A new relation between bond valence and bond distance

A new empirical relationship s = s₀(R⁰ − λ)³/(R − λ)³ between bond distances and bond valences is proposed, where s is the bond valence for the bond distance R, s₀ is the reference bond valence for the reference system with the reference bond distance R⁰ and λ is the sum of the cation radii of bonding atoms defined by Pauling. Since λ is the size of the inner electron region, R − λ represents the valence electron region between bonding atoms. The new relationship was derived based on the following three hypotheses. (i) The number of electrons (p) in the volumes of (R − λ)³ in a coordination polyhedron are equal, even if the bond distances are not equal to each other. (ii) The average electron density p/(R − λ)³ is a measure of covalent bond strength. (iii) The sum of the average electron densities around the central atom is conserved, even if the coordination number changes. The new relationship is applicable not only to polyhedra with one type of ligand atom, but also to polyhedra with two or more types of ligand atoms and explains why the Brown–Shannon formula [Brown & Shannon (1973). Acta Cryst. A29, 266–282] and the Brown–Altermatt formula [Brown & Altermatt (1985). Acta Cryst. B41, 244–247] work well. The new relationship was applied to a penta-coordinated silicon compound, strong hydrogen-bond systems and some organic compounds with carbon–carbon bonds.