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

Abstract

Practical approximation schemes for calculating partition functions of torsional modes are tested against accurate quantum mechanical results for H(2)O(2) 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 oscillator-rigid rotator models with the one-dimensional torsion schemes, (2) almost-separable approximations in which the nonseparable zero-point energy is used to correct the separable approximations, and (3) improved nonseparable Pitzer-Gwinn-type methods in which approaches of type 1 are used as reference methods in the Pitzer-Gwinn approach. The effectiveness of these methods for the calculation of isotope effects is also studied. Based on the results of these studies, the best schemes of each type are recommended for further use on systems where a corresponding amount of information is available.

Symmetry numbers and chemical reaction rates

“…For distinguishable conformers, as is the case here, it may be desirable to use a torsional method that accounts for the multiple wells of the reactant and/or transition state regions instead of using a simple HO approximation. Specifically, the HO approximation for the torsional mode is replaced by the multiconformer HO (MC-HO) treatment: [21,22] Q MC -HO tor…”

First Principles of Prediction of Thermodynamic Properties

“…The proposal of another partition function that is not unitary and so can describe more realistically the effect of the low frequency modes that are no harmonic oscillator is indeed a big challenge in what large molecules are concerned. The most recently reported treatments have been reviewed recently by Ellingson and collaborators (Ellingson et al, 2006) with results for hydrogen peroxide model system presented.…”

“…The symbols Hind-Rot and Anh indicate the use of hindered rotation and anharmonicity correction to vibrational frequencies treatments respectively, to account for deviations from the RR-HO partition function. For more details of mathematical treatments see a recent review by Ellingson et al (Ellingson et al, 2006).…”

Analytic energy-level densities of separable harmonic oscillators including approximate hindered rotor corrections

“…This species has a single anharmonic torsional motion around the O−O axis, which was studied in great detail. [39][40][41][42] Here, the energy levels reported by Ellingson et al 41 are combined with the free rotor energy levels 43 above the torsional barrier. The resulting energy levels and the harmonic oscillator energy levels of H 2 O 2 are used as input for the modified Beyer-Swinehart algorithm.…”