Complexity of Molecular Nets: Topological Approach and Descriptive Statistics

The molecular net complexity (<i>H</i><sub>molNet</sub>) is an extension of the combinatorial complexity (<i>H</i><sub>mol</sub>) of a crystal structure introduced by Krivovichev. It was calculated for a set of 4152 molecular crystal structures with th...

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Bibliographic Details
Main Authors: Alexander M. Banaru, Sergey M. Aksenov
Format: Article
Language:English
Published: MDPI AG 2022-01-01
Series:Symmetry
Subjects:
Online Access:https://www.mdpi.com/2073-8994/14/2/220
Description
Summary:The molecular net complexity (<i>H</i><sub>molNet</sub>) is an extension of the combinatorial complexity (<i>H</i><sub>mol</sub>) of a crystal structure introduced by Krivovichev. It was calculated for a set of 4152 molecular crystal structures with the composition of C<i><sub>x</sub></i>H<i><sub>y</sub></i>O<i><sub>z</sub></i> characterized by the structural class <i>P</i>2<sub>1</sub>/<i>c</i>, <i>Z</i> = 4 (1). The molecular nets were derived from the molecular Voronoi–Dirichlet Polyhedra (VDP<sub>mol</sub>). The values of the molecular coordination number (CN<sub>mol</sub>) and critical coordination number (CN<sub>crit</sub>) 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<sub>mol</sub>, CN<sub>crit</sub>, and the complexity parameters is obtained. More than a half of the considered structures has CN<sub>mol</sub> = 14 and CN<sub>mol</sub>′ = 9 with the Wyckoff set of edges <i>e</i><sup>5</sup><i>dcba</i>. 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 <i>H</i><sub>molNet</sub> is of the logistic distribution type and is distributed near 0.85<i>H</i><sub>molNet</sub> with a small standard deviation. The contribution of <i>H</i><sub>mol</sub> into <i>H</i><sub>molNet</sub> 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.
ISSN:2073-8994