A new generalized expansion for the potential energy curves of diatomic molecules

Abstract

A new generalized expansion for the potential energy curves of diatomic molecules is proposed. It is given by where λ (p) = sgn(p) [1 − (R_e/R)^p], and contains both the Dunham and the Simons−Parr−Finlan (SPF) expansions as special cases corresponding to p = −1 and p = 1, respectively. In order to justify the new expansion, a perturbation theory is developed which yields the Born−Oppenheimer potential as a series identical in form to the new expansion. The perturbation is a purely kinetic−energy perturbation at R_e. Prescriptions are given for obtaining both the expansion coefficients and the optimal value of p either from perturbation theory or from spectral data. In terms of spectral data p = −a₁ −1. Applications of the new expansion to CO, HF, and 20 alkali halides indicate that it predicts dissociation energies in much closer agreement with experiment than the SPF expansion while maintaining the same quality of agreement with the RKR curve as the SPF expansion provides. A number of possible extensions are discussed including potential energy surfaces for polyatomic molecules, techniques for analytic continuation of the new expansion, and expansions for properties other than the potential energy.