A perturbation theory is developed whereby the diatomic molecular potential energy W(R) as a function of the internuclear distance R is expressed, for R near Re, as a power series in the parameter λ = 1 − (Re/R), W(λ) = w0 + ∑ (wn − wn-1)λn.
Truncations of this series have the form of finite power series in R−1. The quantities wn are obtained simply as perturbation energies for a purely kinetic‐energy perturbation at Re, by setting up the problem in confocal elliptic coordinates, in which the kinetic‐energy part of the Hamiltonian is R−2 times an R‐independent operator and the potential‐energy part is R−1 times an R‐independent operator. Expressions for the successive vibrational force constants ke, le, me, ···, are given, and it is shown how it happens, through cancellation of effects in the molecule near Re against effects in the separated atoms, that truncation of the power series in λ at the λ2 level is often a good approximation, as has been shown empirically.
R.G. Parr and R.J. White. Perturbation-theoretic approach to potential-energy curves of diatomic molecules. J. Chem. Phys. 49:1059-1062, 1968.