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Topological complexity of crystal structures: quantitative approach

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Abstract:

The topological complexity of a crystal structure can be quantitatively evaluated using complexity measures of its quotient graph, which is defined as a projection of a periodic network of atoms and bonds onto a finite graph. The Shannon information‐based measures of complexity such as topological information content, IG , and information content of the vertex‐degree distribution of a quotient graph, I vd, are shown to be efficient for comparison of the topological complexity of polymorphs and chemically related structures. The IG measure is sensitive to the symmetry of the structure, whereas the I vd measure better describes the complexity of the bonding network.

Document Type: Research Article

DOI: http://dx.doi.org/10.1107/S0108767312012044

Affiliations: Crystallography, St Petersburg State University, University Emb. 7/9, St Petersburg, 199034, Russian Federation

Publication date: May 1, 2012

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