Two-dimensional free-bound Franck-Condon factors. Application to intramolecular isotope effect in predissociation

Abstract

We calculate free-bound two-dimensional Franck-Condon factors for a molecule HXD with constant angle HXD. We assume separability into normal modes, but the normal modes are different for the attractive and the repulsive potential surfaces. These Franck-Condon factors can be related to the linewidth of a predissociated level and to the relative probability of dissociation into the channel H+XD or the channel D+XH. Classically, we can predict that the Franck-Condon factor will be a maximum as a function of energy if one of the turning points (for vibration in the bound state) happens to be on the repulsive surface at that energy; furthermore, the location of this turning point on the repulsive surface determines the isotope effect, which can be favorable to either D+XH or H+XD. Our two-dimensional study of the O-ν and ν-0 levels shows that these classical predictions are correct, in contrast to the results obtained using a one-dimensional model; in the latter case, strong enhancement of the Franck-Condon factors can occur through interference effects that cannot be predicted classically; interference effects do not show up in the two-dimensional calculation. For the 3–3, 2–2, and 3–2 levels, classical predictions are in rough agreement with the calculations, but we observe strong enhancement of the Franck-Condon factors for certain relative positions of the two surfaces. In conclusion, interference effects do exist for two-dimensional Franck-Condon factors, though they disappear for 0-ν and ν-0 levels.