A test of perturbation theory for determining anharmonic vibrational corrections to properties of diatomic molecules

Abstract

The convergence behaviour of the Rayleigh-Schrödinger perturbation series for obtaining anharmonic vibrational corrections to properties of diatomic molecules is studied. Various procedures for ordering these corrections are examined. It is verified numerically that an asymptotically divergent energy series results when the complete anharmonic potential is taken as the first-order hamiltonian. By contrast, when each term in a Taylor series expansion of the energy about the equilibrium distance is identified with successively higher orders of perturbation, convergence problems are essentially obviated. Properties other than the energy are also investigated with regard to convergence.