On the origin of the combinatorial complexity of the crystal structures with 0D, 1D, or 2D primary motifs

Abstract

Based on Krivovichev information measures for crystal structures and the universal partitioning scheme for different sources of information described previously by Hornfeck, a ladder of information for crystal structures with primary motifs of different dimensionalities (0D, 1D, or 2D) is proposed. Ethanol (0D), SnIP (1D), and TlOH (2D) are discussed as examples of the introduced concept. The proposed calculation technique allows to explicitly obtain contributions of substructures of ordered structures into the information content of a structure conforming to the rule of strong additivity, thus giving a simple assessment of complexity at different hierarchical levels of organization, and takes into account partitioning contacts formed by structural units into equivalence classes, which is poorly dependent on that of the structural units themselves. The technique is a complementation to the multilevel topological analysis performed in the ToposPro program package.