The Non-Rigid Group of Tetraamine Platinum(II) as a Wreath Product

• Published in: Bulletin of the Chemical Society of Japan 2005-06, Vol.78 (6), p.996-1000
• Main Authors: Darafsheh, M. R, Farjami, Y, Ashrafi, A. R
• Format: Article
• Language: English
• ISSN: 0009-2673; 1348-0634
• DOI: 10.1246/bcsj.78.996

A non-rigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field of chemistry. Balasubramanian, Smeyers, and Villa in a series of papers applied this notion to determine the character table of restricted NRG (r-NRG) of some molecules. For example, Balasubramanian computed the NRG of the triple equivalent nitro group rotation in 1,3,5-triamino-2,4,6-trinitrobenzene, and proved that the NRG of this molecule is a group of order 48 (see Chem. Phys. Lett., 398, 15 (2004)). In this work a theoretical method is described for calculating the symmetry group of non-rigid molecules consisting of a number of XYn (n = 2,3,...) groups attached to a rigid framework. The non-rigid group of the molecule is a wreath product of symmetry group of the rigid frame with the permutation group of the XYn group. This algebraic structure of NRG helps us to compute the classes and character tables using the GAP package, even for large groups. We apply this method to find the structure of the non-rigid group of tetraamine platinum(II) with the D2d ordinary point group. It has proved that this is a group of order 5184. The method can be generalized to apply to other non-rigid molecules.