晶体结构的组合和算法复杂性

D. Banaru, S. M. Aksenov
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引用次数: 0

摘要

研究课题。描述晶体结构中结构单元间接触系统复杂程度的数字索引。目的。以岛(分子)结构中结构单元间接触的复杂性指数为基础,为周期性结构单元间接触系统制定复杂性指数。材料和方法。结构数据选自 COD、AMCSD 和 CSD 晶体数据库。通过 ToposPro 软件包中的 Voronoi-Dirichlet 多面体(VDP)方法分析了结构中的接触系统。分析结果分子晶体接触系统拓扑分析方法适用于所有异质晶体结构,并对几类化合物的结构进行了测试。开发了目标复杂性指数。结论。周期性结构单元之间的接触网络是低维的。可以从原始晶体结构数据中推导出此类网络的通用结构类别。异质结构的算法复杂度是次正的,而组合复杂度是超正的。首次计算了周期性结构单元之间的轴承接触数量,反映了在适当结构描述水平上的结构算法复杂性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Combinatorial and algorithmic complexity of crystal structures
Research subject. Numeral indexes describing the complexity of the system of contacts between structural units in crystal structures. Aim. Development of a complexity index for the system of contacts between periodic structural units based on the indices available for those between structural units in island (molecular) structures. Materials and methods. Structural data were selected from the COD, AMCSD, and CSD crystallographic databases. The system of contacts in the structures was analyzed by the Voronoi–Dirichlet polyhedra (VDP) method in the ToposPro software package. Results. The method of topological analysis of the system of contacts in molecular crystals was adapted to all heterodesmic crystal structures and tested on the structures of compounds of several classes. Target complexity indices were developed. Conclusions. Networks of contacts between periodic structural units are low-dimensional. A generalized structural class for such networks can be derived from the original crystal structure data. The algorithmic complexity of heterodesmic structures is subadditive, in contrast to superadditive combinatorial complexity. For the first time, the number of bearing contacts was calculated between periodic structural units, reflecting the algorithmic complexity of the structure at the appropriate level of structural description.
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