A direct potential fitting RKR method: Semiclassical vs. quantal comparisons
Abstract Quantal and semiclassical (SC) eigenvalues are compared for three diatomic molecular potential curves: the X state of CO, the X state of Rb2, and the A state of I2. The comparisons show higher levels of agreement than generally recognized, when the SC calculations incorporate a quantum defect correction to the vibrational quantum number, in keeping with the Kaiser modification. One particular aspect of this is better agreement between quantal and SC estimates of the zero point vibrational energy, supporting the need for the Y00 correction in this context. The pursuit of a direct potential fitting (DPF) RKR method is motivated by the notion that some of the limitations of RKR potentials may be innate, from their generation by an exact inversion of approximate quantities: the vibrational energy Gu and rotational constant Bu from least squares analysis of spectroscopic data. In contrast, the DPF RKR method resembles the quantal DPF methods now increasingly used to analyze diatomic spectral data, but with the eigenvalues obtained from SC phase integrals. Application of this method to the analysis of 9500 assigned lines in the I2 A X spectrum fails to alter the quantal SC disparities found for the A state RKR curve from a previous analysis. On the other hand, the SC method can be much faster than the quantal method in exploratory work with different potential functions, where it is convenient to use finite difference methods to evaluate the partial derivatives required in nonlinear fitting.