Abstract
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 intrinsic 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.
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