POWER SERIES EXPANSIONS ABOUT EQUILIBRIUM OF THE HEITLER LONDON AND RITTNER VIBRATIONAL $POTENTIALS^{*}$

Abstract

“Dunham expansions have been carried out for the Heitler-London potential for $H_{2}$ (as a simple model for covalent molecules), And for the leading terms of Rittner’s $potential^{1}$ (as a simple model for ionic molecules). The latter has been applied to alkali and earth halides. Of particular interest are the resulting values of $Y_{30} (\omega_{e} y_{0})$, and the ratio of the dissociation energy for the potential to the linearly extrapolated value. For the Heitler-London potential $Y_{30}$ is negative and $D_{o}/D_{lin} =0.80$. This indicates negative curvature for a $\Delta G$ vs. v curve near equilibrium and rapid convergence of vibrational levels near dissociation. $Y_{an}$ is positive from Rittner’s potential and$D_{o}/D_{lin} \sim 2.5$. Values of the other spectroscopic constants will be presented. The ranges of convergence of the Heitler-London and Rittner expansions both appear to be $o < r < 2r_{e}$. Heitler-London coefficients of higher powers of $(r-r_{e})/r_{e}$. are close to values obtained from pure Coulomb repulsion. Problems connected with numerical application of Dunham’s technique will be discussed.”