AN ANALYTICAL EXPRESSION FOR THE POTENTIAL CURVE OF $H_{2}$

Abstract

“The existent potential functions for diatomic molecules fall into two general categories: the sprits expansions or the closed exponential functions, with adjustable constants. We want to propose a new type of curve, with three adjustable parameters K, A, B: \begin{equation}V(r) = K \left( \frac{A}{r^{2}} \tan \frac{\pi}{2 + r^{4}} - \frac{\pi}{1 + \frac{r^{2}}{B}} \sin \frac{\pi}{1 + \frac{r^{2}}{B}}\right) \end{equation} where r is the interatomic distance. This kind of function meets all the requirements for the usual potential function including its behaviour for $r \rightarrow 0$ and $r \rightarrow \infty$. If one tries to fit this kind of a function to a Kolos and Roothaan potential curve for the ground State of $H_{2}$ it is necessary, for a good fit, to introduce a second attraction term: \begin{equation} V(r) = K \left( \frac{A}{r^{2}} \tan \frac{\pi}{2 + r^{4}} - \frac{\pi}{1 + \frac{r^{2}}{B}} \sin \frac{\pi}{1 + \frac{r^{2}}{B}} - D \frac{\pi}{1 + \frac{r^{2}}{C}} \sin \frac{\pi}{1 + \frac{r^{2}}{C}}\right) \end{equation} The advantages and disadvantages of such three and five constants potential functions will be discussed.”