Model studies on the systematics and interpolation of Franck-Condon factor arrays

A simple harmonic oscillator approximation is used to derive approximate algebraic expressions for low vibrational quantum number Franck-Condon factors for band systems for which molecular data are sparse. These simple expressions involve a transition parameter u which is characteristic of the electronic transition involved. The expressions provide Franck-Condon factors which agree quite well with RKR values when these are available. The formulae are used to explain quantitatively the dependence on u of the systematic properties of Franck-Condon factor arrays and to provide a method for their interpolation. The formulae are also used to describe quantitatively the dependence on u of the gross appearance of molecular band systems in emission and absorption.