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.