International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 42, Pages 2701-2706

The full nonrigid group theory for 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

Received 23 May 2002

Copyright © 2003 Masood Hamadanian and Ali Reza Ashrafi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The nonrigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field in chemistry. Smeyers in a series of papers applied this notion to determine the character table of restricted NRG of some molecules. In this note, 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 methyl groups attached to a rigid framework. We study the full NRG of trimethylamine N(CH3)3 and prove that it is a group of order 1296 with 28 conjugacy classes. The method can be generalized to apply to other nonrigid molecules. The full nonrigid (f-NRG) molecule group theory is seen to be used advantageously to study the internal dynamics of such molecules.