Chirality Measures for Vectors, Matrices, Operators and Functions

Authors

  • Chaim Dryzun,

    1. Institute of Chemistry and The Lise Meitner Minerva Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel), Fax: (+972) 2-6520099
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  • Prof. David Avnir

    Corresponding author
    1. Institute of Chemistry and The Lise Meitner Minerva Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel), Fax: (+972) 2-6520099
    • Institute of Chemistry and The Lise Meitner Minerva Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel), Fax: (+972) 2-6520099
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Abstract

We introduce the general form of the continuous chirality measure (CCM), which is a quantitative estimation of the degree of chirality for a given object. The generalization makes it possible to calculate the chirality content of any mathematical description of a system by vectors, matrices, operators and functions. Another advantage of the new methodology is the ability to provide analytical expressions for the chirality measures. We apply it for specific cases, including vectors and molecules (amino acids), rotation matrices (metamaterials design), rotational potential operators (representing, for example, parity violation), and functions (the electronic structure of annulenes).

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