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arXiv · 2604.28099

Yukawa screening derivation of the bond-valence rule

Michael L. Whittaker·Pan Wang·Chunhui Li·Naman Katyal·Piotr Zarzycki
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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.

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Michael L. Whittaker, Pan Wang, Chunhui Li, Naman Katyal, Piotr Zarzycki. 2026-04-30. Yukawa screening derivation of the bond-valence rule. https://arxiv.org/abs/2604.28099

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