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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MDPI AG
2022-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/2/220 |
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| author | Alexander M. Banaru Sergey M. Aksenov |
| author_facet | Alexander M. Banaru Sergey M. Aksenov |
| author_sort | Alexander M. Banaru |
| collection | DOAJ |
| description | 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. |
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| language | English |
| last_indexed | 2024-03-09T20:58:42Z |
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| series | Symmetry |
| spelling | doaj.art-cf2e4801e39146ca9bcdef27522c94942023-11-23T22:15:13ZengMDPI AGSymmetry2073-89942022-01-0114222010.3390/sym14020220Complexity of Molecular Nets: Topological Approach and Descriptive StatisticsAlexander M. Banaru0Sergey M. Aksenov1Faculty of Chemistry, Moscow State University, Vorobievy Hills, 119991 Moscow, RussiaLaboratory of Arctic Mineralogy and Materials Sciences, Kola Science Centre, Russian Academy of Sciences, 14 Fersman Str., 184209 Apatity, RussiaThe 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.https://www.mdpi.com/2073-8994/14/2/220information measurecomplexitycrystal structurecrystallographic netcoordination number |
| spellingShingle | Alexander M. Banaru Sergey M. Aksenov Complexity of Molecular Nets: Topological Approach and Descriptive Statistics Symmetry information measure complexity crystal structure crystallographic net coordination number |
| title | Complexity of Molecular Nets: Topological Approach and Descriptive Statistics |
| title_full | Complexity of Molecular Nets: Topological Approach and Descriptive Statistics |
| title_fullStr | Complexity of Molecular Nets: Topological Approach and Descriptive Statistics |
| title_full_unstemmed | Complexity of Molecular Nets: Topological Approach and Descriptive Statistics |
| title_short | Complexity of Molecular Nets: Topological Approach and Descriptive Statistics |
| title_sort | complexity of molecular nets topological approach and descriptive statistics |
| topic | information measure complexity crystal structure crystallographic net coordination number |
| url | https://www.mdpi.com/2073-8994/14/2/220 |
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