A Comparison of the Structural Chemistry of Scandium, Yttrium, Lanthanum and Lutetium: A contribution to the Group 3 debate

Data deposited in the Cambridge Structural Database (CSD) for compounds of scandium, yttrium, lanthanum and lutetium(III) have been analysed to assess the structural similarities of complexes of the different metal ions. 29 sets of compounds of Sc, Y, La and Lu where at least three of the elements form compounds with the same ligands have been identified and their crystal structures analysed. In 14 of them, scandium and lutetium have the same coordination number; in the remaining 15 they do not. Similarly, there are 10 examples where there is a difference in coordination number between Lu and Y for compounds with the same ligands. For the other 19 either the coordination numbers are the same or that compounds for both the elements under consideration have not been reported. Overall structural differences correlate well with the size of the metal ions and provide no true chemical basis for arranging Lu rather than La in one triad with Sc and Y.


1.
Introduction Traditionally, scandium, yttrium and lanthanum have been considered as a triad due to their occupation of successive vertically arranged boxes in Group 3 of the Periodic Table [1].In recent years, the suggestion has been made, not without controversy, that lutetium is better fitted to be member of this group than lanthanum [2][3][4][5][6][7][8] and the arrangement of the Periodic Table is under current debate as a IUPAC project [9,10].In the current IUPAC version of the Periodic Table the 'box' under yttrium contains the word "lanthanoids", rather than either La or Lu, reflecting the lack of consensus at the present time.Most recently, Vernon has presented 'a series of ten interlocking arguments' for La belonging in Group 3 [10].But how similar are scandium and lutetium in their chemistry, particularly as manifest in the structures of their compounds?
In general, the size of successive atoms increases as groups are descended In the Periodic Table , although with heavier elements, including La -Lu, relativistic effects counterbalance this to some extent [11,12], and it is remarkable that atomic radii vary by only a factor of approximately two over the whole Table .Nonetheless, yttrium is larger than scandium, and lanthanum is larger than yttrium, but in the elements immediately following lanthanum this trend is reversed.Because of the poor shielding by the 4 f electrons of the increasing nuclear charge, as the lanthanide series is traversed from La to Lu, the ionic radius of the M 3+ ions decrease by some 16%, the effect well-known as the "lanthanide contraction".The resulting change in ionic radius from La 3+ (radius 1.172 Å for six coordination) to Lu 3+ (radius 1.001 Å) causes lutetium to be smaller than Y 3+ (1.040 Å), the latter having virtually the same ionic radius as Ho 3+ (1.041 Å) and thus very similar chemistry [13].
As Victor Moritz Goldschmidt pointed out, the decreasing ionic radii of the lanthanide ions with increasing atomic number affects not just the properties of the lanthanides but also the succeeding 5d metals, and this is the context in which Goldschmidt originally coined the term 'lanthanide contraction' [14].Thus Zr 4+ ions are virtually the same size as those of Hf 4+ , with ionic (crystal) radii for six coordination of 0.86Å and 0.85Å respectively, the effect of the greater effective nuclear charge almost exactly counterbalancing the effect of the extra electronic subshell, and their chemistry is very similar [15].Zirconium is much more abundant than hafnium and so because they occur together hafnium was not discovered until 1923.Some properties of these metals are different, however.For example, as the hafnium atom is nearly twice as heavy as a zirconium atom, though of (virtually) identical size, its density is 13.35 g cm -3 , compared with the value of 6.51 g cm -3 for zirconium.Likewise, there are very close resemblances in the chemistry of platinum and palladium, most notably in the (+2) oxidation state [16][17][18].Similarly, the Au + ion is smaller than the Ag + ion (experimental radii are 1.25 and 1.33 Å respectively), [19][20][21] though, once again, there are major differences in their properties such as in their ligand substitution rates, and these differences are often attributed to relativistic effects [22].
So where does Sc 3+ fit in?Although it has a significantly smaller ionic radius (0.885 Å) than Y 3+ or even Lu 3+ , the smallest Ln(III), it is sometimes compared to Lu 3+ .
Certain aspects of the chemistry of the compounds of scandium, yttrium, and of the series lanthanum to lutetium, such as their lattice energies, solvation energies and complex stability constants, are closely related to the size of the metal atom or ion, and also to the charge density of the metal ions.In this article a survey of the structures of a range of the compounds of Sc, Y, La and Lu is presented.Metal-ligand bond parameters as well as their coordination numbers and coordination geometries have been analysed with the intent of providing new insights into the relationships between lutetium and the Group 3 elements.

The Radii of the +3 ions of Sc, Y, La and Lu
The largest single repository of structural data for lanthanide complexes is the Cambridge Structural Database (CSD) [23] which contains entries for 45,191 compounds of La and Ce to Lu (CSD Version 5.41(November 2019) + 3 updates).In the same version of the CSD there are 1490 entries for Sc-containing compounds and 3959 entries for Y-containing compounds.It should be noted that all these complexes contain at least one "organic" carbon atom so that simple salts such as [Ln(H2O)9][CF3SO3]3, the oxides Ln2O3 or the binary halides [LnX3; X = F, Cl, Br, I ] are omitted unless accompanied in the crystal structure by a species containing an organic carbon.However information on these salts can be found in the Inorganic Crystal Structure Database (ICSD) [24] provided by FIZ Karlsruhe GmbH.The CSD, with its sophisticated search and analysis software, is an appropriate tool for an investigation of the structural chemistry of the structural chemistry of the Group 3 elements and of the lanthanides.
The +3 ions of Sc, Y, La and Lu, and indeed all the lanthanide(III) ions, are classed as "hard" metal ions and, as such, have a preference for bonding to "hard" bases with oxygen or nitrogen donor atoms as illustrated in Figure 1 (CSD Version 5.41(November 2019) + 3 updates).The lanthanides have been important in providing a basis for attempts to establish a quantitative scale for "oxophilicity" [25].Since M-O bonds are somewhat more prevalent in the structures being considered, the analysis was carried out on these CSD hits.The results of a search for Sc, Y, La and Lu complexes that contain at least one M-O bond for coordination numbers 6 to 9 are presented in Table 1 (additional material is available in the Supporting Information).The mean M-O distance with the associated esd and the variance are shown and, assuming a radius of 0.66 Å for the coordinated O atom (O atom covalent radius), the radius of the M ions in the complexes is obtained by subtraction.For comparison, the atomic radii for the four elements, determined empirically from crystals by J. C. Slater in the 1960s [26], are included in the final column.The comparison shows the improvement in the ability to fine tune the radii values, including accounting for different coordination numbers, over the last sixty years as the number of structural examples of each type that can be used in the analysis has increased.
Figure 2 shows a plot of the M-O mean bond lengths for the 6-, 7-, 8-and 9coordinate complexes of the four 3+ metal ions, which indicates that across the complexes with different coordination numbers the M-O bonds in Lu 3+ and Y 3+ complexes are similar.This would suggest that for chemical and physical properties of compounds of these elements, where the size of the metal ion is important, the chemistry of Lu complexes might most closely resemble that of Y complexes.The analysis of the M-O bond lengths in the complexes of the 3+ ions of the four elements is also consistent with the trends in ionisation energies (Table 2) and in the electronegativities (on both the Pauling and Allred-Rochow scales [27,28]) with the data for Lu most closely resembling that of Y, with Sc showing a higher value for the formation of the 3+ ion and higher electronegativity than that of Lu.

3.
Binary compounds One reason for the perceived similarity of scandium and lutetium lies in the structures of simple binary compounds [29,30].Certainly, the oxide and the halides -except the fluoride -all have the same coordination number (though not necessarily adopting the same structure).Thus, scandium, yttrium and lutetium all have a coordination number of 6 in their oxides M2O3 (M = Sc, Y, Lu) and in all the halides, save the fluoride.Apart from the fluoride (six coordinate WO3 structure), all ScX3 (X = F, Cl, Br, I) have the FeCl3 structure, also adopted by LuX3 (X = Br, I) whilst LuCl3 has the AlCl3 structure.Lutetium fluoride adopts the 9 coordinate YF3 structure.As expected, lanthanum has higher coordination numbers in its halides than either of the other two metals, with 11-coordination in LaF3, 9 coordination in LaX3 (X = Cl, Br) and 8 coordination in LaI3.Lanthanum oxide has capped octahedral seven-coordination.

Hydrated salts and the aqua ions
It has been known for some 80 years that a number of hydrated lanthanide salts [31,32] such as the bromates and ethyl sulfates contain [M(OH2)9] 3+ ions with tricapped trigonal prismatic coordination [33].
Clearly the solubility of these salts is the factor driving their isolation, removing from solution what may be an ion of very low abundance compared with those of higher coordination number.Studies of water ligand exchange rates [51] on the lanthanide(III) aqua cations in solution have been interpreted in terms of both nona-aqua and octa-aqua species being present, with the former predominating for the early lanthanides and the latter for the later.

Other monodentate ligands
Dimethylsulfoxide (DMSO) and N,N'-dimethylpropylene urea (DMPU) are two ligands bulkier than water which form homoleptic complexes with both scandium and the lanthanide (III) ions for which both solution and solid state structural data are available.X-ray diffraction studies of crystalline [Sc(DMSO)6]I3 (Figure 4a) show it to contain octahedral [Sc(DMSO)6] 3+ ions (Sc-O 2.069(3) Å), whilst the bond length of 2.09(1) Å indicated by EXAFS measurements for solvated scandium(III) ions in DMSO solution implies that six co-ordinate species are also present there [52].The yttrium(III) ion in the complex [Y(DMSO)8]I3 (Figure 4b) is eight coordinate with a distorted square antiprismatic geometry and an average Y-O bond length of 2.38 Å [53].
All the lanthanides form complexes [Ln(DMSO)8]I3 (Ln = La-Lu except Pm) and X-ray diffraction confirms the presence in the crystal of [Ln(DMSO)8] 3+ ions, with distorted square antiprismatic coordination [54].The average metal -oxygen bond length decreases from 2.49 Å (La) to 2.30 Å (Lu).EXAFS spectra of the solids indicate very similar Ln-O distances to these and show a close correspondence with the spectra of DMSO solutions of the lanthanide ions, suggesting the presence of eight coordination in solution as well [55].N,N-dimethylpropylene urea is more demanding sterically.Limited published data indicate that the DMPU-solvated scandium ion is six-coordinate [41], while a crystal structure of [Y(DMPU)6]I3 (Figure 5) confirms that the cation adopts an octahedral geometry with an average Y-O bond length of 2.23 Å [53].The X-ray diffraction data on the crystalline complexes show that the octahedrally coordinated [Ln(DMPU)6]I3 complexes are formed across the lanthanide series (La-Lu except Pm).In solution, however, EXAFS spectra of DMPU solutions of the lanthanides are, with the exception of lutetium, quite different to those of solid [Ln(DMPU)6]I3, with Ln-O distances 0.08 Å longer than those in the solid state, but shorter than the values expected for eight-coordination, consistent with seven coordinate [Ln(DMPU)7] 3+ ions [56].In the case of lutetium, solid [Ln(DMPU)6]I3 and solutions of LuI3 in DMPU give identical EXAFS spectra, showing that the smaller Lu 3+ ion is six coordinate in DMPU solution [56].Once again, it is clear that the close ion association enforced in a solid can influence the form of the species isolated and that this form may not be that apparently dominant in solution.In turn, this raises the question of how, in solution, a secondary coordination sphere of solvent may influence the form of the primary coordination sphere.

THF complexes of the chlorides
The THF complexes of the lanthanide chlorides are a case where stoichiometry does not always give a clear indication of structure [57].This, in general, is one of the reasons why Xray crystallography is so important in characterising lanthanide ion coordination chemistry, since electronic spectra of the complexes, where available, are rather insensitive to the nature of the primary coordination sphere and it has been observed in many crystal structures that good ligands incorporated in the crystals are not necessarily bound directly to the metal ions [58].Both mer-[ScCl3(THF)3] [59] (Figure 6) and mer-[LuCl3(THF)3] [60] feature octahedral six coordination and there is no crystal structure of the analogous yttrium complex.

Triphenylphosphine oxide complexes
Triphenylphosphine oxide complexes of the lanthanide nitrates afford structural variety with different coordination numbers.[La(Ph3PO)4(NO3)3] attains nine coordination (Figure 8a) through one monodentate and two bidentate nitrates, but although Lu(Ph3PO)4(NO3)3 has a similar molecular formula the presence of one ionic nitrate leads [62] to the lower coordination number of eight in [Lu(Ph3PO)4(NO3)2] + NO3 -(Figure 8b).The yttrium complex, [Y(Ph3PO)4(NO3)2] + NO3 -, is also eight coordinate with one ionic nitrate [63].The scandium complex has a different stoichiometry, and the presence of just two phosphine oxide ligands means that all three nitrates can adopt the bidentate mode in eight coordinate [Sc(Ph3PO)2(NO3)3] [64] (Figure 8c).Thus, the higher number of nitrates in its coordination sphere helps scandium to attain the same coordination number as lutetium and yttrium.Triphenylphosphine oxide complexes of the triflates have also been examined.They have the same stoichiometry [M(Ph3PO)4(CF3SO3)2] + (CF3SO3) -,but differ in the binding of the triflate groups.While the Y complex has not been reported the Sc and Lu compounds are both six coordinate (Figure 9a), with two monodentate triflates, whilst in the lanthanum complex (Figure 9b) (likewise elements as far as neodymium) one triflate is bidentate, affording seven coordination [65,66].)3] has a pyramidal MN3 core [67] as does the ytrrium analogue [68] both showing disorder of the metal atom above and below the plane of the three N-donor atoms.This structural feature is also found in the crystal structures of their lanthanide analogues (La to Lu except Pm) with N-Ln-N angles around 114 rather than the 120 expected for a planar structure [69,70].Electron diffraction results indicate that the pyramidal structure is retained in the gas phase [71,72], but the complexes are evidently planar in solution as they have no dipole moment.Theoretical calculations [73] suggest that it is -Si-C agostic interactions with the central metal that cause this small pyramidal distortion (Figure 10).Lanthanum compounds with even bulkier amide ligands, [La(N(SiMe2Bu t )2)3] and [La(N(SiMe2Bu t )(SiMe3))3], do not show this distortion, both having planar LaN3 cores [74].In contrast to the bis(trimethylsilyl)amides, the less bulky diisopropylamides form isolable THF adducts, and here there is a significant difference between the metals.Lanthanum and yttrium form five coordinate [Ln(N i Pr2)3(THF)2] [75] (Figure 11a), whilst scandium and lutetium form four coordinate [M(N i Pr2)3(THF)] [75, 76] (Figure 11b).However, these amides were synthesized and crystallized under differing conditions, which may render strict comparisons difficult.The complex (NO)2[Sc(NO3)5] again has a structure based on a trigonal bipyramid (Figure 12c).There are four bidentate nitrates with one of the equatorial nitrates being monodentate, leading to nine coordination, whereas in the yttrium analogue the five nitrate groups are symmetrically bidentate, giving an overall coordination number of ten [79] similar to that of the lutetium complex.In Rb2[Sc(NO3)5], however, there are three bidentate and two monodentate nitrates, resulting in eight coordinate scandium [80].

Carbonate complexes
The carbonate complexes of these metals are less well studied than the nitrates, though similarly they involve bidentate carbonates.Early lanthanides form [Ln(CO3)4(H2O)]  13), as the [C(NH2)3] + salt, also adopts a distorted dodecahedral geometry with an average Y-O bond length of 2.348 (15) Å which is similar to the value for the Lu anion.No corresponding lanthanum complex has been reported in the solid state, though the [La(CO3)4] 5-ion (degree of hydration not known) has been identified in aqueous solution [84], and lanthanum is known to be 10 coordinate in Na4La2(CO3)5 [83].

Acetates
The anhydrous lanthanide acetates [Ln(OAc)3] have structures [95] involving several types of bridging and chelating acetate, displaying a decrease in coordination number from 10 at the beginning of the series to 7 at the end.The [Sc((OAc)3] complex has a simple polymeric structure with a linear chain of metal ions connected by three bridging acetate groups on either side, affording octahedral six coordination [96] (Figure 18a).[Ln(OAc)3] (Ln = Tm-Lu) are similar, except that two of the bridging acetates have a single oxygen bridging the two metals, whilst the acetate group acts as a chelating ligand to one lutetium, resulting in seven coordination [97] (Figure 18b).The acetates of yttrium and the lanthanides from Sm to Er are eight coordinate and involve both chelating and chelating bridging acetates.[Nd(OAc)3] has both 8 and 9 coordinate metal ions, whilst praseodymium is 9 and 10 coordinate in Pr(OAc)3.Finally [Ln(OAc)3] (Ln = La, Ce) have 10 coordination, with tetradentate doublebridging and bridging bidentate acetate groups [98].

Terpyridine complexes of the metal nitrates, [M(terpy)(NO3)3(H2O)n]
As already noted, the bidentate nitrate group with its small bite angle is often associated with high coordination numbers, and these complexes are no exception [100].The compounds show smooth progression in bond length with decreasing ionic radius of Ln 3+ , clearly seen in the short series [Ln(terpy)(NO3)3] (Ln = Er to Lu) which makes a cogent point about congestion in the coordination sphere.Comparing Er(terpy)(NO3)3 with Lu(terpy)(NO3)3, the average Ln-N bond length decreases from 2.424 Å in the erbium compound to 2.394 Å in the lutetium compound, corresponding changes in Ln-O (nitrate) being from 2.406 Å to 2.380 Å, in keeping with a decrease from 1.030 to 1.001 Å in ionic radius for the nine-coordinate ions [13].The spread of Ln-O distances involving the coordinated nitrate groups increases from 0.070 Å in the erbium complex to 0.090 Å in the lutetium compound, which may indicate growing congestion.
The scandium compound (Figure 21a) has the same stoichiometry as those of the later lanthanides, but examination of its molecular structure [103] reveals a significant increase in congestion over the lutetium compound (Figure 21b).The Sc-O distances in [Sc(terpy)(NO3)3] range from 2.232(2) Å to 2.458(2) Å, a considerably bigger spread of distances (0.226 Å) than observed even in [Lu(terpy)(NO3)3], reflecting the difficulty in arranging the nine donor atoms round the small Sc 3+ ion.Here the longest Sc-O distance of 2.458 Å is over 0.14 Å longer than the next longest (2.315 Å), and nine-coordinate is an optimistic description of the complex ( '8.5 coordinate' is a possible description).The mean Sc-N bond length (2.30 Å) is significantly shorter than that of Lu-N bond (2.394 Å), a factor which may contribute to partial displacement of the nitrate ligands.Interestingly, depending on the recrystallisation conditions, two different structures have been obtained for the yttrium terpy tris-nitrate complex by recrystallisation from acetonitrile.One complex [Y(terpy)(NO3)3(H2O)] is nine co-ordinate with two bidentate nitrates and one  22b).In all of these complexes, the EDTA is hexadentate, binding through two nitrogen donor and four oxygen donor atoms and wrapping itself round the metal ions, leaving space for additional water molecules to come into the coordination sphere.It is pertinent to remark again that, allowing for solubility effects, the counter-ion can influence the thermodynamic product that crystallises from solution, so that sodium ions crystallise the [Er(EDTA)(H2O)3] -ion, with NH4 + cation favouring [Er(EDTA)(H2O)2] -.However, this complication is only likely to occur around the point (Ho-Er) where both the eight and nine-coordinate anions are present in solution in significant amounts, and is unlikely to affect metals at the extremes of the series [108].
The solid state structure of Na[La(HDOTA)La(DOTA)].10H2Oshows it [114] to contain a dimerised unit with a bridging carboxylate group, but in solution it is believed to exist as a [La(DOTA)(H2O)] -ion, similar to cerium and other lanthanides [115,116].

Organometallic compounds 7.1 Benzyls
Tribenzyls are formed by scandium, yttrium and all the lanthanides; they are isolated as THF adducts with the formula [M(benzyl)3(THF)3].There is more to this than at first meets the eye.[Sc(benzyl)3(THF)3], [Y(benzyl)3(THF)3] and [Lu(benzyl)3(THF)3] are all six-coordinate with  1 -benzyls [117,118] (Figure 25a), but the greater size of the lanthanum ion means that the adoption of this structure would leave space around the ion to accommodate additional ligands.In this case three additional ipso-interactions are observed (with La-C distances some 0.3 Å longer than the other La-C bonds) and this results in the benzyl groups adopting  2 -coordination (Figure 25b) [119].All the benzyl groups remain  1 -in the five coordinate Sc compound [117] (Figure 26a), but one benzyl has an ipso-interaction in the lutetium compound (Figure 26b), evidently on account of the slightly greater size of lutetium(III) [120].

Tris(cyclopentadienyl) compounds
The tris(cyclopentadienyl) compounds of the rare earths, [(C5H5)3Ln], display an interesting variety of structures (Figure 28).Essentially molecular structures are only displayed by the yttrium compound [124] and those of a few lanthanides of similar size (e.g.Ho, Er, Tm).Larger lanthanides have polymeric structures, illustrated by the lanthanum compound [125], where lanthanum is attached to three  5 -rings, one of which also participates in a  2 attachment to a neighbouring lanthanum.If a Cp ring is thought of as occupying three coordination sites, then this approximates to 11-coordinate lanthanum.It should be noted that our use of coordination number assignments for Cp-rings differs from the more rigid IUPAC/Werner guidelines that are based on the number of atoms that form dative bonds.At the other end of the lanthanide series, lutetium can only bind to two  5 -rings, also forming two  1 -attachments to bridging rings, approximating to eight-coordination [126].The scandium compound is isostructural [127].
The metal ion evidently attains the highest coordination number possible consistent with its size, making use of the ability of the cyclopentadienyl ligand to adopt more than one bonding mode.Cyclopentadienyl derivatives of the lanthanides have been studied for many years, but it is only relatively recently that more bulky ligands have been investigated.It was believed for a long while that compounds [(C5Me5)3Ln] were not likely to be isolable on account of the bulk of the substituted ring, but following a breakthrough in the synthesis of the samarium compound, imaginative synthetic techniques have led to the synthesis of the series up to [(C5Me5)3Er] [128] There is no report of the isolation of the lutetium or scandium compounds.
Use of the less demanding C5Me4H ligand affords interesting comparisons.[(C5Me4H)3Ln)] (Ln = La [129], Lu [130]) (Figure 29a) are isostructural, with three pentahapto cyclopentadienyl rings.Assuming that a Cp ring takes up three coordination sites, this corresponds to nine coordination.The metal-to-ring centroid distance decreases from 2.616 Å in the lanthanum compound to 2.406 Å in the lutetium compound, rather more than the 0.164 Å predicted from ionic radii [13].It is notable (and counter-intuitive) that lutetium can accommodate three pentahapto-C5Me4H rings, but not three of the less bulky C5H5, in the solid state, at least.The yttrium complex, [(C5Me4H)3Y)], also accommodates three pentahapto-C5Me4H rings [131,132].
However, in the solid state the corresponding scandium compound has the structure [( 5 -C5Me4H)2Sc( 1 -C5Me4H)] with one monohapto C5Me4H ligand, a consequence of the smaller size of scandium (Figure 29b).Only one type of C5Me4H ring is seen in the solutions down to -80 °C, evidently due to fluxional behaviour [133].
It needs to be borne in mind that the species isolated in the solid-state may not be that favoured in other phases.Most strikingly, scandium, lanthanum and lutetium (and the intervening lanthanides) all form crystalline perchlorate salts containing octahedral [M(H2O)6] 3+ ions, whilst the coordination number of the metal in the aqua ions in solution varies from seven (Sc) through 8 (Lu) to 9 (La) (Section 4.1).
The fact that 7-coordination is observed in crystalline [Ln(diketonato)3(H2O)] species [90,145,146] while 8-or 9-coordination is found in solution can be rationalised [147] as due to H-bonding interactions of the aqua ligand in the solid which block access to a possible eighth coordination site.Even dispersion interactions between ligands on separate molecules in the solid state appear to be sufficient to enforce 7-coordination in analogous [Ln(diketonato)3(solvent)] complexes [147].
The analysis of the structural data for the complexes of the Sc 3+ , Y 3+ , La 3+ and Lu 3+ ions and, by implication, the rest of the lanthanide series described in the preceding pages is more complex than perhaps the common generalisations would suggest and, often, the "devil is in the detail".That the size of a cation is a factor limiting its coordination number may seem obvious on the basis of minimising donor atom repulsions but it is not so obvious when regarding actual structures how great the difference in cation radius must be before a change in coordination number occurs.Lanthanide(III) complexes provide numerous examples of changes in solid state coordination number at various points across the series depending seemingly on the size of the ligand [100] but there are also examples where a given ligand provides an isostructural series across the complete range of lanthanides [151-153, 160, 161], indicating that cation size alone must be an influence in competition with others [161].In comparing Sc 3+ and Lu 3+ , an obvious source of differences is the valence shell, with d-orbital involvement more important for Sc than Lu, and it is course possible that the electronic interactions between metal ion and ligand can affect the interactions of the ligand with its "external" environment within a crystal.In this context it is informative to look at the solution pKa values of the 3+ aqua ions (Sc 3+ pKa 4.3; Y 3+ pKa 7.7; Lu 3+ pKa 7.6; La 3+ pKa 8.5) [162] and note the similarity between the values for Y 3+ and Lu 3+ , matching the similarities in their radii.
In summary, because of their ionic character the structural chemistry of the Group 3 metal ions and that of the lanthanides is governed by the size of the metal ions and the steric requirements of the ligands, with the largest of the +3 ions, La 3+ , displaying the highest coordination number for a given set of ligands.As illustrated by the examples discussed above it is the ligand set that is the dominant factor in determining the coordination number and geometry of the metal ion.For the coordination numbers greater than six, where there are several limiting geometries with similar energies, such as square antiprismatic or trigonal dodecahedral arrangements for 8-coordinate complexes, the geometry adopted can be determined by the ligand set or indeed the crystal environment, and the complexes are fluxional in solution.Chemical properties such as lattice energies, solvation energies and complex stability constants of the complexes are closely related to the size of the metal ions.In the direct comparison of the Group 3 metals with Lu the analysis of M-O bonds shows that the radius of Lu 3+ is closest in size to that of Y 3+ and in more than half of the comparative series of 29 sets of structures analysed above these two elements have similar coordination numbers and geometries for the same ligand set; whereas, for complexes of the smaller Sc 3+ when compared to Lu 3+ there are about equal numbers of similarities and differences in coordination number and geometry between complexes of the two ions.Whilst in many of these comparative series lutetium resembles scandium in its behaviour, there are more cases where lutetium resembles yttrium.So, in the discussion of whether the order of the elements for Group 3 should be Sc, Y and La, or whether Lu should replace La in the group, this detailed review of the structural chemistry indicates that there is a logical progression in chemistry as the size of the Sc, Y and La ions increase.The structural chemistry of Lu most closely matches that of Y and not of La, so we feel that the case for replacing La by Lu in Group 3 has not been made on structural grounds.In the absence of more compelling evidence, the Periodic Table as presented currently, not least in the IUPAC form, gives the most appropriate description of the chemistry of Group 3 and of the lanthanides.

Figure 1 .
Figure 1.The distribution of structural hits for complexes of Sc, Y, La and Lu in the CSD for which there is at least one M-O or M-N bond (complexes containing both M-O and M-N bonds will appear in both records of the element).

Figure 2 .
Figure 2. The mean M-O bond lengths (M = Sc, Y, La and Lu) for all the 6-, 7-, 8-and 9coordinated complexes that contain at least one M-O bond whose structures have been deposited in the CSD.

Figure 7 .
Figure 7.A schematic of the structure of [La(-Cl)3(thf)2]n showing the polymeric nature of the structure (the polymeric links are shown as wiggly lines).

Figure 10 .
Figure 10.A schematic of the structure of the [Ln(N(SiMe3)2))3] (La to Lu except Pm) showing the proposed agostic interactions.

Figure 18 . 6 .Figure 19 .
Figure 18.Schematic diagrams of [Sc(OAc)3]∞ and [Lu(OAc)3]∞ showing the polymeric nature of the structures (the wiggly lines showing the connections to the next Lu atoms in the chain and the dashed lines emphasise the delocalisation within the acetate groups).

Figure 28 .
Figure 28.Schematic structures of the Tris(cyclopentadienyl) complexes of Sc, Y and the lanthanides.

Table 1
This radius was calculated by subtracting 0.66 Å from the mean M-O bond length.
[26]ere are not enough examples for these data to be meaningful.¥Radiifor the metal ions taken from Atomic Radii in Crystals[26].

Table 2 .
The sum of the first three ionisation energies (KJ/mole) and Pauling and Allred-

Table 3 .
Co-ordination Numbers for Compounds and Co-ordination Complexes of the Sc 3+ , Y 3+ , La 3+ and Lu 3+ Ions