency to strengthen the bonds of 4f-electrons" but that "this can hardly serve as a sufficient basis for considering La as the first element of 4f-family."
   
4. For atomic volume, radius, ionisation energy and density he says vertical trends going down groups 3 to 7 favour Sc-Y-Lu but that horizontal trends in periods 4 to 6 for groups 1 to 3 favour Sc-Y-La.
   
5. On basic character he says that increasing basicity with increasing atomic number is a general principle for the entire periodic system and since Sc-Y-La follows this pattern, whereas Sc-Y-Lu does not, he overall favours La in group 3.

Analysis:

1. Depending on what Trifonov means by "transition metals proper" we note that his pattern does not hold true for copper (2, 8, 18, 1), zinc (2, 8, 18, 2) and palladium (2, 8, 18, 18), each of which have only one incomplete shell. We further observe, for example, that B (2, 3), Al (2, 8, 3) and Ga (2, 8, 18, 3) each have one incomplete shell whereas the remaining members of group 13 namely In (2, 8, 18, 18, 3) and Tl (2, 8, 18, 32, 18, 3) each have two incomplete shells. Accordingly, we do not think much of this argument.
   
2. As noted in the Irregular electron configurations section of our submission, we are happy with this as a "tipping point" argument, presuming all other considerations are equal. We note that a precedent has been set between periods 1 and 2, with the placement of H at the top of group 1 (difference 2 to Li) and He at the top of group 18 (difference 8 to Ne).
   
3. We accept that the spectrum of La features a low-lying 4f orbital but do not understand the rest of this argument. If the intention is to note the possibility of 4f involvement in bonding involving lanthanum atoms, this only occurs at very non-standard conditions, under which caesium and barium also show 5d involvement despite being in the s block.
   
4. Trifonov overlooks the fact that vertical trends in groups 1 and 2 favour Sc-Y-La.
   
5. We think this argument is inconclusive as, while increasing basicity is seen as general principle across the periodic table there are exceptions (group 12, for example) and Trinfonov does not address the question of whether this would be the case for group 3.

Historical note: Further to Trifonov's argument #5, Smith (1927 p. 2036) discussed which element went below Sc-Y, as follows:

It is...necessary to make a decision, on chemical grounds if possible, as to the [rare-earth] element presenting the closest resemblance to yttrium and scandium...and to place the other fourteen in a transition sub-series. Scandium and yttrium have no valency higher than three, whilst yttrium (certainly) and scandium (probably) exhibit the valency of two in acetylene carbides of the form YC₂. Both yield colourless, diamagnetic salts, while yttrium oxide is a stronger base than scandium oxide, the basicity of the former only just falling short of alkalinity. Consequently the element to be placed in Group III of the third transition series should have no higher valency than three, exhibit a valency of two in an acetylene carbide, and possess colourless, diamagnetic salts and a strongly alkaline oxide. These properties are possessed only by the lightest of these elements, lanthanum, which must, accordingly, be regarded as the Group III representative in the transition series of the third long period, the remaining 14 from cerium to lutecium, being relegated to a transition sub-series...

While we could criticise Smith for seeming to fall into the trap of confusing similarity with periodic trends, and not being aware of, or overlooking, the existence of lutetium acetylide, he was on the mark in distinguishing between lanthanum oxide as a relatively strong base, and lutetium oxide as a weak base (the weakest of the lanthanide series) (Dulina et al. 2011, p. 1647).

On the other hand, his observation of increasing basicity with increasing atomic weight in each main group (1927, pp. 2031; 2033) does lend support to Sc-Y-La-Ac, given the chemical behaviour of the group 3 metals as, effectively, main-group elements (Earnshaw & Harrington 1973, p. 50), an observation we revisit later in this submission.

1974: Integrity of the f block

Shchukarev (1974, p. 118) appears to support La-Ac on the grounds that the 4f shell does not start filling until Ce and that (effectively) the filling sequence—which runs from Ce to Lu—is periodic, with two periods. Thus, after the occurrence of a half-full 4f shell at Eu and Gd, the filling sequence repeats with the occurrence of a full shell at Yb and Lu (Rokhlin 2003, pp. 4–5). A similar, but weaker, periodicity (Wiberg 2001, p. 1643–1645) is seen in the actinides, with a half full 5f shell at Am (in the gas phase) and Cm, and a full shell at No and Lr. Placing Lu and Lr under Y obscures the start of the filling of the f block (it would appear to start at La) and visually truncates its double periodicity (it would be cut off at Yb whereas it would actually end in the d block).

The reference is in Russian and is written in the style of Soviet scientific literature of the time, which makes it a little hard to follow. What we have written above is therefore our interpretation of what we understand the author appears to be saying. A translation of what Shchukarev wrote reads as follows:

"If we [...] considered the latter [Lu and 103] not as 4f and 5f elements but rather as members of 5d and 6d series, the d-electron prevention† determining filling f vacancies as stable would be lost as well as the correctness of placing of imitators before Gd and Cm as well as Lu and 103. The exceptional uniqueness of Gd and Cm, akin to that of Mg and Ca, would also be unclear."

We do not understand the reference to Mg and Ca having a uniqueness akin to Gd and Cm.

†Translator's note: Probably you find that this word doesn't really fit in the context of English. It doesn't look any better in Russian.

Analysis: We agree with the basis of Shchukarev's support for -La-Ac, noting the most important periodic property of the Ln and An is their valency. Thus, in the Ln, we see the analogous +2 ions of Eu and Yb, and the +4 ions of Ce and Tb (Wiberg 2001, p. 1644–1645). The double periodicity of the Ln and An is further explored by Ternstrom (1976) and (for the Ln only) by Horovitz and Sârbu (2005, pp. 473, 483). The former treats the Ln as running from Ce–Lu; the latter refers to 15 Ln from La to Lu. For reasons previously explained we think the approach of Horovitz and Sârbu lacks rigour.

2004: La-Ac remains the most popular form

The popularity of La-Ac, some thirty years after Jensen called for the adoption of Lu-Lr, must call into question the merits of the latter.

Several authors have commented to this effect. Myers, Oldham and Tocci (2004, p. 130) found that La and Ac was the most popular form of periodic table, a sentiment echoed by Clarke and White (2008); and Lavelle (2008; 2009). As noted, Scerri (2015) observed that while some textbook authors had taken up Lu-Lr in group 3, the majority seemed reluctant.

In electronic structure terms, lanthanum appears to have the advantage of incumbency, since the 5d¹ electron appears for the first time in its structure whereas it appears for the third time in lutetium, having already made a brief appearance in gadolinium (Trifonov 1970, p.  201–202). Not only would the merits of -Lu-Lr need to be demonstrated but so to would the merits of -La-Ac need to be surpassed.

Analysis: Our impression concurs with that of the cited authors. However, we are reluctant to say that the majority "rules" noting the phenomenon of text-book errors (see, for example, Jensen 2010) and the absence of a critical examination in the literature of the merits of -La-Ac.

2008: A pair out of place

Lavelle (2008) criticises La and Ac in the f block since this would represent the only case of a vertical pair of elements with incongruous electron configurations. He says that, "the entire modern basis of the periodic table is the grouping of elements by occupied outer orbital type giving rise to the s block (two outer electrons in an s orbital and two groups), the p block (six outer electrons in three p orbitals and six groups); the d block (ten outer electrons in five d orbitals and ten groups), and the f block (14 outer electrons in seven f orbitals and 14 groups)." He says that placing Lu and Lr in the d block, and La and Ac in the f block leads to a worse outcome than leaving La and Ac in the d block since this would represent, "the only case where a pair of elements [i.e. La-Ac] is placed such that they are part of block [i.e., the f block] with no outer electrons in common with that block." He also relies on the fact that several well-known reference books show La and Ac in the d block. His position is that, "we [should] use well-established forms of the periodic table…and that, "to suggest otherwise may result in a Pandora's box of a never-ending multitude of different periodic tables" (Lavelle 2009).

Analysis: We agree with Lavelle's argument about La-Ac being the only example of "a pair out of place", if they were in the f block, and we also feel that it is strengthened by a lack of comparable f orbital involvement in La and Ac in anything other than a second order fashion—which we feel justified in ignoring as this would also imply that K, Ca, Rb, Sr, Cs, and Ba would be d block elements. And we agree Sc-Y-La-Ac is well established in the literature, although that of course does not in itself constitute a justification.

We also suggest that, contrary to the critique of Jensen (2009), it is not necessarily a weakness of Lavelle's argument to allow Th ([Rn]6d²7s²) in the f block but not Ac ([Rn]6d¹7s²), since there are low-lying 5f orbitals present in Th but not (as we understand the situation) in Ac.

While lanthanum has a small-radius non-hydrogenic f orbital this does not occur in the actinides, on account of relativistic effects, until thorium (Cowan 1981, p. 612). By way of illustration, the energy of the 6d to 5f transition in thorium has been described as "rather low", at 7790 cm^-1 or less than 1 ev (Kanellakopulos 1989, p. 2) and can be contrasted with its ionisation energy of 50867 or 6.3 ev (Kramida et al. 2015). The 5d to 4f transition in lanthanum is more energetic: 15196 as against ionisation occurring at 44981 (Kramida et al. 2015a). In the case of actinium, the lowest 5f level is given as occurring at some 30000 cm^-1 above the ground state (Brewer 1971, p. 1108) compared to only 41700 cm^-1 for ionisation (Kramida et al. 2015b). In this sense, the contrast between La and Ac is such that thorium has been referred to as the analog of La, rather than Ac (Cowan 1981, p. 612; Kanellakopulos 1989, p. 3). A more recent review of actinide spectroscopy observed that whilst the collapse of the 5f wave function in the actinides is not as clear as is the case of the 4f function in the lanthanides, most theoretical calculations place it as occurring in thorium, rather than actinium (Bonnelle & Spector 2015, p. 7).

Given the foregoing we would query Jensen's comment that actinium has a low lying f orbital (Jensen 2015a, p. 3) and suggest that Lavelle's argument to allow Th in the f block, but not Ac, may have some merit.

Scerri (2009) criticises Lavelle's argument on the grounds that there is no requirement for each block to necessarily consist of atoms containing the expected number and type of electrons. We partly agree with Scerri however we do not think the case for a vertical pair of elements with an incongruous electron type has yet been made. We also note that -La-Ac results in a pair of elements (Lu-Lr) at the end of the f-block having a differentiating electron being added past a complete shell. We note however, an almost comparable situation at the end of the d-block where Zn-Cd-Hg have a differentiating s electron being added past a complete d shell, and the peculiar situation in the middle of the f block, with the Gd-Cm pair showing a d differentiating electron being added past a half complete shell. Overall, we think that a vertical pair of elements with no outer electrons in common with that block is a more incongruous than a vertical pair of elements having differentiating electrons added past a complete shell since in the case of Lu-Lr pair they at least have outer electrons in common with their block.

2016: Condensed- v gas-phase electron configurations

Whereas gas phase electron configurations of the Ln and An appear to support Sc-Y-Lu, condensed phase configurations—which are more pertinent to the chemistry of the elements—support Sc-Y-La-Ac.

Analysis

Gas phase
Jensen (1982, 2015) has argued for Sc-Y-Lu-Lr on the basis that the ideal electron configurations of the f-block elements are 4fⁿ 6s² and 5fⁿ 7s². The actual f count of these elements are compared with these ideal counts in tables 1 and 2. We see that a Sc-Y-La-Ac layout yields 8 matches compared to 19 matches for a Sc-Y-Lu-Lr layout.

TABLE 1: Sc-Y-La-Ac periodic table (underlined, dark grey shading = match with idealized number of f electrons)

Period 6	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb	Lu
Idealized f electrons	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Actual number	1	3	4	5	6	7	7	9	10	11	12	13	14	14
Period 7	Th	Pa	U	Np	Pu	Am	Cm	Bk	Cf	Es	Fm	Md	No	Lr
Actual number	0	2	3	4	6	7	7	9	10	11	12	13	14	14

TABLE 2: Sc-Y-Lu-Lr periodic table f block showing electron configurations

Period 6	La	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb
Idealized f electrons	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Actual number	0	1	3	4	5	6	7	7	9	10	11	12	13	14
Period 7	Ac	Th	Pa	U	Np	Pu	Am	Cm	Bk	Cf	Es	Fm	Md	No
Actual number	0	0	2	3	4	6	7	7	9	10	11	12	13	14

Jensen's support for -Lu(Lr) is based on gas phase electron configurations and we agree with his argument on that basis.

Condensed phase
We agree with Scerri (2015) that solid state electron configurations are more relevant to the chemistry of the elements.

In this regard, tables 3 and 4 compare the idealized numbers of f electrons for the f block elements with the actual numbers of f electrons in their solid states, rather than their gaseous states. There are 21½ matches in the first table compared to 6 in the second, out of a total of 28 elements.

TABLE 3: Sc-Y-La-Ac periodic table f block showing electron configurations (underlined, dark grey shading = match with idealized number of f electrons)

Idealized f electrons ✱	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Period 6	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb	Lu
Actual number †	1	2	3	4	5	~7	7	8	9	10	11	12	~14	14
Period 7	Th	Pa	U	Np	Pu	Am	Cm	Bk	Cf	Es	Fm	Md	No	Lr
Actual number ‡	~½	~2	~3	~4	~5	6	7	8	9	11	12	13	14	14

TABLE 4: Sc-Y-Lu-Lr periodic table

Idealized f electrons ✱	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Period 6	La	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb
Actual number †	0	1	2	3	4	5	~7	7	8	9	10	11	12	~14
Period 7	Ac	Th	Pa	U	Np	Pu	Am	Cm	Bk	Cf	Es	Fm	Md	No
Actual number ‡	0	~½	~2	~3	~4	~5	6	7	8	9	11	12	13	14

^✱ The position of each element in the f block determines its idealized number of f electrons. For example, in a Sc-Y-La-Ac periodic table, promethium is the fourth f block element in period 6; its idealized number of f electrons is therefore 4.

† Johansson and Rosengren (1975, p. 1367); Greenwood and Earnshaw (2002, pp. 1232, 1234): "…most of the metals are composed of a lattice of Ln^III ions with a 4fⁿ configuration and 3 electrons in the 5d/6s conduction band. Metallic Eu and Yb, however, are composed predominately of the larger Ln^II ions with 4fⁿ⁺¹ configurations and only 2 electrons in the conduction band."

‡ Haire (2007, p.  65); Moore and van der Laan (2009, pp. 269; 270; 272; 275; 276; 283; 286); Lawson (2016, p. 87)

~  Some or all f electrons in the early actinides are itinerant, and become hybridized with ds electrons and orbitals. That, and the radioactivity and relative scarcity of the metals involved, makes it hard to pin down their f electron numbers beyond approximations, as denoted by a tilde. In thorium, the number of f electrons is shown as a fraction due to a 5f /6d overlap (Johansson et al. 1995, p. 282).

Discussion
In the gas phase, the electron configurations of most of the lanthanides is [Xe]4fⁿ6s², which seems to correspond better to the Sc-Y-Lu-Lr hypothesis. There are four exceptions. Gd and Lu may be rationalised by invoking the greater stability of a half- or fully-filled 4f shell, corresponding to the easy reduction of Eu and Yb to the +2 state.

Yet La and Ce are a little odd here.

If 4f is supposed to, by the Aufbau principle, be lower in energy than 5d, then why is 5d filled preferentially in La, with the [Xe]4f¹6s² configuration only appearing at an appreciably higher energy?

Why is it that, even with the sudden contraction of the 4f orbitals after La, we cannot avoid 5d occupancy in Ce even in the gas phase?

Additionally, chemical arguments also call into question the predictions of a Sc-Y-Lu-Lr table. We know that the 4f subshell is buried deeply in the core due to its low principal quantum number. So why are the lanthanides not predominantly divalent (with the exception of Eu and Yb), losing only the 6s electrons?

To answer these questions, we should look at the condensed-phase electron configurations, since they tend to be more chemically relevant than the gas-phase ones. We find instead that, with two exceptions, all of the lanthanides have a [Xe]4f^n–15d¹6s² configuration. The exceptions are Eu and Yb, because of the greater stability of a half- or fully-filled 4f shell. This certainly supports a Sc-Y-La-Ac table, in which one column of the d block is filled in group 3, the f block intervenes starting at Ce and Th, and then the other nine columns of the d block fill until Hg and Cn. It also appears to be consistent with their chemistry: for if it were really true that their configuration is for the most part [Xe]4fⁿ⁺¹6s², with 4f supposedly drowned into the core, it is difficult to explain the massive preference for trivalence along the lanthanide series. We further note that—in compounds—the trivalent state is rare in europium and limited for ytterbium (Gschneidner 1968, p. 13), consistent with their irregular electron configurations.

The actinides tell a similar story. It is only when 5f is drowned deeply into the core near the end of the actinide series, from Es to No, that things change and we obtain the expected [Rn]5fⁿ⁺¹7s² configuration. (Although Lr is expected to have an anomalous p electron in the gaseous phase, we think it plausible that it will have an [Rn]5f¹⁴6d¹7s² configuration in the condensed phase.)† And these four elements are exceptional in preferring the divalent state. Only for the late actinides is the divalent state even stable in aqueous solution, let alone the most stable state for nobelium.

† Even if condensed Lr has a p electron, simple modelling studies suggest it will still behave like a lanthanide (Xu & Pyykko 2016).

Conclusion
On the basis of solid phase electron configurations we submit that the case for Sc-Y-La-Ac is quite clear.

Blocks

While aspects of this argument were previously considered in our analysis of Lavelle's (2008) "pair out of place" argument, we consider the concept of a block merits further exploration.

We submit that the concept of periodic table blocks supports Sc-Y-La-Ac.

Analysis: A block starts when the first electron of its name enters the applicable subshell. Thus, the s block starts at group 1 with H, the p block starts in group 13 with B, the d block starts in group 3 with Sc, and the f block starts at Ce. The filling sequence of the d and f blocks is somewhat irregular. In the d block, Cu, Zn; Pd, Ag, Cd; and Au and Hg have the same number of d electrons for their period due to the higher stability of a filled d shell. The filling of the d block is also interrupted by the start of the f block i.e. La [Xe]5d¹6s² is followed by Ce [Xe]4f¹5d¹6s², and does not resume filling (Lawrance 2013, pp. 177–178) until hafnium, which is [Xe]4f¹⁴5d²6s². As noted previously, the filling of the the f block occurs in a slightly irregular manner due to narrow differences in the energy levels of f and d electrons, or the higher stability of a half-filled or full f shell. Now, if we were to start the f block at La and end it at Yb, it would start before the f orbitals are capable of becoming chemically active and stop just before they sink completely into the core.

It is worth considering the Sc–Zn case similarly. At the end of the block we have Cu, [Ar]3d¹⁰4s¹, with a filled 3d shell that can still be ionised. The next element is Zn, [Ar]3d¹⁰4s², with a 4s differentiating electron; but the d block effectively ends here because this is where the d shell first becomes chemically inactive. Is this not more similar to Yb (in an -La-Ac table) and Lu than to Tm and Yb (in an -Lu-Lr table)?

Just as 3d only collapses and drops below 4s after Ca and thus the d block begins at Sc, 4f only collapses and drops below 5d and 6s after La and thus the f block begins at Ce. (5d had already collapsed after Ba.) The fact that Lu at the end of the f block cannot use its f electrons for bonding is immaterial. Neither can Zn at the end of the d block or Ne at the end of the p block, reflecting the great stability of a full shell configuration (not a "pseudo" full shell like Cu or Yb where the Aufbau-expected configuration is in a low excited state, and thus the shell may be breached). The important thing is that the f block must correspond to the filling of the f orbitals with 14 f electrons and thus it has to have 14 columns. Since it starts at Ce, it must end at Lu.

Jensen's criteria
The preceding viewpoint of block assignment is similar to that promoted by Jensen (2009) in Misapplying the Periodic Law:

"Classification of an element in the periodic table is based on four steps:

1. Assignment to a major block based on the kinds of available valence electrons (i.e., s, p, d, f, etc.).
2. Assignment of the elements within each block to groups based on the total number of available valence electrons.
3. 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.
4. Verification that the elements are arranged in order of increasing atomic number as required by the periodic law."

In the case of the last column of each block, i.e. He, Ne, Ar, Zn, Cd, Hg, Lu, and Lr, we would note that criterion 1 would have to be slightly amended to accommodate the fact that some "theoretically available" valence electrons may not actually be ionisable, but we do not think that this seriously affects our argument. To make the block assignment even clearer, we would also add that block assignment is determined by the orbital occupied with the highest angular momentum: thus, for example, an fds² configuration is characteristic of an f-block element.

Jensen claims that criteria 1 and 2 do not lead to an unambiguous assignment in the case of La and Ac, but we find that they actually do. With the understanding that everything said in the following of lanthanum and the succeeding lanthanides is equally true of actinium and the succeeding actinides, La is easily assigned to the d block because it only has 5d and 6s orbitals available for bonding. Lu, however, has a newly filled 4f shell, similar to Zn with a newly filled 3d shell, that forms the last step to fill the d or f orbitals. This firmly assigns La to the d block and Lu to the f block, which inexorably leads to a Sc-Y-La-Ac table through the application of criterion 2. The trends obtained are quite valid, even more so than for Sc-Y-Lu-Lr, thus fulfilling criterion 3. Finally, criterion 4 implies that the d block must be split apart to accommodate the placement of La and Ac in group 3. If this does not seem symmetrical, it at least fits the facts of chemistry, in which the d subshells collapse and become chemically active after group 2, but the f subshells only do so after group 3.

Superheavy elements: eka-actinium and eka-thorium: A possible wrinkle in this argument for block assignment is that by period 8, relativistic effects are expected to become so large that the overlaps produced from such a strict definition of where blocks start and end would be intolerable, and may not accurately reflect the elements' chemistry: for example, the 8p level is expected to split into an 8p_1/2 level, that begins filling at Z = 121, and an 8p_3/2 level, that does not finish filling until Z = 172.

No complete and accurate calculations are available for elements past Z = 122 (eka-thorium), and the chemical interpretation of their expected properties is disputed between authors. Hence, for example, Fricke, Greiner and Waber (1971) considered Z = 164 to be a dvi-mercury, while Nefedov, Trzhaskovskaya and Yarzhenskii (2006) considered it to be a dvi-platinum, and Pennemann, Mann and Jørgensen (1971) predicted that it might show some dvi-lead properties as well (Fricke, Greiner and Waber also consider some possible dvi-radon character). Even the actual electron configurations of some of these elements are in dispute. Therefore, we submit that this wrinkle is of questionable relevance today. Indeed Fricke and McMinn (1976) wrote: "For the elements beyond 120, one must contend with the unknown chemical behavior of five rather loosely bound shells and with the totally unknown chemical behavior of g electrons. Conclusions can be drawn only by analogy and even the chemical classification of these elements can no longer be straightforward."

The only possible exception might be in the cases of eka-actinium and eka-thorium, respectively elements 121 and 122, which have received complete calculations by Eliav et al. (1998, 2002) and thus may be of some relevance here (proceeding with caution as predicted properties are obviously not on the same footing as those empirically determined).

While element 121 is expected to have [Og]8s²8p¹ as the ground state, the first excited state should be [Og]7d¹8s² at a mere 0.412 eV; thus the 7d, 8s, and 8p orbitals contribute, and 7d is of highest angular momentum and firmly puts eka-actinium in the d block with scandium, yttrium, lanthanum, and actinium. Thus, eka-actinium—despite the d electron being substituted by a p electron at least in the gaseous phase—has more of a familial relationship to Ac than it has to Nh (the latter with its superficially similar 7s²7p¹ gas-phase outer electron configuration). And given Lr has shown no inclination to adopt the +1 state, despite its anticipated [Rn]7s²7p¹ configuration, it likewise shows more of a familial relationship with Lu than to Tl (again, with the latter's superficially similar 6s²6p¹ outer electron configuration). Each of these observations have been informed by relativistic calculations of the chemical behaviour of Lr and eka-actinium. The possible alternative of placing element 121 as starting a new g-block column is ruled out by the complete lack of 5g involvement: indeed, the radial collapse of the 5g orbitals is not expected to happen until around element 125, a more extreme version of the deviation from Aufbau with the 4f collapse delayed from La to Ce.

In element 122, the ground state is predicted to be [Og]7d¹8s²8p¹, but low-lying configurations involving the 6f level are predicted for the +1, +2, and +3 cations. (Note that this is more than has been predicted for La and Ac, where the 4f and 5f levels are not actually occupied in even the lowest few excited states, and are at the most used as a lowest unoccupied orbital for hybridisation.) The 5g level is instead not yet involved, firmly putting eka-thorium as the beginning of the f block with cerium and thorium. We would note however that since the filling of the 5g and 6f orbitals is expected to overlap very heavily indeed, it may be chemically sounder to combine them into a long 'superactinide' series interrupting the more distinct filling of the 7d shell with elements 121 and 156 to 164, and indeed Fricke, Greiner and Waber (1971) show such a table (with element 121 in group 3, 122-155 ungrouped, then 156-164 in groups 4-12)—noting, of course, the extreme speculativeness of such an endeavour.

So, while the beginning of the 5g series remains as yet unexplored, the first four undiscovered elements do not appear to necessitate any revision of the concept of blocks at the moment, instead taking their places quite naturally below Fr, Ra, Ac, and thorium. As Scerri has noted, 'This seems to be further testament to the underlying fundamental nature of the periodic law, which continues to stand firm against the threats from quantum mechanics and relativity combined together.' Indeed, if may indulge in mixed metaphors, Mendeleev continues to steer deftly and skillfully between Scylla and Charybdis, out to the furthest reaches yet explored of the Sea of Instability.

Conclusion
On the basis of what we consider the principles of the periodic table as it is currently drawn, we contend that the above definition of blocks is operative and that it clearly supports the case of Sc-Y-La-Ac. Once this assignment is made, the splitting of the d block follows to preserve the ascending sequence of atomic numbers in the periodic table, as mandated by the periodic law.

Chemical behaviour

The chemical behaviour of Group 3, which is like that of pre-transition metals, favours Sc-Y-La.

Analysis: Group 3 shows chemical behaviour that is manifestly uncharacteristic of the transition metals proper. Group 3 does not show the complex coordination chemistry that is characteristic of transition metals; they do not show multiple oxidation states; and they are more reactive and electropositive than any other transition metals, approaching the s-block metals in both properties. In fact, they largely show the behaviour expected of main-group elements following the alkaline-earth metals. This is true for the lanthanide series from La to Lu, as well as in Ac and the late actinides from Cm to Lr (Greenwood & Harrington 1973, p. 50; King 1995, p. 289).†

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

Given, as previously examined, that Sc-Y-La-Ac matches better with group 1 and 2 trends, whereas Sc-Y-Lu has been shown several times (including by Jensen), to more closely parallel trends in groups 4 to 10, we contend that the choice of Sc-Y-La-Ac over Sc-Y-Lu-Lr is clear. Indeed, Laing (2009, p. 12) says a reasonable case could be made for La below Y on the basis of comparing the pairs Ca-Sc and Sr-Y with Ba-La.

Conclusion: Periodic trends and chemical properties favour Sc-Y-La.

† Here are some illustrative quotes concerning the behaviour of group 3 as Sc-Y-La-Ac, and the behaviour of the lanthanides:

Sc-Y-La-Ac
"…If scandium, yttrium, lanthanum and actinium are the only rare-earth elements, the series would have revealed the same gradual change in properties as the calcium, strontium, barium and radium series, and hence it would not have been of any special interest." (Hevesy 1929, cited in Trifonov 1970, p. 188).

"For each element…all three outer electrons are easily lost and the chemistry of the elements is confined to the +3 oxidation state. Their monatomic cations are colourless and diamagnetic, and have no catalytic properties. This is the behaviour that would be expected of main-group elements following the alkaline-earth metals." (Greenwood & Harrington 1973, p. 50)

"The trends in properties in the family…are quite regular, and similar to the trends in Groups 1 and 2." (Lee 1996, p. 679)

"…although each member of this group is the first member of a transition series, its chemistry is largely atypical of the transition elements. The variable oxidation states and the marked ability to form coordination compounds…are barely hinted at…although materials containing the metals in low oxidation states can be prepared and a limited organometallic chemistry (predominately cyclopentadienyl) has been developed." (Greenwood & Earnshaw 2002, p. 948).

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

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

Arguments compared

Lu-Lr

Arguments in favour of Lu-Lr generally do not withstand close scrutiny. Those based on a similarity in the trends of Sc-Y-Lu to groups 4–10 ignore the similarity in trends of Sc-Y-La-Ac to groups 2 and 1, or lack data or supporting references, or are not replicated in other groups, or are incomplete. Some arguments are based on a greater commonality of the properties of Lu to Sc and Y than is the case with La. We consider this approach to be flawed. Similarity, absent of any consideration of periodic trends, does not imply group kinship; in fact, the two are often at odds with each other. Other arguments are inconsequential, lacking in substance or contradictory. Table 5 summarises our evaluation of the arguments in question:

Table 5: Argument summary

Argument	Summary	Type	Analysis	Status
1958: Electron configurations	4f shell complete in Lu	Commonality	Inconsistent with group 12 as part of d block	Baseless
1965: Similarity of Lu with Sc, Y	Lu is closer to Sc, Y than is La	Commonality	Fails to address relevance of similarity v. linearity	Inconclusive
1967: f-character of La	Literature suggests this could explain some properties	Commonality	Plausible for La but also conceivable for Lu	2nd-order tipping point
1982: Separation groups	Y, less so Sc, chemically closer to Lu than to La	Commonality	Ignores expected periodic trends	Meaningless
Irregular electron configurations	Gas phase electron configs support Lu under Y	Commonality	Solid phase configs do not support; no significant f orbital involvement in La	Tipping point argument
Electron configuration analogy	Consistent atomic number difference of 32 between heavy d block metals	Trend similarity	True	Tipping point argument
Ionization potentials	IE 1 + IE 2 for Sc-Y-Lu similar to groups 4–8, unlike Sc-Y-La	Trend similarity	Why first two IE? First three IE for Sc-Y-La fits better with groups 1–2	Inconclusive
Atomic radii	Periodic trends favour Sc-Y-Lu	Trend similarity	Sc-Y-La is similar to groups 1–2	Inconclusive
Ionic radii	Trends favour Sc-Y-Lu	Trend similarity	No data nor references given; Sc-Y-La similar to groups 1–2	Unsubstantiated; incomplete; contradicted
Redox potentials	Comparison of periodic trends favour Sc-Y-Lu	Trend similarity	No data nor reference given; NIST data inconclusive	Unsubstantiated
Electronegativities	Allred-Rochow trends favour Sc-Y-Lu	Trend similarity	Sc-Y-La similar to groups 2, 1; Pauling EN favours Sc-Y-La	Inconclusive; unsubstantiated
Melting points	Sc-Y-Lu trend fits better with groups 4–10	Trend similarity	Sc-Y-La similar to groups 2, 1	Inconclusive
Crystal structures (elements)	Sc, Y, Lu are HCP but La is double-HCP	Commonality	Structures in other groups vary, too	Meaningless
Crystal structures (oxides etc)	M2O3 etc for Sc, Y, Lu are = whereas La different	Commonality	Structures in other groups vary, too	Meaningless
Excited state spectra	Spectra for Sc, Y, Lu differ from La	Commonality	Empty d-bands in Ca, Sr and Ba precede d block proper and differ from spectra for Be, Mg	Tipping point argument
Superconductivity	Sc, Y, Lu incapable of superconductivity in bulk at normal pressure whereas La is	Commonality	Lu may or may not also be capable	Inconclusive
Conduction band structures	Sc, Y, Lu have conductivity bands with d block like structure but La does not	Commonality	X-ray isochromats of Gd to Lu do not support this argument	Baseless
1985: Seven properties	Density triads, and some mechanical and thermodynamic properties support Lu under Y	Periodic trends/Commonality	Density triads ignore d and f block insertions; properties listed show no consistent trend	Groundless, inconclusive
2005: Physical properties	Sc, Y dissimilar to Ln; as Lu is also an Ln outlier it should be in group 3	Commonality	La is also an outlier	Inconclusive
2006: Characteristic electron configurations of ions	Configurations of ions are more important than those of gas phase atoms	Other	Agree in spirit; otherwise misguided	Argument supports -La-Ac
2011: Triads	Y-Lu-Lr is a triad; Y-La-Ac is not	Other	Sc-Y-La form triad but not Sc-Y-Lu	Inconsequential
2012: Split d block	Sc-Y-La-Ac yields symmetry deficit in 32-column version	Other	Triumph of Platonic ideal over inconvenient facts of chemistry	Baseless
2013: Carbonyls	Periodicity in carbonyl valencies supports Lu under Y	Commonality	Not representative; breaks down in s block	Unsubstantiated
2014: Lu as a TM	Lu shares many properties and similarities with period 6 TMs	Commonality	Argument incomplete and contradicted by other evidence	Inconclusive
Name matches position	La, Ac in f block is consistent with names	Commonality	Simplification does not dictate reality; not always consistent with actual treatment	Baseless
2015: Dimer spectroscopy	Spectra of Lu M2 dimers is more like those of other period 6 transition metals, so Lu is better fit under Y than is case for La.	Commonality	Doesn't say anthing about group 2, 1 or other Ln spectra	Meaningless, inconclusive, incomplete
Relativistic contraction of 6s shell	Lu falls on period 6 TM trend line and off the lanthanide trend line	Commonality	Pt and Au fall off the period 6 TM trend line; the other lanthanides with a d electron (La, Ce, Gd) also fall off the lanthanide trend line	Inconclusive
Aluminide dimers	AlLa dimer different bond compared with AlSc, AlY, AlLu	Commonality	Bonds of other groups' compounds vary, too	Meaningless, incomplete
Heat of vaporization	Sc-Y-Lu trend fits better with early d block than does Sc-Y-La	Trend similarity	Too close to call	Unsubstantiated
IE of Lr	Experimental determination of Lr IE has no implication	Other	Agree with Jensen	Meaningless

La-Ac

Most arguments in favour of La-Ac withstand close scrutiny. The argument based on the increasing basicity of Sc-Y-La-Ac down a group whereas this is not the case for Sc-Y-Lu, is inconclusive given other exceptions to the trend of increasing basicity down groups. The fact that La-Ac is the most popular format is notable but has never, as far as we know, been subjected to a critcal examination and for that reason we do not rely on it. The remaining five arguments—all of which are substantiated—essentially concern the electron configurations of elements in the f block (noting that these arguments overlap to some extent), and the chemical behaviour of Group 3 as pre-transition metals. Table 6 summarises our evaluation of the arguments:

Table 6: Argument summary

Argument	Summary	Type	Analysis	Status
1970: Six properties	Basicity increase down a group is a general principle	Trend similarity	La is more basic than Y; Lu is less basic than Y	Inconclusive, given exceptions elsewhere in PT
1974: Integrity of the f block	Double periodicity in the f block is apparent	Periodicity	True	Substantiated
2004: La-Ac remains the most popular form	Popularity of La-Ac calls into question the merits of Lu-Lr	Popularity	True	Inconclusive, given lack of critical examination in literature
2008: A pair out of place	Lu-Lr would mean La-Ac become only case of a vertical pair with no outer electrons in common with their block	Commonality	True	Substantiated
2016: Condensed-phase v gas-phase electron configurations	Condensed phase configurations are more pertinent to the chemistry of the elements, and support Sc-Y-La-Ac	Commonality	True	Substantiated
Blocks	Concept of periodic table blocks supports Sc-Y-La-Ac	Commonality	True	Substantiated
Chemical behaviour	Group 3 chemical behaviour is like groups 1–2; Sc-Y-La trends fit better with groups 1–2; Sc-Y-Lu trends fit better with groups 4–10; ergo Sc-Y-La preferred	Trend similarity, commonality	True	Substantiated

Comparison and findings

Arguments based on trend similarities are inconclusive. That is to say, while vertical trends for Sc-Y-Lu fit better with groups 4–10, those for Sc-Y-La-Ac fit better with groups 1–2. The two sets of arguments have equal merits.

A pivotal consideration is that chemical behaviour of group 3, as either -Lu(Lr) or -La-Ac, generally resembles that of groups 1–2. Combined with the previously mentioned "trend similarity" arguments, this skews the balance in favour of La-Ac. Thus, faced with a choice of Sc-Y-Lu, which behave like pre-transition metals (PTM) but show vertical trends like groups 4–10; or Sc-Y-La-Ac, which also behave like PTM and show vertical trends matching those of groups 1–2, we contend that the weight of arguments rests with Sc-Y-La-Ac. The balance is further skewed this way by the resulting preservation of double periodicity in the f block.

Arguments based on the greater commonality of Lu to Sc and Y then become essentially moot.

Finally, the various electron configuration arguments (including Wulfsberg's 2006 Lu-Lr ion-based argument) support Sc-Y-La-Ac. In particular, basing these arguments on the condensed phase—which is more pertinent to the chemistry of the elements than the gas phase—substantiates the assignment of -La-Ac under Y.

Conclusion

Drawing on the literature, arguments in support of Sc-Y-Lu-Lr were reviewed and analysed for their validity. Most of these arguments were based either on: group trends compared with other members of the d block; or similarities between Lu and Sc and Y. The same process was applied to Sc-Y-La-Ac, in terms of basicity, chemical behaviour, the integrity of the f block, and electron configurations. In particular, the chemical behaviour of group 3 as pre-transition metals, combined with the greater relevance of condensed phase electron configurations, settles the group 3 constitution question clearly in favour of Sc-Y-La-Ac. The popularity of periodic tables showing group 3 with -La-Ac, as a manifestation of the wisdom of the masses, is (in this case) confirmed.

References

• ASM International 1990, Metals handbook, vol. 1, 10th ed., American Society for Metals, Metals Park, Ohio
• Atkins P, Overton T, Rourke J, Weller M & Armstrong F 2006, Shriver & Atkins inorganic chemistry, 4th ed., Oxford University Press, Oxford (see also http://bilbo.chm.uri.edu/CHM401/Problem1_14.html)
• Aylward G & Findlay T 2008, SI chemical data, 6th ed., John Wiley & Sons, Milton, Queensland
• Bartsch SG 1989, "Standard electrode potentials and temperature coefficients in water at 298.15 K", Journal of Physical and Chemical Reference Data, vol. 18, no. 1, pp. 1–21
• Bergwall S 1966, "X-ray isochromats of some rare earth elements", Zeitschrift for Physik, vol. 193, no. 1, pp. 13–22, doi:10.1007/BF01326456
• Boeyens JCA 2008, "The periodic electronegativity table", Zeitschrift für Naturforschung B, vol. 63, no. 2, pp. 199–209
• Bonnelle C & Spector N 2015, Rare-earths and actinides in high energy spectroscopy, Springer, Dordrecht
• Brewer L 1971, "Energies of the electron configurations of the lanthanides and actinides," Journal of the Optical Society of America, vol. 61, no. 8, pp. 1101–1111
• Buzea C & Robbie K 2004, "Assembling the puzzle of superconducting elements: a review", Superconductor Science and Technology, vol. 18, no. 1, pre-print version https://arxiv.org/pdf/cond-mat/0410302.pdf, accessed 20 Nov 2016
• Chistyakov VM 1968, "Biron's secondary periodicity of the side d-subgroups of Mendeleev's short table", Journal of General Chemistry of the USSR, vol. 38, no. 2, pp. 213–214
• Clark RW & White GD 2008, "The flyleaf periodic table", Journal of Chemical Education, vol. 85, no. 4, p. 497
• Clavaguéra C, Dognon J-P & Pyykkö P 2006, "Calculated lanthanide contractions for molecular trihalides and fully hydrated ions: The contributions from relativity and 4f-shell hybridization", Chemical Physics Letters, vol. 429, nos. 1–3, pp. 8–12
• Cotton S 2007, Lanthanide and actinide chemistry, John Wiley, Chichester
• Cowan RD 1981, The theory of atomic structure and spectra, University of California Press, Berkeley
• Cowley 2002, Ionization energies (eV) of atoms and ions, https://dept.astro.lsa.umich.edu/~cowley/ionen.htm, accessed 20 November 2016
• Desclaux JP 1973, 'Relativistic Dirac-Fock expectation values for atoms with Z = 1 to 120, Atomic Data and Nuclear Data Tables, vol. 12, pp. 311–406 (370–371), doi:10.1016/0092-640X(73)90020-X
• Dolg M & Stoll H 1996, "Electronic structure calculations for molecules containing lanthanide atoms", Handbook on the Physics and Chemistry of Rare Earths, vol. 22, KA Gschneider Jr. & L Eyring (eds), Elsevier, Amsterdam, pp. 607–729
• Dougherty RC 2009?, Superconductivity, a physical chemical perspective, accessed 7 Dec 2016
• Dulina NA, Deineka TG, Yavetskiy RP, Sergienko ZP, Doroshenko AG, Mateychenko PV, Vovk OM & Matveevskaya NA 2011, "Comparison of dispersants performance on the suspension Lu₂O₃: Eu³⁺ stability and high-density compacts on their basis", Ceramics International, vol. 37, no. 5, pp. 1645–1651
• Earnshaw A & Harrington TJ 1973, The chemistry of the transition elements, Clarendon Press, Oxford
• Eliav E, Shmulyian S, Kaldor U & Ishikawa Y 1998, "Transition energies of lanthanum, actinium, and eka-actinium (element 121)", Journal of Chemical Physics, vol. 109, no. 10, pp. 3594–3598, doi:10.1063/1.476995
• Eliav E, Landau A, Ishikawa Y & Kaldor U 2002, "Electronic structure of eka-thorium (element 122) compared with thorium", Journal of Physics B, vol. 35, no. 7, pp. 1693–1700
• Fang L, Chen X, Shen X & Lombardi JR 2000, "Raman and absorption spectrum of mass-selected lutetium dimers in argon matrices," Journal of Chemical Physics, vol. 113, no. 22, pp. 10202–10206, doi:10.1063/1.1322635
• Fricke B, Greiner W & Waber JT 1971, "The continuation of the periodic table up to Z = 172. The chemistry of superheavy elements," Theoretica chimica acta, vol. 21, no. 3, pp. 235–260
• Fricke B & McMinn J 1976, "Chemical and physical properties of superheavy elements," Naturwissenschaften, vol. 63, pp. 162–170
• Glotzel D 1978, "Ground-state properties of f band metals: Lanthanum, cerium and thorium", Journal of Physics F: Metal Physics, vol. 8, no. 7, pp. L163–L168
• Goncharova VA & Il'ina GG 1984, "Anomalies in the elastic properties of polycrystalline lanthanum at phase transitions under pressure", Soviet Physics JETP, vol. 59, no. 5, pp. 995–998
• Greenwood NN & Earnshaw A 2002, Chemistry of the elements, 2nd ed., Butterworth-Heinemann, Oxford
• Greenwood NN & Harrington TJ 1973, The chemistry of the transition elements, Clarendon Press, Oxford
• Gschneidner KA 1968, "On the valences of europium and ytterbium in compounds", Journal of the Less-common Metals, vol. 17, no. 1, pp. 13–24
• —— 1971, "On the nature of 4 f bonding in the lanthanide elements and their compounds", Journal of the Less-common Metals, vol. 25, no. 4, pp. 405–422
• —— 1980, "Phase relationships in rare earth metal alloy systems—Contribution to theory of alloy formation", in EC Subbarao & WE Wallace (eds), Science and technology of rare earth materials, Academic Press, New York, pp. 51–76
• —— 1993, "Systematics and anomalies", Journal of Alloys and Compounds, vol. 192, nos. 1–2, pp. 1–10
• —— 2006, "The theory of phase formation in rare earth metal systems", Archives of Metallurgy and Materials, vol. 51, No. 4, pp. 519–524
• —— 2016, "Systematics", in J-CG Bünzli & VK Pecharsky (eds) Handbook on the Physics and Chemistry of Rare Earths, vol. 50, pp. 1–18
• Haire RG 2007, "Insights into the bonding and electronic nature of heavy element materials", Journal of Alloys and Compounds, vols. 444–445, pp. 63–71
• Hamilton DC 1965, "Position of lanthanum in the periodic table", American Journal of Physics, vol. 33, no. 8, pp. 637–640
• Hevesy G 1929, Redkie zemeli s tochki zreniya stroeniya atoma, (Rare earths from the point of view of structure of atom), NKhTI, Lenningrad, cited in Trifonov 1970
• Holden NE 1985, Status of the lanthanides and actinides in the periodic table, http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/17/024/17024322.pdf, accessed 24 November 2016
• Horovitz O & Sârbu C 2005, "Characterisation and classification of lanthanides by multivariate-analysis methods", Journal of Chemical Education, vol. 82 no. 3, pp. 473–483
• Jensen MA 1965, Superconductivity in the transition metals at very low temperatures, PhD thesis, University of California, San Diego
• Jensen WB 1982, 'The positions of lanthanum (actinium) and lutetium (lawrencium) in the periodic table,' Journal of Chemical Education, vol. 59, no. 8, pp. 634–636, doi:10.1021/ed059p634
• —— 1986, "Classification, symmetry and the periodic table," Computers & Mathematics with Applications, vol. 12, nos. 1–2, part B, pp. 487–510
• —— 2003, "The place of zinc, cadmium, and mercury in the periodic table", Journal of Chemical Education, vol. 80, no. 8, pp. 952–961
• —— 2009, "Misapplying the periodic law", Journal of Chemical Education, vol. 86, no. 10, p. 1186
• —— 2010, Inorganic myths in the freshman textbook, invited lecture, 240^th National ACS Meeting, Boston, 26 August 2010, accessed 27 December 2016
• —— 2015, "The positions of lanthanum (actinium) and lutetium (lawrencium) in the periodic table: An update", Foundations of Chemistry, vol. 17, no. 1, pp. 23–31
• —— 2015a, Some comments on the position of lawrencium in the periodic table, Department of Chemistry, University of Cincinnati, Cincinnati
• Ji W-X, Xu W, Schawrz WHE & Wang S-G 2015, "Ionic bonding of lanthanides, as influences by d- and f-atomic orbitals, by core-shells and by relativity", Journal of Computational Chemistry, vol. 36, no. 7, pp. 449–458
• Johansson B & Rosengren A 1975, "Interpolation scheme for the cohesive energies for the lanthanides and actinides", Physical Review B, vol. 11, no. 4, pp. 1367–1373
• Johansson B, Abuja R, Eriksson O & Wills JM 1995, "Anomalous fcc crystal structure of thorium metal", Physical Review Letters, vol. 75, no. 2, pp. 280–283
• Kanellakopulos B 1989, "General properties of the thorium atom and thorium ions", in RG Behrens et al. (eds), Th Thorium, Gmelin Handbook, Th Supplement vol. A 4, Springer-Verlag, Berlin, pp. 1–16
• Kenichi T 1997, "Structural study of Zn and Cd to ultrahigh pressures", Physical Review B, vol. 56, no. 9, pp. 5170–5179
• King RB 1995, Inorganic chemistry of main group elements, Wiley-VCH, New York
• Kmetko EA & Hill HH 1976, "Anomalous melting of f electron metals (with attention to Pu)", Journal of Physics F: Metal Physics, vol. 6, no. 6, pp. 1025–1037
• Kramida A, Ralchenko Yu, Reader J & NIST ASD Team 2015, Th I (energy levels of neutral thorium), NIST Atomic Spectra Database, version 5.3, National Institute of Standards and Technology, accessed 1 January 2017
• —— 2015a, La I (energy levels of neutral lanthanum) , NIST Atomic Spectra Database, version 5.3, National Institute of Standards and Technology, accessed 1 January 2017
• —— 2015b, Ac I (energy levels of neutral actinium) , NIST Atomic Spectra Database, version 5.3, National Institute of Standards and Technology, accessed 1 January 2017
• Laing M 2009, "The place of gadolinium amongst the lanthanoid elements", supplementary material version to "Gadolinium: Central metal of the lanthanides", Journal of Chemical Education, vol. 86, no. 2, pp. 188–189, http://pubs.acs.org/doi/suppl/10.1021/ed086p188, accessed 13 November 2016
• Landau LD & Lifshitz EM 1958, Quantum Mechanics (Non-relativistic Theory), Pergamon Press, Oxford
• Langley RH 1981, "Structure and phase transitions of the lanthanide metals", Journal of Solid State Chemistry, vol. 38, no. 3, pp. 300–306
• Lavelle L 2008, "Lanthanum (La) and actinium (Ac) should remain in the d-block", Journal of Chemical Education, vol. 85, no. 11, pp. 1482–1483
• —— 2009, "Response to misapplying the periodic law", Journal of Chemical Education, vol. 86, no. 10, p. 1187
• Lawrance GA 2013, Introduction to coordination chemistry, John Wiley & Sons, Chichester
• Lawson AC 2016, "5f-electron localisation in the actinide metals: Thorides, actinides and the Mott transition", Philosophical Magazine Letters, vol. 96, no. 3, pp. 85–89
• Leal W, Restrepo G & Bernal A 2012, "A network study of chemical elements: From binary compounds to chemical trends", Communications in Mathematical and in Computer Chemistry, vol. 68, pp. 417–442, http://match.pmf.kg.ac.rs/electronic_versions/Match68/n2/match68n2_417-442.pdf, accessed 10 December 2016
• Lee JD 1996, Concise inorganic chemistry,' 5th ed., Blackwell Science, Oxford
• Liu SH 1980 "Electronic structure of rare earth systems", in Science and Technology of Rare Earth Materials, EC Subbarao & WE Wallace (eds), Academic Press, New York, pp. 121–142
• MacKay KM, MacKay RA & Henderson W 2002, Introduction to modern inorganic chemistry, 6th ed., Nelson Thornes, Cheltenham, p. 256
• Martienssen W & Warlimont H (eds) 2005, Springer handbook of condensed matter and materials data, Springer, Berlin
• Matthias BT, Zachariasen WH, Webb GW & Engelhard JJ 1967, "Melting point anomalies", Physical Review Letters, vol. 18, no. 19, pp. 781–784
• McCaw C 2015, "Thanks Eric for promoting this point of view...," in Five ideas in chemical education that must die: Part five, posted by E Scerri, http://www.rsc.org/blogs/eic/2015/09/periodic-table-group-3, accessed 12 November 2016
• Merz H & Ulmer K 1967, "Position of lanthanum and lutetium in the periodic table", Physics Letters, vol. 26A, no. 1, pp. 6–7
• Moeller T 1973, The chemistry of the lanthanides, Pergamon texts in inorganic chemistry, vol. 26, Pergamon Press, Oxford
• Moeller T, Bailar JC, Kleinberg J, Guss CO, Castellion ME & Metz C 1989, Chemistry with inorganic qualitative analysis, 3rd ed., Harcourt Brace Jovanovich Publishers, San Diego, pp. 955–956, 958
• Moore KT & van der Laan G 2009, "Nature of the 5f states in actinide metals", Reviews of Modern Physics, vol. 81, no. 1, pp. 235–298
• Myers HP 1997, Introductory solid state physics, 2nd ed., CRC Press, Boca Raton, Florida
• Myers RT, Oldham KB & Tocci S 2004, Holt chemistry, Holt, Rinehart and Winston, Orlando
• Nefedov VI, Trzhaskovskaya MB & Yarzhenskii VG 2006, "Electron configurations and the periodic table for superheavy elements", Doklady Physical Chemistry, vol. 408, part 2, pp. 149–151
• Nelson PG 2013, "Periodicity in the formulae of carbonyls and the electronic basis of the periodic table," Foundations of Chemistry, vol. 15, no. 2, pp. 199–208
• Nikulin EI 1975, "Critical magnetic field of superconducting lutetium", Fizika Tverdogo Tela, vol. 17, no. 9, pp. 2795–2796
• Nikulin EI, Volkenshtein NV & Staftsev VE 1973, "Superconductivity of lutecium", JETP Letters, vol. 17, no. 9, pp. 337–338
• Ouyang Y, Wang J, Hou Y, Zhong X, Du Y & Feng Y 2008, "First principle study of AlX (X=3d, 4d, 5d elements and Lu) dimer", Journal of Chemical Physics, vol. 128, no. 7, pp. 074305-1–074305-6, doi:10.1063/1.2831506
• Pennemann RA, Mann JB and Jørgensen CK 1971, "Speculations on the chemistry of superheavy elements such as Z = 164", Chemical Physics Letters, vol. 8, no. 4, pp. 321–326
• Probst C & Witting J 1978, "Superconductivity: Metals, alloys and compounds", Handbook on the Physics and Chemistry of Rare Earths, vol. 1, pp. 749–795
• Ramakrishnan R, Matveev AV & Rösch N 2009, "The DFT + U method in the linear combination of Gaussian-type orbitals framework: Role of 4f orbitals in the bonding of LuF₃", Chemical Physics Letters, vol. 468, nos. 1–3, pp. 158–161
• Ratto CF, Coqblin B & d'Agliano EG 1969, "Superconductivity of lanthanum and cerium at high pressures", Advances in Physics, vol. 18, pp. 489–513
• Reger DL, Goode SR & Ball DW 2010, Chemistry principles and practice, 3rd ed., Brooks/Cole Cengage Leaning, Australia
• Rokhlin LL 2003, Magnesium alloys containing rare earth metals: Structure and properties, Taylor & Francis, London
• Roos B, Lindh R, Malmqvist PA, Veryazov V, Widmark P, & Borin AC 2008, "New relativistic atomic natural orbital basis sets for lanthanide atoms with applications to the Ce diatom and LuF₃, Journal of Physical Chemistry A, vol. 112, no. 45, pp. 11431–11435
• Russell AM & Lee KL 2005, Structure-property relations in nonferrous metals, Wiley-Interscience, New York
• Sastri VS, Bünzli J, Rao V, Rayudu GVS & Perumareddi JR 2003, Modern aspects of rare earths and their complexes, Elsevier, Amsterdam
• Scerri E 2009, "Which elements belong in group 3?", Journal of Chemical Education, vol. 86, no. 10, p. 1188
• —— 2011, The periodic table: A very short introduction, Oxford University Press, Oxford
• —— 2012, "Mendeleev's periodic table is finally completed and what to do about group 3?", Chemistry International, vol. 34, no. 4
• —— 2015, "Five ideas in chemical education that must die - part four", Education in Chemistry blog, accessed 22 November 2016
• Shchukarev SA 1974, Neorganicheskaya khimiya, vol. 2, Vysshaya Shkola, Moscow (in Russian)
• Settouti N & Aouragi H 2014, "A study of the physical and mechanical properties of lutetium compared with those of transition metals: A data mining approach", JOM, vol. 67. no. 1, pp. 87–93, doi:10.1007/s11837-014-1247-x
• Smith JDM 1927, "CCLXVII.—The electronic structure of atoms. Part I. The periodic classification", Journal of the Chemical Society (Resumed), pp. 2029–2038
• Smith JL 1980, "Superconductivity in the actinides", in Superconductivity in d- and f-band metals, H Suhl and MB Maple (eds), Academic Press, New York
• Smith NV, Wertheim GK, Andrews AB & Chen C.-T. 1993, "Inelastic electron mean free paths in the alkali metals", Surface Science Letters, vol. 282, nos. 1–2, pp. L359–L363
• Spedding FH & Beadry BJ 1968, "Lutetium", in CA Hampel (ed.), The encyclopedia of the chemical elements, Reinhold Book Corporation, New York, pp. 374–378
• Steurer W & Dshemuchadse J 2016, Intermetallics: Structures, properties, and statistics, Oxford University Press, Oxford
• Ternström T 1976, "Subclassification of lanthanides and actinides", Journal of Chemical Education, vol. 53, no. 10, pp. 629–631
• Tibbetts TA & Harmon BN 1982, "The electronic structure of Lu", Solid State Communications, vol. 44, no. 10, pp. 1409–1412
• Trifonov DN 1970, Rare-earth elements and their position in the periodic system, translated from the 1966 Russian edition, Academy of Sciences of the USSR Institute of the History of Natural Sciences and Technology, Moscow, published for the Atomic Energy Commission and the National Science Foundation, Washington, by the Indian National Scientific Documentation Centre
• Welling F 1978, "Soft phonons in La: An ⨍-band induced instability", Solid State Communications, vol. 26, no. 12, pp. 913–917
• Wiberg N 2001, Inorganic Chemistry, Academic Press, San Diego
• Wulfsberg G 2000, Inorganic Chemistry, University Science Books, Sausalito, California
• Wulfsberg GP 2006, "Periodic table: Trends in the properties of the elements", Encyclopedia of inorganic chemistry, 2nd ed., John Wiley & Sons, New York, doi:10.1002/0470862106.ia182, accessed 31 December 2016
• Xu W, Ji W-Z, Qui Y-X, Schwarz WHE & Wang S-G 2013, "On structure and bonding of lanthanoid trifluorides LnF₃ (n = La to Lu)", Physical Chemistry Chemical Physics, vol. 15, no. 20, pp. 7839–7847
• Xu W-H & Pyykkö P 2016, "Is the chemistry of lawrencium peculiar?", Physical Chemistry Chemical Physics, vol. 18, no. 26, pp. 17351–17355
• Zhang et al., 2014, "Preparation, characterization, and photocatalytic activity of boron and lanthanum co-doped TiO₂", Catalysis Communications, vol. 45, pp. 144–147 (144)