Knowledge Bank

The simple potential function \begin{equation}{V}={D}{e}(1-{e}^{-{n}\Delta{r}^{2}}/2{r})\end{equation} has been derived for one- and two-electron systems from a simple quantum mechanical model. This function has been used previously to describe the properties of a large number of diatomic and polyatomic molecules in their ground states. This function has now been applied to a number of excited states of diatomic molecules and the results indicate that the dissociation energies of these states may be predicted with 4% accuracy using the equation \begin{equation}{D}{e}={k}{e}/[(64\pi^{2}{c}\mu\omega{e}{x}{e}/3{h})-1/{r}{e}^{2}]\end{equation} which has been derived from equation (1). The results for the excited states of $H2$, $O2$, $N2$, CO, and other molecules are discussed.