RECURSION-RELATIONS FOR MULTIDIMENSIONAL FRANCK-CONDON OVERLAP INTEGRALS

We derive a set of simple recursion relations for multi-dimensional Fr anck-Condon overlap integrals in a clear and systematic way. The deriv ation is made within the harmonic approximation and incorporates the s o-called Duschinsky mixing effect of the normal modes in the initial a nd final states of the molecule under investigation. The numerical pro perties of the derived recursion relations are investigated in detail, showing that the large number of additions performed during the recur sion under certain circumstances can result in a strong propagation of relative error into the result. Finally, the recursion relations are used to calculate relative transition probabilities of the B-2(2)-2A1 transition in NO2.