Abstract
The molecular net complexity (HmolNet) is an extension of the combinatorial complexity (Hmol) of a crystal structure introduced by Krivovichev. It was calculated for a set of 4152 molecular crystal structures with the composition of CxHyOz characterized by the structural class P21/c, Z = 4 (1). The molecular nets were derived from the molecular Voronoi–Dirichlet Polyhedra (VDPmol). The values of the molecular coordination number (CNmol) and critical coordination number (CNcrit) 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 CNmol, CNcrit, and the complexity parameters is obtained. More than a half of the considered structures has CNmol = 14 and CNmol′ = 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 HmolNet is of the logistic distribution type and is distributed near 0.85HmolNet with a small standard deviation. The contribution of Hmol into HmolNet 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.
Highlights
According to the approach initially developed by Shannon in his theory of communication [1], the complexity of a message consisting of symbols depends on the probability of occurrence of each symbol in the message
Finite graphs corresponding to the molecules belong to a wide class of so-called chemical graphs, and the approaches of measuring information content for them were introduced in the 1950s by Trucco [2] and in the early 2000s reviewed by Bonchev [3]
Studied crystal structure of 2-(tert-butyl)-4-chloro6-phenyl-1,3,5-triazine with 2 symmetrically independent molecules [42] is characterized by the 14T319 type topology, which occupies the opposite side of 14-coordinated molecular nets with respect to TD10 (Table 2)
Summary
According to the approach initially developed by Shannon in his theory of communication [1], the complexity of a message consisting of symbols depends on the probability of occurrence of each symbol in the message. The minimal multiplicity is 1.375 (3 structures) for the hole net of molecular contacts unlike 1.000 (1 structure with refcode KOLRAF [39]) for the critical subnet (Table 1).
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