The full nonrigid group theory for trimethylamine (Q1415126)

Summary: The nonrigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field in chemistry. \textit{Y.G. Smeyers} and coworkers in a series of papers applied this notion to determine the character table of restricted NRG of some molecules [see J. Math.Chem 28, 377-388 (2000; Zbl 1017.92047); ibid. 18, 209-216 (1995; Zbl 0901.92030)]. 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 \(\text{N}(\text{CH}_{3})_{3}\) 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.