On the use of divergent series in vibrational spectroscopy. Two- and three-dimensional oscillators

Abstract

Prospects for higher order perturbation theory in evaluating accurate eigenvalues and eigenvectors of the vibrational Hamiltonian are investigated by performing calculations on a series of two- and three-dimensional quartic anharmonic oscillators imitating vibrational motions in the H2O, H2S, NO2, SO2, and HOF triatomic molecules. Despite the fact that most of the corresponding perturbation expansion series diverge strongly they can be summed efficiently using the same methods as in previous studies on one-dimensional oscillators. Hence, higher order perturbation theory appears as a reasonable alternative to accurate variational methods in the case of small molecular systems and as a very promising tool for a proper treatment of larger systems.