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Symmetry operation measures

Authors

  • Mark Pinsky,

    1. Institute of Chemistry, The Lise Meitner Minerva Center for Computational Quantum Chemistry, Hebrew University of Jerusalem, Jerusalem 91904, Israel
    2. Institute of Earth Sciences, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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  • David Casanova,

    1. Departament de Química Inorgànica, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
    2. Centre de Recerca en Química Teòrica, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
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  • Pere Alemany,

    Corresponding author
    1. Centre de Recerca en Química Teòrica, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
    2. Departament de Química Física, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
    • Centre de Recerca en Química Teòrica, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
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  • Santiago Alvarez,

    1. Departament de Química Inorgànica, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
    2. Centre de Recerca en Química Teòrica, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
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  • David Avnir,

    Corresponding author
    1. Institute of Chemistry, The Lise Meitner Minerva Center for Computational Quantum Chemistry, Hebrew University of Jerusalem, Jerusalem 91904, Israel
    • Institute of Chemistry, The Lise Meitner Minerva Center for Computational Quantum Chemistry, Hebrew University of Jerusalem, Jerusalem 91904, Israel
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  • Chaim Dryzun,

    1. Institute of Chemistry, The Lise Meitner Minerva Center for Computational Quantum Chemistry, Hebrew University of Jerusalem, Jerusalem 91904, Israel
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  • Ziv Kizner,

    1. Departments of Physics and Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
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  • Alexander Sterkin

    1. Institute of Chemistry, The Lise Meitner Minerva Center for Computational Quantum Chemistry, Hebrew University of Jerusalem, Jerusalem 91904, Israel
    2. Department of Neurobiology, Weizmann Institute, Rehovot 76100, Israel
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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, Smath image, including mirror symmetry and inversion, as well as for all pure rotations, Cmath image. 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. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008

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