Symmetry-specific densities of vibrational levels for polyatomic molecules

An extension of the algorithm of Stein and Rabinovitch for exact counting of the densities and sums of vibrational states of polyatomic molecules is described. The new algorithm permits the same sort of efficient computation of exact counts by symmetry species. Several examples for molecules belonging to various point groups are given, and a high-energy limiting distribution among various symmetry species is conjectured.