A study of the internal dynamics of inverting trimethylamine by means of the non-rigid group theory

Abstract

The non-rigid molecule group (NRG), defined as the complete set of the symmetry physical operations which commute with some Hamiltonian operator, is applied to determine the character table for the three-fold methyl rotation and pyramidal inversion in trimethylamine. The restricted NRG of this molecule is seen to be a group of order 324, isomorphic to the G₃₂₄ of planar trimethylborane. For this purpose, the group structure of the r-NRG of inverting trimethylamine is first deduced, i.e. the character table, the number of classes and irreducible representations, as well as their dimensions. The symmetry eigenvectors for each representation were deduced by developing them on the basis of quadruple products of trigonometric functions. The dynamical properties of trimethylamine are analysed by inspecting the symmetries of the potential energy function. The r-NRG molecule group theory is seen to be a powerful tool for studying the internal dynamics of such highly symmetric molecules.