Franck-Condon factors for the β and γ bands of the NO molecule based on realistic potential functions

Abstract

Matrices of Frank-Condon factors have been computed for the β and γ bands of NO. The matrices extend to the vibrational quantum number υ″ = 36, υ′ = 12 for the γ bands and υ″ = 33, υ′ = 12 for the β bands. This is an extension to higher vibrational quantum numbers than previous tabulations. An indication of the completeness of the tabulations is given by the fact that the rows satisfy the vibrational sum rule to within 1 per cent. For the γ-bands the vertical sum rule is satisfied to one per cent for the first six columns; the maximum column sum for the β-bands is 0.4522. It is thought that these tabulations will prove adequate for most purposes since relatively few molecules populate the very high vibrational levels of the upper states in ordinary situations.The wave functions used in the calculations were obtained from solutions to Schrödinger's amplitude equation using molecular potential energy functions constructed by the Rydberg-Klein-Rees method. An electronic analog computer was used to calculate the wave functions. Since an analog computer gives a continuous solution, the difficulties presented by the highly oscillatory nature of the wave functions at the higher vibrational quantum numbers was avoided.The Franck-Condo factors presented in this paper differ from previously published values computed using Morse potential energy functions. It is shown that these differences are due to the potential functions used. Since the RKR potential function is thought to represent the true potential energy of a diatomic molecule better than the Morse potential, the Franck-Condon factors presented herein are thought to be an improvement over previously published values.