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 *R*_{e}, as a power series in the parameter λ = 1 − (R_{e}/R), W(λ) = w_{0} + **∑ **(w_{n} − w_{n-1})λ^{n.}
Truncations of this series have the form of finite power series in *R*^{−1}. The quantities *w*_{n} are obtained simply as perturbation energies for a purely kinetic‐energy perturbation at *R*_{e}, 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 k_{e}, l_{e}, m_{e}, ···, are given, and it is shown how it happens, through cancellation of effects in the molecule near *R*_{e} against effects in the separated atoms, that truncation of the power series in λ at the λ^{2} level is often a good approximation, as has been shown empirically.

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