Abstract: MATH/CHEM/COMP 2002, Dubrovnik,
June 2429, 2002

The Full NonRigid
Group Theory for cis & trans DiaminoDicholoroPlatinum(II)
and Trimethylamine
Masood Hamadanian^{1} and Ali Reza Ashrafi^{2} ^{1}Department of Chemistry, Faculty of
Science, University of Kashan, Kashan, Iran ^{2}Department of Mathematics, Faculty of
Science, University of Kashan, Kashan, Iran The nonrigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field of chemistry. Smeyers in a series of papers applied this notion to determine the character table of restricted NRG (rNRG) of some molecules. For example, Smeyers and Villa computed the rNRG of the triple equivalent methyl rotation in pyramidal trimethylamine with inversion and proved that the rNRG of this molecule is a group of order 648, containing two subgroups of order 324 without inversions (see J. Math. Chem. 28 (2000) 377). In this work, a simple method is described, by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of AH_{3} groups attached to a rigid framework. We study the full nonrigid group (fNRG) of cis and trans diaminodicholoroplatinum(II) and trimethylamine. We prove that they are groups of order 36, 72 and 1296 with 9, 18 and 28 conjugacy classes, respectively. This shows that the full nonrigid group and the restricted nonrigid group of these molecules are not isomorphic. The method can be generalized to apply to other nonrigid molecules. The fNRG molecule group theory is seen to be used advantageously to study the internal dynamic of such molecules.
transdiaminodicholoroplatinum(II),
trimethylamine 