A popular rule of thumb used by chemists for decades has been turned into a rigorous law of physics.
The bond-valence rule is a simple way to estimate how strong the bonds are between atoms in a crystal. Chemists have used it as a handy estimation tool, but they never quite knew why it worked so well. This derivation proves the rule comes from fundamental electrostatics and the way electrons shield each other. It takes a purely empirical guess and turns it into a mathematical certainty based on first principles. This discovery gives scientists a much more reliable way to design new materials for batteries and electronics.
Yukawa screening derivation of the bond-valence rule
arXiv · 2604.28099
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 re