Information-based measures of structural complexity: application to fluorite-related structures

Topological complexity of fluorite-related structures consisting of edge- and corner-sharing tetrahedra is investigated using information-based complexity measures: topological information content, I (G), normalized topological information content, I (G,norm), vertex-degree distribution information content, I (vd), and average edge complexity, E (a). The I (G) and I (G,norm) parameters are quite sensitive to complexity of structural units and work well for homologous series as demonstrated for finite clusters and multiple chains. In addition, these parameters have high discriminative power and can be used for identification of structural units and crystal structures in general. The I (vd) and E (a) parameters are additional useful measures of complexity that are sensitive to the coordination numbers of particular atoms within the structural units.