Semi-empirical groundwork of the bond-valence model

Abstract

The bond-valence model (BVM) which relates the length R of a bond to its bond valence s is a widely used empirical approach to the interpretation and prediction of atomic arrangements in crystals. However, a theoretical foundation of the BVM appears to be fairly inadequate so far. In this paper derivations of the main expressions of R(s) for both versions of the BVM (in inverse-power and exponential forms) are reproduced and refined by the use of various semi-empirical potentials for interatomic interactions that are appropriate for ionic, covalent and intermediate ionic-covalent bonding, respectively. Independence of the BVM from bonding character is the result of such a treatment. Interrelations between both versions of the BVM are also analyzed. Much attention is given to the question of transferability of the single bond-length parameter and to the special role of bond-specific values of the softness parameter. The latter is proved to be a simple function of the ionization potentials of bonded atoms. In turn, this explains the strong linear correlations between the single bond lengths from cations to a pair of anions and the relation between single bond lengths and atom sizes (sum of the covalent radii). It is demonstrated that a correction related to electronegativity difference is involved in this consideration. In general, one might conclude that the BVM becomes soundly based from both the empirical and semi-empirical viewpoints