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The dispute on the composition of group 3 concerns whether the elements under scandium (Sc) and yttrium (Y) in the periodic table should be lanthanum (La) and actinium (Ac), or lutetium (Lu) and lawrencium (Lr). Some compromises between the two can also be found.

The dispute grew out of the problems that Dmitri Mendeleev had with inserting the rare earth elements, and has been discussed in the literature since at least 1921. It arises because of differing viewpoints on the importance and interpretation of electronic and physicochemical considerations.

As variation in the literature on this issue can puzzle students and instructors, IUPAC began a project in 2015 to make a decision on the composition of group 3. In 2021, this project issued a provisional report. This report took the position that the matter was one of convention rather than objectively resolvable, and supported Sc-Y-Lu-Lr as group 3 based on three desiderata: (1) retaining the order of increasing atomic number throughout the table; (2) avoiding any split blocks; and (3) ensuring that the widths of the blocks are 2, 6, 10, and 14, conforming with the quantum mechanical bases of the periodic table.

Early history

From 1871 onward, Dmitri Mendeleev attempted to fit the rare earths into his periodic table as analogues of other known elements. He found this difficult as they did not show the valences that his classification expected. Lanthanum and cerium, whose maximal valences were 3 and 4, could be accommodated in groups III and IV; didymium seemed to be the next element, and he recognised that it would be important to show that it can have valence 5. Bohuslav Brauner spent decades attempting to show this, but was unsuccessful; moreover, in 1885 Carl Auer von Welsbach found that didymium was not an element at all, but a mixture of praseodymium and neodymium. After 25 years of fruitless labour, Brauner came to the conclusion that the maximum valence of the rare earths is 3 or 4. As such, in 1902, Brauner advocated a classification in which all rare earths would be placed in group IV. He named this the asteroid hypothesis, as all the rare earths would then share one place in the periodic system, just as there is an asteroid belt between Mars and Jupiter rather than one planet. Other authors agreed with having the rare earths share a box, though they disagreed over whether they should be placed in group IV, group III, across both, or even across groups II through IV together. This is the origin of the Sc-Y-*-** form sometimes used as a compromise.

However, with the advent of Niels Bohr's theory of the atom in 1912, alternatives began to emerge where the rare earths were viewed as belonging to their own groups in the periodic system, unrelated to any others. This is consistent with quantum mechanics, where they are the first f-block elements, and it became the preferred way to show the rare earths in the 20th century. Some early tables following this approach were drawn by Henry Bassett (1892), Julius Thomson (1895), and Alfred Werner (1905). Werner's table is the first modern long-form table: it isolates La–Yb as the rare earth elements and draws them between groups II and III. Lutetium (then appearing as a blank space as it had not yet been discovered) is treated as a transition metal, below scandium and yttrium. Bassett and Werner mark the first appearances of group 3 as Sc-Y-Lu-Lr (though Lu and Lr were not yet discovered then). Though they both treated the known actinides as analogues of the rare earths, it was not until Glenn T. Seaborg synthesised more transuranium elements in the 1940s that this became standard.

By the 1940s, tables based on electronic configurations and the idea of the differentiating electron started to be adopted, often showing the Sc-Y-La-Ac composition of group 3 – though the electronic configurations that they had been based on were not always accurate according to modern knowledge. Particularly influential was the Sc-Y-La-Ac table published by the Sargent-Welch company, which increased the popularity of this form.

From the 1940s onwards, physicists and chemists began publishing on the composition of group 3. Most authors who published arguments supported Sc-Y-Lu-Lr, but authors of textbooks tended to retain Sc-Y-La-Ac. Over the years, the prevalence of Sc-Y-La-Ac in textbooks decreased; by the 2010s, it had lost its majority, but still retained a plurality over Sc-Y-*-** and Sc-Y-Lu-Lr.

Physical and chemical considerations

Before the time that ion-exchange methods and elution were available, the separation of the rare earths was primarily achieved by repeated precipitation or crystallization. The first separation achieved by these methods was into two main groups: the cerium group and the yttrium group. The reason for this division arose from the difference in solubility of rare-earth double sulfates with sodium and potassium. The sodium double sulfates of the cerium group are poorly soluble, while those of the yttrium group are very soluble. Sc, Y, and Lu appear in the yttrium group, while La and Ac appear in the cerium group. This is also true for the occurrence of Sc, Y, Lu (yttrium group) and La (cerium group) in minerals. Thus La and Ac differ chemically from Sc, Y, and Lu and some chemists have used this as an argument for group 3 as Sc-Y-Lu-Lr.

In the 1960s and 1970s, physicists amassed evidence based on properties where Sc, Y, Lu behave the same way, but La behaves differently. In 1982, Jensen quoted some cases of this in an influential article in the Journal of Chemical Education: the metallic crystal structure at room temperature; the structure of the oxides; the structure of the chlorides; a d-block like structure for the conduction band; and the presence or absence of superconductivity.

In 1985, Norman E. Holden gave a presentation at the 33rd IUPAC General Assembly in Lyon, France. Referring to some physical properties for Sc, Y, La, and Lu (density, crystal structure of the metals and oxides, melting points, shear modulus, Young's modulus, and coefficient of thermal expansion) where La differs from Sc, Y, and Lu, he argued that Sc-Y-Lu-Lr should replace Sc-Y-La-Ac.

Jensen also noted that if trends are plotted for atomic radius, sum of the first two ionisation energies, melting points, and Allred-Rochow electronegativity, Sc-Y-Lu is consistently a better match for the trends down the other groups of the d-block (Ti-Zr-Hf, V-Nb-Ta, etc.) than Sc-Y-La. Eric Scerri has nonetheless criticised his case on the grounds of selectivity, as if one sums the first three ionisation energies, Sc-Y-La matches the typical d-block trend better for this property than Sc-Y-Lu. Scerri thus argues that cases based on specific physical or chemical data cannot be conclusive on this problem.

Chistyakov, a Soviet chemist, argued for Sc-Y-Lu on the grounds of the secondary periodicity trend, where a zig-zag or alternating trend in properties appears when one descends a group of elements. He noted that Sc-Y-Lu exhibits secondary periodicity for example in atomic radii, just like Ti-Zr-Hf and other d-block groups, whereas Sc-Y-La does not. On this basis he supported Sc-Y-Lu.

Some authors have argued for all fifteen lanthanides to be placed below yttrium, which is a reversion to Brauner's asteroid hypothesis. The reasoning is that it clarifies the similarity and continuity of properties across the entire set of lanthanides from La to Lu. However, this intermingles the f- and d-blocks. Moreover, an f-subshell has a maximum occupancy of 14 electrons and hence the f-block should only be 14 elements long. Jensen criticises this as "chemical nonsense" and an "antiquated interpretation", as this puts the f-block elements all into group 3, while many of them can achieve an oxidation state higher than +3.

Electronic considerations

Atomic electron configurations

The electron configurations of the relevant atoms are as follows: scandium 3d4s, yttrium 4d5s, lanthanum 5d6s, lutetium 4f5d6s, actinium 6d7s, and lawrencium 5f7s7p. (The electron configuration of Lr was not determined till fairly recently, so in many early papers discussing the dispute, it was thought to be 5f6d7s like lutetium.)

Most of the lanthanides were originally thought to have the configuration 4f5d6s. The tables from the 1940s that first introduced Sc-Y-La-Ac did so on the basis of the differentiating electron from the previous element. Barium has configuration 6s, so lanthanum 5d6s was taken as the first d-block element of the sixth period. Still in period 6, it was thought that ytterbium had the configuration 4f5d6s, so lutetium 4f5d6s added the last f-electron and was regarded as the last f-block element. However, already in 1937 it had been experimentally determined that ytterbium's true configuration is 4f6s, so lutetium 4f5d6s in fact adds a d-electron to the preceding element. Therefore, differentiating electrons would make La and Lu equally valid candidates for the position below scandium and yttrium.

As more experimental data came in, it emerged that most of the lanthanides have a configuration 4f6s, with no d electron. Eleven of the fifteen lanthanides have no d electron; only four do (La, Ce, Gd, and Lu). As for the actinides, eight have a 5f7s configuration with no d electron; five have one (Ac, Pa, U, Np, and Cm); and one has two (Th). In particular, the filling of the 4f subshell spans only thirteen elements (Ce–Yb), which means that both Sc-Y-La-Ac and Sc-Y-Lu-Lr encounter a problem as quantum mechanics suggests that there should be fourteen 4f elements. Because the majority of the lanthanides and actinides have the fs configuration, it has been argued that this is the ideal configuration, and that the exceptional fds configurations (including those for La and Ac) are an anomaly: this argument would support Sc-Y-Lu-Lr.

Since neither La nor Ac actually has an f-electron as a single atom, some authors have argued that they cannot be f-elements, especially because they form the only paired anomaly where all elements in a group do not have the correct valence electrons for their block. This would support Sc-Y-La-Ac. However, others have pointed out that thorium 6d7s has no f-electron either, but was accepted since Seaborg as part of the f-block without controversy; thus they considered it an inconsistency to allow thorium to be an f-block element, but not lanthanum and actinium. Jensen has also noted that there are other cases where the majority of the elements in a group are anomalies (e.g. group 11). When lawrencium's correct configuration was measured, it led to further discussion. Laurence Lavelle argued that its 5f7s7p prohibited it from being a d-block element and suggested that it was an analogue of Tl in the p-block. But since he simultaneously argued that lawrencium should remain in the f-block, Jensen's rebuttal accused him of inconsistency.

It has also been argued that the configurations of La and Ac are closer to Sc and Y, because Sc, Y, La, and Ac do not have a filled f subshell above the core, whereas Lu and Lr do. However, Jensen argues that this is misleading, as all nine other d-block elements of period 6 add such a f subshell. For example, in group 4 the configurations are Ti 3d4s, Zr 4d5s, and Hf 4f5d6s. Thus, in his opinion the analogy instead favours Sc-Y-Lu-Lr. Lev Landau and Evgeny Lifshitz wrote in their Course of Theoretical Physics that since "the 4f shell is complete in lutetium", it was incorrect to place Lu as a rare-earth, and that it should therefore be a transition metal; this argument was repeated by Holden in his 1985 presentation to IUPAC.

Other electronic considerations

It has sometimes been argued that atomic configurations in the gas-phase are not very relevant. Some authors have argued that the periodic table is based on ideal rather than real configurations, pointing to other elements for evidence: there are many anomalies in the d-block, but they have not been used to question the placements of those elements. Chemists generally agree that the elements ending the d-block in periods 4 through 6 are zinc (3d4s), cadmium (4d5s), and mercury (4f5d6s), even though the d-orbitals are actually fully occupied earlier, at copper (3d4s), palladium (4d), and gold (4f5d6s). The ideal configurations fs can exist as excited states even when they are not the real ground-state configurations, which has also been used as evidence for Sc-Y-Lu-Lr.

The Aufbau principle states that:

1. Electron shells fill in order of increasing n + ℓ.
2. If two electron shells are available with the same value of n + ℓ, then the one with the smaller n fills first.

It is typically used to determine ideal electron configurations, and is correct for all but 20 elements, which suggests that those twenty are simply exceptions to a general rule. According to the Aufbau principle, all the orbitals will n + ℓ values up to 6 have been filled at barium. For the next n + ℓ value, 7, the orbitals available are 4f, 5d, 6p, and 7s. As 4f has the lowest value of n (4), the Aufbau principle states that it should fill first (from La to Yb), before the 5d shell fills (n = 5) from Lu to Hg. Hence the Aufbau principle supports Sc-Y-Lu-Lr.

Ground-state gas-phase configurations consider only isolated atoms as opposed to bonding atoms in compounds (the latter being more relevant for chemistry), which often show different configurations. Moreover, the lowest levels of two different configurations often are separated by only very small energies. There are multiple excited states for each configuration and in some cases they can overlap (e.g. nickel or terbium), making which configuration happens to be the ground state chemically quite irrelevant. W. H. Eugen Schwarz contends that it is the dominant electron configuration of atoms in chemical environments, and not free gaseous atoms in a vacuum, that can rationalise qualitative chemical behaviour. Gas-phase ground state electron configurations are only important for a few specialised topics, such as atom–molecular gas-phase reactions.

Schwarz considers that La/Ac and Lu/Lr are all d-block elements, and duplicates Sc and Y over each pair, because in his opinion none of them have '"active" f valence electrons'. However, not all authors agree with Schwarz's opinion on the activity of f valence electrons. Jensen notes that La and Ac have low-lying f-orbitals that do not behave like the high-up ones in the hydrogen atom, whereas Lu and Lr do not. In other words, in hydrogen through barium, the 4f orbitals are far enough from the nucleus that when analysing them, one can approximate the core and remaining electrons as a point charge; starting from lanthanum, this ceases to be the case, with lanthanum showing 4f levels more similar to those of the following rare earths. Christian K. Jørgensen considers the amount of 4f valence involvement for lanthanum to be approximately equal to the amount of 5f valence involvement for thorium, and that Lu "can most conveniently be considered as the first member of the 5d series". Jørgensen notes that Pr through Yb show characteristic narrow bands with their positions almost completely independent on the ligands, but the following 5d elements (along with the 3d and 4d elements) behave significantly differently; while both types of elements show electron-transfer bands, ligand field theory becomes important for the d elements.

Some physicists contend that La has a 4f valence contribution that is lacking in Sc, Y, and Lu, on the grounds that it would explain some of the aforementioned properties where La differs from Sc, Y, and Lu. For instance, while Sc, Y, and Lu crystallise in the hcp crystal structure, La crystallises in the dhcp crystal structure. This is a singular anomaly among the nonmagnetic transition metals. Jörg Wittig argued that this difference is due to a 4f valence band for La that is absent from Lu. In support of his hypothesis, he points to the fact that the grounds that the dhcp structure is only otherwise seen in f-block elements, and that the pressure-temperature phase diagram of lanthanum is isomorphic to those of Pr and Nd, which are uncontroversially f-block. Wittig argued that a 4f valence band may similarly be responsible for low-temperature superconductivity of La, which Sc, Y, and Lu do not exhibit. Karl Gschneidner was of a similar opinion; he noted that a "pseudo-La" without 4f involvement should have a higher melting point than it actually does, and argued that 4f valence bands were responsible.

Other properties

If elements are to be placed in order of increasing atomic number, then a Sc-Y-La-Ac table requires a split in the d-block. Lanthanum appears as the first d-block element, but then fourteen f-block elements intervene (Ce to Lu), before the d-block finishes with Hf through Hg. No such thing is necessary in a Sc-Y-Lu-Lr table. This has widely been considered undesirable, although a few authors have defended it based on the atomic configurations of La and Ac. In particular, Eric Scerri considers it to be an ad hoc move that for justification requires an independent argument, that "is especially not available to authors ... who maintain that the d-block perfectly reflects the filling of five d orbitals by ten outer electrons. Why should there be a break only between the first and second of these electron-filling processes?"

Scerri has noted that Y, Lu, and Lr form an atomic number triad (71 is the average of 39 and 103), whereas Y, La, and Ac do not. Michael Laing has responded noting that Sc, Y, La form an atomic number triad (39 is the average of 21 and 57) while Sc, Y, Lu do not. However, Scerri argued back that the situations are different, because La/Lu and Ac/Lr lie inside periods of equal length, whereas Y and La/Lu do not.

IUPAC

In 1988, IUPAC published a report on the numbering of groups in the periodic table that also touched on the group 3 problem. It wrote:

According to the electron configurations of the elements, the scandium group consists of the elements

Sc, Y, Lu, Lr.

This was pointed out as early as 1959 by L.D. Landau (ref. 20) and later by other authors (ref. 13, 14, 20 to 25). Most periodic tables in textbooks and classrooms, however, list Sc, Y, La, and Ac as elements of the scandium group and designate the elements Ce to Lu and Th to Lr as lanthanides and actinides, respectively. The historical background for this arrangement is given in a paper by W.B. Jensen (ref. 21). Based upon their electronic configurations and their chemical and physical properties, the elements La to Yb and Ac to No should be inserted between barium and lutetium and between radium and lawrencium or for practical reasons be listed at the bottom of the table.

Despite this, it also stated that the forthcoming IUPAC Red Book (a collection of nomenclature rules for inorganic chemistry) would use a compromise, which turned out to be the Sc-Y-*-** form. The 1990 Red Book displayed the periodic table in three formats, 8-column (based on Mendeleev's original), 18-column, and 32-column; the first two showed Sc-Y-*-** in group 3, but the third showed Sc-Y-Lu-Lr as group 3. In 2005, the 8-column and 32-column forms were dropped from the IUPAC Red Book, leaving only the compromise version in 18-column format. Since then, the so-called IUPAC periodic table has shown Sc-Y-*-** (though IUPAC has not approved any specific form of the periodic table), though the IUPAC newsmagazine Chemistry International has continued to publish articles by Scerri arguing for Sc-Y-Lu-Lr.

In 2015 IUPAC began a project to form a view as to whether either lanthanum and actinium or lutetium and lawrencium should appear in group 3, chaired by Scerri and including Jensen and Lavelle. It considered the question to be "of considerable importance" for chemists, physicists, and students, noting that the variation in published periodic tables on this point typically puzzled students and instructors.

A provisional report appeared from the project in 2021. It concluded that the group 3 dispute cannot be decided by any objective means and that that made it more important for IUPAC to decide it as a matter of convention. The report noted the following points:

• Sc-Y-La-Ac requires a very unevenly split d-block, while Sc-Y-Lu-Lr does not. While both forms "seem to be equally plausible" in the 18-column form, this is because the d-block split is masked by that form; it is much more obvious in the 32-column form.
• Sc-Y-*-** makes the f-block rows appear with 15 elements, breaking the connection with orbital capacity as the quantum mechanical bases of the periodic table require (as an f-subshell can hold at most 14 elements).
• Only Sc-Y-Lu-Lr avoids a split d-block and retains 14-element f-block rows.
• Assigning electron configurations to atoms, as well as assigning elements to blocks, is an approximation. For example, all forms under consideration assign Th to the f-block even though its atom does not have any f-electrons.
• The Sc-Y-*-** table was stated to have been "designed by practitioners of specialized branch of relativistic quantum mechanics concerned with the properties of super-heavy elements". While such considerations may support grouping together 15 elements rather than 14 as the f-block, it is "interest-dependence" and should not "be imposed on the majority of users of the periodic table".
• Quantum mechanics explain the periodic table, as proven by "historical developments", though they do not provide a "full and exact reduction".

As such, the report concluded that "perhaps a compromise could be reached on" Sc-Y-Lu-Lr, based on the following three stated desiderata:

First, it displays all the elements in order of increasing atomic number. Secondly, it avoids splitting the d-block into two highly uneven portions, and thirdly, it depicts all the blocks of the periodic table in accordance with the underlying quantum mechanical account of the periodic table which calls for 2, 6, 10 and 14 orbitals to occur in the extra-nuclear electron-shells.

The project ended that year. Currently, IUPAC's website on the periodic table still shows the 1988 compromise, but mentions the group 3 problem and project to resolve it, and writes "Stay tune".

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