Convergence of a perturbation technique for evaluating isotopic partition function ratios

Abstract

Schwinger perturbation theory for partition functions is developed in a form which makes practical the numerical evaluation of higher order terms. The vibrational Hamiltonian of a molecule in the harmonic approximation, H=(1/2)∑(gijpipj+fijq iqj), has been partitioned into an unperturbed Hamiltonian (the diagonal part, terms with i≠j) and a perturbation term (the off-diagonal part, terms with i=j). The perturbation theory technique up to fourth order is used to calculate vibrational partition functions for a number of molecules. Vibrational partition functions so calculated are employed to calculate reduced partition functions and reduced isotopic partition function ratios. The results obtained by perturbation theory are compared with those of exact calculations carried out by actually obtaining the normal mode vibrational frequencies of the vibrational Hamiltonian. The previously observed good agreement, especially for the reduced isotopic partition function ratios, between perturbation theory in second order and exact calculations, becomes usually even better in fourth order perturbation theory.