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Quantifying similarity of coordination

"What compounds have structures similar to the compound that I am currently studying?" is a question often asked by people working in the field of inorganic crystals. They are often surprised to find that there is no simple answer. The problem lies in what one means by "similar". Isostructural examples of simple binary compounds that crystallize with the NaCl or calcium fluoride structure can be easily found because all NaCl-type structures are identical, but this is not true of more complex compounds. The coordination environments of "similar" compounds are rarely identical. But how does one quantify the difference? Two recent papers in Acta Cryst. B provide partial answers to this question. The purpose of the paper by Makovicky & Balic-Zunic ["A New Measure of Distortion for Coordination Polyhedra", Acta Cryst. B54 (1998), 766-773] is to quantify the degree of distortion of a coordination polyhedron from regularity. By plotting the volume of the coordination polyhedron against the volume of the circumscribed sphere for a number of isostructural compounds, the structures can be quickly classified by their degree of polyhedral distortion. The paper by Bergerhoff, Berndt, Brandenburg & Degen ["Concerning Inorganic Structure Types", Acta Cryst. B55 (1999), 147-156] proposes a more direct way of finding similar structures by scanning the databases for isopointal compounds that crystallize in the same space group and have atoms occupying the same Wyckoff positions. They have constructed a database of Standard Inorganic Crystal Structures (SICS) selecting the best structure determination for each compound reported in the Inorganic Crystal Structure Database and transforming it to a standard setting. Numerical descriptors stored in SICS measure the degree of difference between each pair of isopointal compounds. We may not yet have found the perfect measure of similarity, but these two papers point the way.

I.D. Brown
McMaster U.
Hamilton, Canada