Analytical Methods for Calculating Continuous Symmetry Measures and the Chirality Measure

作者：Pinsky Mark; Dryzun Chaim; Casanova David; Alemany Pere; Avnir David^*

来源：Journal of Computational Chemistry, 2008, 29(16): 2712-2721.

DOI：10.1002/jcc.20990

• symmetry
• chirality
• continuous symmetry
• inversion
• reflection
• rotation
• improper-rotation

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-1) 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.

• 出版日期2008-12