On the densities and numbers of rovibronic states of a given symmetry species: Rigid and nonrigid molecules, transition states, and scattering channels

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Abstract
A simple interpretation of the decomposition of the densities of states in the classical mechanical limit according to the regular representation of the permutation group and—under certain circumstances—the molecular symmetry group is presented. The relationship between recent results on densities of states of a given point group symmetry species and previous results based upon the molecular symmetry group is established. Some restrictions are discussed as well as the definition and application of symmetry numbers for the densities of states and partition functions of nonrigid and rigid molecules and transition states.