Terms of parity and distortion of coordination polyhedra in inorganic crystal chemistry

Abstract

The coordination number parity law is formulated: the coordination polyhedra (CP) with the odd number of vertices, except for 3 (CP is a triangle), occur far less often than the polyhedra with the even number of vertices. CP with the odd number of vertices, except for the triangle, cannot be regular and have at least two different types of vertices and two sets of interatomic lengths. The main and first c.n. always keeps parity. A CP distortion due to crystal chemical causes tends to be minimum, obeying the pseudo-symmetry laws. A CP distortion, other things being equal, leads to an increase in the average bond length as compared to the regular polyhedron (distortion theorem). The value of the increase in the average interatomic distance depends on the degree of distortion by the linear or (for a very strong distortion) the square dependence. The histograms of the distribution frequencies of the interatomic lengths have a positive deviation from the Gauss normal distribution law. A free molecule or a complex ion having a distortion due to the directed configuration of chemical bonds or to the electronic effects of the Jahn-Teller type for transition metals, maintain it in the crystal structure as well. During the polymerization of radicals there arise specific distortion effects due to a various coordination environment of the bridging and apical ligands. One of the most general rules of the CP distortion is associated with a less symmetric and less homogenous environment of anions in comparison with that of cations and a higher polarizability of anions. An important exception from this rule is the group of compounds with the so called anion-centered tetrahedra in which more symmetrical positions are occupied, as a rule, by anions in the center of the tetrahedra.