The use of cation-cation and anion-anion bonds to augment the bond-valence model

Abstract

The bond-valence model has, for several decades, been widely used for creating quantitative structure-activity relationships (QSARs), crystal structure modeling, and verification of proposed structures. Certain limitations of the model, such as the neglect of interactions between cations and between anions, have prevented it from being more broadly applied. In this work, we use cation-cation and anion-anion bonds to augment the existing bonding model in the systems H-Al-Si-O and K-Al-Si-O. The bond valence-length curves for these interactions employ the same mathematical form as ionic bonds, but make only a small contribution to the overall bonding in ionic materials. In the systems examined here, oxygen-oxygen interactions were much more important than those between cations for producing accurate bond-valence sums. Both anion-anion and cation-cation bonding could prove important, however, for our ultimate goal of producing valence-based force fields for use in molecular dynamics simulations. Rolling these interactions into the bond-valence framework would produce behavior similar to hard-sphere repulsive or van der Waals terms, but would more flexibly account for the complete bonding environment. The overall improvement in valence sums was robust, was maintained outside the calibration set, and was invariant to elemental substitution. We conclude that this minor alteration of the bond-valence approach will significantly improve bond-valence models in conjunction with other recent extensions of the approach.

AIM analysis and the form of the bond-valence equation

“…Here we have argued that the bond valence-length curve shape should vary systematically as a function of bond character, but it has long been known that other properties, such as the dissociation energies of bonds with the same nominal bond order, also vary quite strongly as a function of bond character (Pauling 1960;Sanderson 1983;Wander et al 2015).…”

“…8) is needed for some purposes. While the standard exponential and power-law forms are probably adequate for modeling equilibrium geometries in most crystals, they will exhibit systematic deficiencies as their application broadens to include different bond types (O'Keeffe and Brese 1992;Wander et al 2015) and non-equilibrium energy calculations (Adams and Swenson 2002;Grinberg et al 2002Grinberg et al , 2009Cooper et al 2003;Shin et al 2005;Adams and Rao 2009;Liu et al 2013aLiu et al , 2013b.…”

Bond-Valence Parameterization for the Accurate Description of DFT Energetics

“…However, optimizing both R 0,GS‑DFT and B values is a relatively straightforward extension that could improve the GII’s ability to capture the trends in DFT energies . GIIs could be further modified to include anion contributions beyond the first coordination sphere, otherwise known as softBV parameters, and cation–cation and/or anion–anion interactions . Additionally, high-spin versus low-spin R 0,GS‑DFT parameters could be derived for magnetic elements, as these modifications are readily accommodated by the parameterization framework presented herein.…”

“…35 GIIs could be further modified to include anion contributions beyond the first coordination sphere, otherwise known as softBV parameters, 36 and cation−cation and/or anion−anion interactions. 37 Additionally, high-spin versus low-spin R 0,GS-DFT parameters could be derived for magnetic elements, 38 as these modifications are readily accommodated by the parameterization framework presented herein. Although general R 0,GS-DFT parameters sufficiently describe DFT energies for most experimental ABO 3 perovskite oxides, if more accurate descriptions of competing phase stabilities are desired, we recommend either modifying the BVM framework in these ways and/or using composition-specific BVM parameters, which we have shown to be exceptionally accurate for describing DFT energetics with GIIs.…”