Complexity of Molecular Nets: Topological Approach and Descriptive Statistics

Abstract

The molecular net complexity (H_molNet) is an extension of the combinatorial complexity (H_mol) of a crystal structure introduced by Krivovichev. It was calculated for a set of 4152 molecular crystal structures with the composition of C_xH_yO_z characterized by the structural class P2₁/c, Z = 4 (1). The molecular nets were derived from the molecular Voronoi–Dirichlet Polyhedra (VDP_mol). The values of the molecular coordination number (CN_mol) and critical coordination number (CN_crit) are discussed in relation with the complexity of the crystal structures. A statistical distribution of the set of molecular crystals based on the values of CN_mol, CN_crit, and the complexity parameters is obtained. More than a half of the considered structures has CN_mol = 14 and CN_mol′ = 9 with the Wyckoff set of edges e⁵dcba. The average multiplicity of intermolecular contacts statistically significantly decreases from 1.58 to 1.51 upon excluding all contacts except those bearing the molecular net. The normalized value of H_molNet is of the logistic distribution type and is distributed near 0.85H_molNet with a small standard deviation. The contribution of H_mol into H_molNet ranges from 35 to 95% (mean 79%, SD 6%), and the subset of bearing intermolecular contacts accounts for 41 to 100% (mean 62%, SD 11%) of the complexity of the full set of intermolecular contacts.