The bond-valence rule's exponential form is the leading-order limit of screened Coulomb interactions, with softness as screening length, matching 150 fitted valences (R²=0.986) and first-principles charge densities.
Pauling, The principles determining the structure of complex ionic crystals, Journal of the American Chemical Society51, 1010 (1929)
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Yukawa screening derivation of the bond-valence rule
The bond-valence rule's exponential form is the leading-order limit of screened Coulomb interactions, with softness as screening length, matching 150 fitted valences (R²=0.986) and first-principles charge densities.