Density of vibrational states of a given symmetry type for octahedral AB6 molecules

Crude estimations of the densities of states of different symmetry types are made on the basis of the ratio of fundamental frequencies. The theoretical calculation is based on the generating function approach developed recently for this kind of problem. The behavior of the regular and oscillatory parts of the density of states in the limit of high vibrational excitations is compared with the simplest estimate based on the proportionality between density of states of a given symmetry type and the dimension of corresponding irreducible representations. SF6 and UF6 molecules are studied as examples.