A bond-valence investigation of two series of isostructural lanthanide compounds

Abstract

Since the days of Pauling it has been tacitly assumed that the valence, which is distributed between the bonds to neighbouring atoms, is the stoichiometric valence, (stoich)V, which has integer values. It is shown here that this is not true. Instead, bond-valence sums (BVS) calculated for lanthanide (Ln) atoms of a series of garnet-type compounds Ln(3)(III)Te(2)(VI)Li(3)(I)O(12) deviate significantly from (stoich)V. Values of (BVS)(Ln) of this series, plotted versus the element number Z(Ln), show the same irregular sequence as: (i) the third ionization potentials of Ln atoms, (ii) the valence values previously calculated with quantum-chemical methods for lanthanide metals and sulfides, and (iii) the experimental efficiencies of the reactions between Ln(I) and SF(6) in the gas phase. This indicates that in the Ln(3)Te(2)Li(3)O(12) series the BVS values of the Ln atoms, which are ;rattling' in rather large and rigid voids of the structure, reflect the electronic structure of Ln. It is, therefore, concluded that BVS represent a non-integer valence, which is based on the electronic structure of bonded atoms, rather than (stoich)V. For this non-integer valence the term ;structural valence' and the symbol (struct)V have been proposed. In another series of lanthanide chelates the (BVS)(Ln) values deviate even more from (stoich)V(Ln) = 3 v.u. than in the garnet-type series. In the chelates the Ln atoms are ;squeezed' in rather small voids so that the electronic effects of Ln acting on (BVS)(Ln) are overridden by stronger steric effects exerted by the organic ligands.

Stoichiometric Valence and Structural Valence—Two Different Sides of the Same Coin: “Bonding Power”

“…1) Strange et al [8] calculated with quantum-chemical methods the valences of Ln atoms in lanthanide metals and sulfides, and plotted them versus Z Ln (Figure 1c). The similarity between Figures 1a and 1c suggests that these valence values and the calculated bond-valence sums (BVS) Ln [23] represent the same valence property. 2) This conclusion is strengthened by a study of Cheng and Bohme, [35] who determined the reaction efficiency of the gas-phase reaction between singly ionised Ln I and neutral SF 6 molecules.…”

“…[27] The calculated BVS values for the Ln atoms are 12 to 22 % higher than their stoichiometric valence values, [23] which is far more than the 2.7 % estimated error according to Equation (3), listed in Table S1 of the Supporting Information. 4) The precision of tabulated values of r 0 and b that were used to calculate V i is low.…”

“…It has become widespread practice by most authors to use b = 0.37 and tabulated r 0 values from references [15] and [22] [23] or cationic atoms with a lone electron pair. [24] Estimated Accuracy of Calculated Bond-ValenceSum Values…”

“…The steric effects exerted on the Ln atoms by the surrounding oxygen atoms overcompensate the electronic effects of the Ln atoms. [23] Bond-valence sums of transition-metal atoms: Within a crystal structure, different components have different spatial requirements. For instance, smaller coordination polyhedra have to adjust to neighbouring larger ones and vice versa.…”

“…In each framework, the Ln atoms occupy triangular dodecahedral cavities forming LnO 8 polyhedra. A BVS analysis of all atoms within this structure series [23] revealed [34] of Ln versus Z Ln , c) valence values of Ln atoms in metallic Ln (open circles) and Ln sulfides (crosses), calculated with quantum chemical methods, [8] versus Z Ln , and d) the efficiency of the reactions between Ln I and SF 6 [35] versus Z Ln , respectively. is, however, not the case.…”