Statistical thermodynamics of bond torsional modes: Tests of separable, almost-separable, and improved Pitzer-Gwinn approximations

Practical approximation schemes for calculating partition functions of torsional modes are tested against accurate quantum mechanical results for H2O2 and six isotopically substituted hydrogen peroxides. The schemes are classified on the basis of the type and amount of information that is required. First, approximate one-dimensional hindered-rotator partition functions are benchmarked against exact one-dimensional torsion results obtained by eigenvalue summation. The approximate one-dimensional methods tested in this stage include schemes that only require the equilibrium geometries and frequencies, schemes that also require the barrier heights of internal rotation, and schemes that require the whole one-dimensional torsional potential. Then, three classes of approximate full-dimensional vibrational-rotational partition functions are calculated and are compared with the accurate full-dimensional path integral partition functions. These three classes are (1) separable approximations combining harmonic osci...