Anharmonic Vibrational Properties from Intrinsic <i>n</i>‑Mode State Densities

A method for calculating fully anharmonic vibrational state counts, state densities, and partition functions for molecules is presented. The method makes use of a new quantity, the <i>intrinsic</i> density of states, which is associated with the states that uniquely arise from a given mode, mode pairing, or higher-order mode coupling. By using only low-order intrinsic densities, the fully coupled anharmonic vibrational result can be constructed, as shown by our application of the method to methane, CH₄, and cyclopropene, C₃H₄. Truncation of the intrinsic expansion at the coupling of pairs of modes yields greatly improved scaling over direct evaluation of the full-dimensional result and recovers a large fraction of the total anharmonicity. We also discuss the relation of the new quantities to the structure of the potential energy surface.