Accurate evaluation of internal energy level sums and densities including anharmonic oscillators and hindered rotors

TLDR

Calculating molecular energy level sums and densities is essential for many physical and chemical problems, such as reaction rate determination. The study extends Beyer and Swinehart’s algorithm to directly compute harmonic oscillator eigenstate sums and densities. The extended algorithm can compute exact or near‑exact sums and densities for free and hindered rotors and anharmonic oscillators, and is practical for large molecules with only minor rounding errors. Comparisons with literature values show the algorithm’s results enable more rigorous testing of approximate treatments and assessment of their errors.

Abstract

The calculation of molecular energy level sums and densities is necessary for the treatment of many physical and chemical problems including reaction rates. An extension of Beyer and Swinehart's algorithm for directly computing harmonic oscillator eigenstate sums and densities is described. With this new algorithm it is possible to compute exact or near-exact energy level sums and densities for degrees of freedom such as free and hindered rotors and anharmonic oscillators so long as the energy levels for each degree of freedom can be specified. Computer calculation by this technique is practical even for large molecules up to all chemically interesting energies and error is confined to small rounding errors. Results by this algorithm are compared to values of energy level sums that have been given in the literature by various alternative approximate treatments and permit more rigorous testing of the latter and assessment of the approximations involved.