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Pinsky M, Dryzun C, Casanova D, et al. Analytical methods for calculating Continuous Symmetry Measures and the Chirality Measure. J Comput Chem. 2008;29(16):2712-21doi: 10.1002/jcc.20990.
Pinsky, M., Dryzun, C., Casanova, D., Alemany, P., & Avnir, D. (2008). Analytical methods for calculating Continuous Symmetry Measures and the Chirality Measure. Journal of computational chemistry, 29(16), 2712-21. https://doi.org/10.1002/jcc.20990
Pinsky, Mark, et al. "Analytical methods for calculating Continuous Symmetry Measures and the Chirality Measure." Journal of computational chemistry vol. 29,16 (2008): 2712-21. doi: https://doi.org/10.1002/jcc.20990
Pinsky M, Dryzun C, Casanova D, Alemany P, Avnir D. Analytical methods for calculating Continuous Symmetry Measures and the Chirality Measure. J Comput Chem. 2008 Dec;29(16):2712-21. doi: 10.1002/jcc.20990. PMID: 18484634.
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J Comput Chem. 2008 Dec;29(16):2712-21. doi: 10.1002/jcc.20990.

Analytical methods for calculating Continuous Symmetry Measures and the Chirality Measure.

Journal of computational chemistry

Mark Pinsky, Chaim Dryzun, David Casanova, Pere Alemany, David Avnir

Affiliations

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

PMID: 18484634 DOI: 10.1002/jcc.20990

Abstract

We provide analytical solutions of the Continuous Symmetry Measure (CSM) equation for several symmetry point-groups, and for the associated Continuous Chirality Measure (CCM), which are quantitative estimates of the degree of a symmetry-point group or chirality in a structure, respectively. We do it by solving analytically the problem of finding the minimal distance between the original structure and the result obtained by operating on it all of the operations of a specific G symmetry point group. Specifically, we provide solutions for the symmetry measures of all of the improper rotations point group symmetries, S(n), including the mirror (S(1), C(S)), inversion (S(2), C(i)) as well as the higher S(n)s (n > 2 is even) point group symmetries, for the rotational C(2) point group symmetry, for the higher rotational C(n) symmetries (n > 2), and finally for the C(nh) symmetry point group. The chirality measure is the minimal of all S(n) measures.

2008 Wiley Periodicals, Inc.

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