#### Document Type

Article

#### Publication Date

8-1-1968

#### Abstract

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

*− w*

_{n}_{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

*, m*

_{e}*, ···, are given, and it is shown how it happens, through cancellation of effects in the molecule near*

_{e}*R*against effects in the separated atoms, that truncation of the power series in λ at the λ

_{e}^{2}level is often a good approximation, as has been shown empirically.

#### Recommended Citation

R.G. Parr and R.J. White. Perturbation-theoretic approach to potential-energy curves of diatomic molecules. J. Chem. Phys. 49:1059-1062, 1968.

## Comments

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.

The following article appeared in J. of Chem. Phys.

49, 1059 (1968); http://doi.org/10.1063/1.1670192 and may be found at http://aip.scitation.org/doi/abs/10.1063/1.1670192