SEMIEMPIRICAL GROUNDWORK OF THE BOND-VALENCE MODEL

The bond-valence model (BVM) which relates the length R of a bond to i ts bond valence s is a widely used empirical approach to the interpret ation and prediction of atomic arrangements in crystals. However, a th eoretical foundation of the BVM appears to be fairly inadequate so far . In this paper derivations of the main expressions of R(s) for both v ersions of the BVM (in inverse-power and exponential forms) are reprod uced and refined by the use of various semi-empirical potentials for i nteratomic interactions that are appropriate for ionic, covalent and i ntermediate ionic-covalent bonding, respectively. Independence of the BVM from bonding character is the result of such a treatment. Interrel ations between both versions of the BVM are also analyzed. Much attent ion is given to the question of transferability of the single bond-len gth parameter and to the special role of bond-specific values of the s oftness parameter. The latter is proved to be a simple function of the ionization potentials of bonded atoms. In turn, this explains the str ong linear correlations between the single bond lengths from cations t o a pair of anions and the relation between single bond lengths and at om sizes (sum of the covalent radii). It is demonstrated that a correc tion related to electronegativity difference is involved in this consi deration. In general, one might conclude that the BVM becomes soundly based from both the empirical and semi-empirical viewpoints.