Vibration—Rotation Interaction Factors for Diatomic Molecules Calculated by Numerical Methods

Abstract

The influence of vibration—rotation interaction on transition probabilities for diatomic molecules has been studied through numerical solution of the Schrödinger radial equation. The numerical method employed is readily applicable to any choice of potential and dipole moment functions for the molecule, its accuracy considerably exceeds the requirements of practical applications, and it is very economical in terms of computer‐time requirements. Its use is demonstrated here in two applications. First, it has been used to check the accuracy of the approximate formulas for the F factors of a rotating Morse oscillator with a linear dipole‐moment function derived by Herman, Rothery, and Rubin. It was found that their formulas were very accurate for Δv=1 transitions, but that the two formulas given by them for the first and second overtones could introduce errors of several percent at moderate J values. Secondly, quadratic and cubic terms were added to the dipole‐moment function in order to estimate the sensitivity of F factors to changes in this function. The results indicate that for all transitions in which Δv>1, the higher terms can have considerable significance. For example, F factors for the lines R(19) and R(20) of the 3–0 band of LiH were changed by factors of more than 3 when the dipole‐moment function employed was carried from a linear to a cubic approximation in a Taylor's series expansion.