POTENTIAL FUNCTIONS FOR THE $H_{3}^{+}$ MOLECULE ION

Abstract

For this molecular ion of $D_{3h}$ symmetry, it is natural to express the potential function in terms of the three inter-nuclear distances rather than using the change in valence angle as one coordinate. A Simons-Parr-Finlan potential can then be used in which all three expansion variables are of form $\Delta R / R$. Convergence in band positions with expansion length indicates that this is a satisfactory way to express the potential function for this molecule. Constant energy contour maps for this force field are chemically meaningful. In addition, a Generalized Morse Function Interpolation procedure previously $reported^{1}$ leads to band positions that are equivalent to those obtained from the Simons-Parr-Finlan expansion.