Continuous symmetry analyses: Cnv and Dn measures of molecules, complexes, and proteins



The continuous symmetry methodology has been developed to provide a quantitative estimation for the degree of a selected symmetry point-group in a molecular structure. Previous developed measures included the CS, Cn, Sn (including Ci) symmetries, several polyhedral symmetries, and the related chirality measure. Motivated by the abundance and importance of Cnv symmetry in many key molecules and by the abundance of Dn symmetry in many organometallic complexes and in many protein clusters, measures for these symmetries, based on the general definition of the continuous symmetry measure, were developed. Detailed description of the derivation of the measures, along with plenty of examples for their application, is provided. © 2012 Wiley Periodicals, Inc.