Pinsky M, Casanova D, Alemany P, Alvarez S, Avnir D, Dryzun C, Kizner Z, Sterkin A. Symmetry operation measures.
J Comput Chem 2007;
29:190-7. [PMID:
17559057 DOI:
10.1002/jcc.20772]
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Abstract
We introduce a new mathematical tool for quantifying the symmetry contents of molecular structures: the Symmetry Operation Measures. In this approach, we measure the minimal distance between a given structure and the structure which is obtained after applying a selected symmetry operation on it. If the given operation is a true symmetry operation for the structure, this distance is zero; otherwise it gives an indication of how different the transformed structure is from the original one. Specifically, we provide analytical solutions for measures of all the improper rotations, S n p, including mirror symmetry and inversion, as well as for all pure rotations, C n p. These measures provide information complementary to the Continuous Symmetry Measures (CSM) that evaluate the distance between a given structure and the nearest structure which belongs to a selected symmetry point-group.
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