Abstract: MATH/CHEM/COMP 2002, Dubrovnik, June 24-29, 2002
The Full Non-Rigid Group Theory for cis- & trans- DiaminoDicholoroPlatinum(II) and Trimethylamine
Masood Hamadanian1 and Ali Reza Ashrafi2
1Department of Chemistry, Faculty of Science, University of Kashan, Kashan, Iran
2Department of Mathematics, Faculty of
Science, University of Kashan, Kashan, Iran
The non-rigid 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 (r-NRG) of some molecules. For example, Smeyers and Villa computed the r-NRG of the triple equivalent methyl rotation in pyramidal trimethylamine with inversion and proved that the r-NRG 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 AH3 groups attached to a rigid framework. We study the full non-rigid group (f-NRG) 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 non-rigid group and the restricted non-rigid group of these molecules are not isomorphic. The method can be generalized to apply to other non-rigid molecules. The f-NRG molecule group theory is seen to be used advantageously to study the internal dynamic of such molecules.