Analysis of the conformational polymorph crystal structures by means of molecular Voronoi-Dirichlet polyhedra

New criterion for conformational polymorphism

“…Hereinafter, the numerical value of RF is indicated as the х superscript in symbols of the х s ij or х v ij type. It is known [2,5] that, in a crystal structure of any substance, interatomic interactions in the A i -A j pairs refer to one of the three following pos sible types, depending on the RF value: faces with RF = 1 are equivalent to chemical bonds, all faces with RF > 1 correspond to intramolecular nonvalent inter actions, and faces with RF = 0 correspond to intermo lecular nonvalent interactions. Based on the VDP characteristics of all crystallographically different atoms in a crystal structure, one can determine the parameters of molecular VDPs, which result from the integration of VDPs of atoms comprising a molecule.…”

“…Polymorphs of 2,4,6,8,10,12 hexaazaisowurzitane. Of the four modifications of 2,4,6,8,10,12 hexaazai sowurzitane (hereinafter, HNIW) studied, one modi fication (α) is a hemihydrate; therefore, only three other polymorphs will be included in a further discus sion of the specific features of polymorphism.…”

“…The total number of all faces with RF = 0 ( 0 k), as well as the shortest and the longest dis tances ( 0 d min and 0 d max , respectively) between the atoms of contacting molecules, serve as additional parameters of molecular VDPs. For the sake of sim plicity and following the designations in [2], nonvalent contacts will hereinafter be designated in the general case as А/Z, in which the symbol / denotes that VDPs of the А and Z atoms share a face. If a substance includes atoms of several (for example, g) different elements, nonvalent interactions of g(g + 1)/2 types can theoretically be formed in its crystal structure.…”

“…If a substance includes atoms of several (for example, g) different elements, nonvalent interactions of g(g + 1)/2 types can theoretically be formed in its crystal structure. In order to evaluate qualitatively relative contributions of intermolecular contacts of different nature, the Δ AZ parameter, which indicates the partial contribution (in percent) to the integral 0 V parameter of the molecular VDP, is introduced as previously [2] for each type of A/Z interaction. For example, in the structures of crystals of the С а Н b N c O d composition with g = 4, intermolecular contacts of only ten types (4⋅5/2) can be formed, and, for the general case,…”

“…ANALYSIS Within the method of molecular VDPs, the coordi nation numbers of all t crystallographically different atoms А i (i = 1, 2, 3, .., j, .., t) are determined and the main characteristics of the corresponding atomic VDPs are calculated for each substance based on the initial crystal chemical data (space group, unit cell parameters, and coordinates of basis atoms) as described in [2]. For this purpose, the TOPOS pro gram package [3] and the method of intersecting spheres [4] are used.…”