Numerical potential functions for diatomic molecules

Recently, we have reported diode laser measurements of the halocarbons CCl+ and CF+ vibrationally excited up to the v = 7 state. In this paper, we present a more detailed analysis of their potential functions as test cases for direct numerical integration of the rovibrational Schrödinger equation. The f-potential, a new parameterization more suitable for numerical fitting, is derived by mapping the potential function into an analytically simpler representation. The results are compared to the standard semiclassical approaches, which are found to have shortcomings in the precision with which they represent spectroscopic data. These problems can become severe if one desires to determine corrections to the Born-Oppenheimer approximation.