CONTENTS 6524 4.2. Bond-Length Variations 6524 4.3. Bond-Angle Variations 6524 4.4. Variations of the A•••A Distances 6524 5. Concluding Remarks 6524 Author Information 6525 Corresponding Author 6525 Notes 6525 Biographies 6525 Acknowledgments 6526 References 6526

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The discovery of the diffraction of X-rays on crystals opened up a new era in our understanding of nature, leading to a multitude of striking discoveries about the structures and functions of matter on the atomic and molecular scales. Over the last hundred years, about 150,000 of inorganic crystal structures have been elucidated and visualized. The advent of new technologies, such as area detectors and synchrotron radiation, led to the solution of structures of unprecedented complexity. However, the very notion of structural complexity of crystals still lacks an unambiguous quantitative definition. In this Minireview we use information theory to characterize complexity of inorganic structures in terms of their information content.

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, I(G), 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 I(G) measure is sensitive to the symmetry of the structure, whereas the I(vd) measure better describes the complexity of the bonding network.