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

We present an efficient method for the calculation of the phase space hyper volume from which the number of states W(E), the density of states rho (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 spher e is carried out analytically, thus reducing the six dimensional numerical integration to three dimensions. A method for the calculation of accurate p artition functions is proposed which employs quantum mechanically calculate d eigenvalues for low energies and the classical number of states W-cl(E) f or high energies.