A new relation between bond valence and bond distance

A new empirical relationship s = s(0)(R-0 - lambda)(3)/(R - lambda)(3) betw een bond distances and bond valences is proposed, where s is the bond valen ce for the bond distance R, s0 is the reference bond valence for the refere nce system with the reference bond distance R-0 and lambda is the sum of th e cation radii of bonding atoms defined by Pauling. Since lambda is the siz e of the inner electron region, R - lambda 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 - lambda)(3) in a coordination polyhedron are equal, even if the bon d distances are not equal to each other. (ii) The average electron density p/(R - lambda)(3) is a measure of covalent bond strength. (iii) The sum of the average electron densities around the central atom is conserved, even i f the coordination number changes. The new relationship is applicable not o nly to polyhedra with one type of ligand atom, but also to polyhedra with t wo 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. Th e new relationship was applied to a penta-coordinated silicon compound, str ong hydrogen-bond systems and some organic compounds with carbon-carbon bon ds.