Diatomic Partition Functions from Classical and Semiclassical Phase Integrals

Abstract

Two methods for calculating diatomic partition functions directly from potential curves are examined with regard to their computational efficiency and accuracy. The first utilizes semiclassical phase integrals to estimate the rotation-vibration eigenvalues and may be considered exact. The second method entails numerical integration of the classical phase integral. The two methods are compared in test calculations of the bound and metastable contributions to the partition functions q _vr for Ar₂ and HgBr. These calculations show that the classical method, which is typically one to two orders of magnitude faster than the semiclassical method, gives results for the bound contributions to q _vr within 1% of exact when kT is at least twice the vibrational energy. For the metastable contributions, two alternative modifications of the classical expression perform less well, and it appears that these contributions can best be estimated by the semiclassical method.

The calculations for HgBr employ the latest spectroscopic constants for this molecule. The resulting values of q _vr are represented within 0.2% over the range 200–3000 K by an empirical expression containing six parameters, with the latter determined by the method of least squares.