Analytic evaluation of Franck-Condon integrals for anharmonic vibrational wave functions

The problem of calculating Franck-Condon overlap integrals in molecular transitions between vibrational states in different electronic configurations is addressed. An exact and easily applicable analytical expression is obtained when the vibrational states can be approximated by eigenstates of Morse potentials with different strengths and locations but identical ranges. An approximate analytical expression is obtained for the general case. The method is applied to the stretching S-S mode corresponding to [Formula Presented] transitions in the [Formula Presented] molecule.