Yukawa screening derivation of the bond-valence rule

TL;DR

This paper derives the bond-valence model from screened Coulomb electrostatics, linking empirical bond strengths to physical charge response and validating predictions with extensive data and first-principles calculations.

Contribution

It provides a physical derivation of the bond-valence rule from electrostatics, enhancing its theoretical foundation and predictive power.

Findings

Bond-valence form emerges as leading-order screened Coulomb interaction.

Predicted bond-valence parameters match extensive fitted data.

Shell radius correlates strongly with electronic screening cloud.

Abstract

The bond-valence model is a standard way to estimate bond strengths in crystals, but its exponential dependence on bond length has lacked a derivation from a specific physical interaction. We show that this form emerges as the leading-order limit of screened Coulomb electrostatics and that the fitted bond-valence softness can be interpreted in terms of an electronic screening length. This turns bond valence from an empirical fitting rule into a transferable descriptor of local screened charge response across coordination environments. The resulting theory predicts how the bond-valence parameters should vary with ionic charge and coordination number, and that prediction agrees with 150 fitted valences from 94 cation-oxygen species, including 68 in fourfold coordination and 82 in sixfold coordination, at an abundance-weighted coefficient of determination of 0.986. A comparison with first-principles charge densities shows that the bond-valence shell radius tracks the electronic screening cloud with coefficients of determination of 0.9998 for ten alkali and alkaline-earth oxides and 0.967 for 21 other binary oxides whose nearest-neighbor environments match the theory's assumptions. The widely used bond-valence model is thus the leading-order expression of screened electrostatics in ionic solids.