Theoretical analysis and empirical manifestation of the distortion theorem

The distortion theorem is analyzed by the use of the Bond Valence Model for the case of an isolated coordination polyhedron with bonds of different lengths. It is shown that a correlation should exist between the average bond length increase and the mean-square deviation of individual bond lengths from the average one, at least for nonstrained crystal structures. It is proved that the correlation parameters are strongly dependent on a mode of distortion (symmetry of coordination environment). These conclusions are in general and sometimes in quantitative agreement with available experimental data, although in most cases the distortion of coordination polyhedra results from a variety of factors of chemical, geometric and electronic origin. It is assumed that an observed correlation between the average bond distance and the distortion degree may be taken as a measure of relative role of intrinsic bond strengths and influence of crystalline environment.