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Continuous symmetry measures for complex symmetry group
Author(s) -
Dryzun Chaim
Publication year - 2014
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.23548
Subject(s) - symmetry operation , icosahedral symmetry , symmetry (geometry) , tetrahedral symmetry , one dimensional symmetry group , molecular symmetry , global symmetry , rotational symmetry , symmetry group , octahedral symmetry , symmetry number , group (periodic table) , theoretical physics , point group , tetrahedron , explicit symmetry breaking , dihedral group , physics , mathematics , quantum mechanics , spontaneous symmetry breaking , symmetry breaking , geometry , molecule , ion
Symmetry is a fundamental property of nature, used extensively in physics, chemistry, and biology. The Continuous symmetry measures (CSM) is a method for estimating the deviation of a given system from having a certain perfect symmetry, which enables us to formulate quantitative relation between symmetry and other physical properties. Analytical procedures for calculating the CSM of all simple cyclic point groups are available for several years. Here, we present a methodology for calculating the CSM of any complex point group, including the dihedral, tetrahedral, octahedral, and icosahedral symmetry groups. We present the method and analyze its performances and errors. We also introduce an analytical method for calculating the CSM of the linear symmetry groups. As an example, we apply these methods for examining the symmetry of water, the symmetry maps of AB 4 complexes, and the symmetry of several Lennard‐Jones clusters. © 2014 Wiley Periodicals, Inc.