Reassessment of the Parameterization of the Bond-Valence Model: Results and Applications

English Abstract:

We have recently completed a bond-length dispersion analysis for atoms bonded to oxygen that has led to the collection of 188,797 bond distances from 33,543 coordination polyhedra originating from ~9650 unique crystal structure refinements. We use this data to evaluate 237 published pairs of bond-valence parameters for atoms bonded to oxygen. The range of deviations from the valence-sum rule as well as the average fit obtained from these parameters leads us to conclude that the parameterization of the bond-valence model is not satisfactory; we thus investigate for (1) new equations that can describe the relation between bond length and bond strength, and (2) the best way of deriving the bond-valence parameters of these equations. Following the determination of (1) and (2), we derive 137 new pairs of bond-valence parameters for ions bonded to oxygen using a new method of derivation, the GRG-RMSD (Generalized Reduced Gradient Root-Mean-Square-Deviation) method. We usually find small but consistent improvements in fit for all ions compared to the best published parameters, although some less common ions show a striking improvement; the RMSD from the valence-sum rule for ^[4]P³⁺ changes from 0.946 to 0.243 v.u., Re⁷⁺ from 1.000 to 0.276 v.u, Np⁶⁺ changes from 1.209 to 0.078 v.u, etc. Agreement for the anion bond-valence sums is also improved. Moreover, we find a positive correlation between coordination number and bond-valence sum for most multiple-coordination numbers-cations, where low coordination number configurations give low bond-valence sums and vice-versa. We also find a positive correlation between RMSD and mean bond-length for groups of ions with a similar crystal-chemical behaviour. This new parameterization adds a crucial level of confidence to the bond-valence method for use in bonding analysis and modeling. To that effect, we use the results of the bond-length survey to assign a range of bond-valences that ions can adopt, which we use to predict the full range of site occupancy of crystal structures.