Accurate and Facile Approximation for Vibrational Energy-Level Sums

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Abstract
Some exact sums of harmonic vibrational‐energy‐level densities for 45 molecules were obtained at various energies with a digital computer. An improved ``corresponding vibrational states'' type of approximation to these sums at low and moderate energies is described. The approximation has the great advantage or being very rapid, of requiring scarcely any calculational detail and of using the actual molecular frequencies. The agreement of the approximation with a smoothed true count is usually within a few percent at quite low energies, ε≳0.1 εz. It has the further advantage of being good also for the difficult case of a complex polyatomic molecule with noncommensurable frequencies. The behavior of the sums for various vibrational patterns is considered. The importance of noncommensurability and number of frequency groups is displayed.