The Full Non-Rigid Group Theory of cis-Tetraamminedichlorocobalt(III)

Abstract

The non-rigid molecule group theory (NRG), in which the dynamical symmetry operations are defined as physical operations, is a new field of chemistry. In a series of papers Smeyers 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. In this paper, a simple method is used, by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of XH₃ groups attached to a rigid framework. We have studied the full non-rigid group (f-NRG) of cis-tetraamminedichloro-cobalt(III). By separating the type of conjugacy classes of the point group, we construct the full non-rigid group of the molecule. We show that this group has 33 conjugacy classes and therefore 33 irreducible characters. This group has eight non-real valued irreducible characters which computed by inducing the characters of a subgroup of G.