Centrifugal distortion constants for diatomic molecules: an improved computational method

The perturbation theory approach to calculating centrifugal distortion constants is reformulated to eliminate summations over excited vibrational states. In the usual formulation of Rayleigh-Schrodinger perturbation theory, these summations appear when the solution of an inhomogeneous differential equation is expressed as a sum over the eigenfunctions of the unperturbed Hamiltonian. In the present method, this differential equation is solved numerically, eliminating the summations and giving an exact solution using much less computer time than in the original perturbation theory method. The centrifugal distortion constants are then calculated by a straightforward numerical integration. The effects of continuum levels are included exactly, so that the results remain valid for vibrational levels near dissociation. Numerical tests are performed for realistic potential curves, and the method is shown to give accurate results.