State-of-art and perspectives of the bond-valence model in inorganic crystal chemistry

The band valence method (BVM) is one of modern methods for predicting bond lengths in crystal structures based on the modified second Pauling rule, which requires the exact fulfillment. of the valence balance with due regard for the empirical bond valence-bond length relations. The review includes the detailed analysis of the mathematical apparatus of the method, its limitations, and also its program implementation, Various modifications of the BVM procedure suggested by the authors are analyzed. A number of examples of modeling are given. In most of the cases, the error in prediction of interatomic distances does not exceed 5-8%. Much attention is also given to other possible applications of the method in crystal chemistry. Among them, of great importance is the prediction of coordination-polyhedron distortion based on the use of the distortion theorem, the determination of the valence of atoms from the corresponding structural data, the refinement of the bond network, and also the analysis of geometrical strains in structures.