ITERATIVE METHODS TO COMPUTE ONE-DIMENSIONAL AND 2-DIMENSIONAL FRANCK-CONDON FACTORS - TESTS OF ACCURACY AND APPLICATION TO STUDY INDIRECT MOLECULAR-TRANSITIONS

We derive by a systematic mathematical way explicit recursion formulas to compute one- and two-dimensional Franck-Condon factors required in molecular models where the following hypotheses are assumed: (i) the harmonic approximation for the attractive potential energy curves; (ii) the Airy function approximation for the continuum wavefunctions. Nevertheless these algorithms can be used when the harmonic or Condon approximations are relaxed. Illustrative examples are reported to show the evolution of the Franck-Condon factors as a function of the quantum numbers, and the accuracy of these iterative methods is investigated. The precision of the algorithms is turned to account to point out the spectacular destructive interferences between the intermediate reactional paths in non-resonant indirect molecular transitions (two-step mechanism). © 1990.