The symmetry groups of non-rigid molecules: a Lie algebraic and group contraction approach

Abstract

The description of the symmetry of non-rigid molecules is explored through a Lie algebraic approach. It is shown that the abstract process of contraction to an appropriate Lie algebra corresponds to restriction of molecular motion to regions located around the minima of a global potential. The contracted algebra may be determined by recasting the Hamiltonian in terms of variables which vanish at global potential minima, and the resultant direct or semidirect product group structure accords with that proposed by other workers. This approach is applied to two familiar problems of molecular symmetry, namely inversion through a potential barrier and hindered rotation; the results derived confirm and extend those obtained by other methods.