Numbers and densities of states and partition functions from an efficient approach to phase space integration

Abstract

We present an efficient method for the calculation of the phase space hypervolume from which the number of states W(E), the density of states ρ(E) and the partition function Q(T) can be obtained. The HN₂⁺ molecular ion and an ozone-like model potential are used to demonstrate the applicability of the method. For HN₂⁺, an analytical potential energy surface based on high-level ab initio calculations is employed, whereas a quartic force field is used as model potential for ozone. The integration over the momentum sphere is carried out analytically, thus reducing the six dimensional numerical integration to three dimensions. A method for the calculation of accurate partition functions is proposed which employs quantum mechanically calculated eigenvalues for low energies and the classical number of states W_cl(E) for high energies.