Comparison of semiclassical treatments for evaluating Franck–Condon transition amplitudes for molecular dissociation

Abstract

The full Franck–Condon amplitude for molecular dissociation processes can be written as a sum of products of half collision amplitudes, for vibrational–rotational transitions between single channel states of the repulsive electronic surface, and Franck–Condon (e.g., vertical) amplitudes, for transitions from the bound electronic state to the single channel states of the repulsive surface. The single channel Franck–Condon amplitudes, involving bound-continuum overlap integrals, are evaluated using various semiclassical approximations. A comparison is made between the semiclassical and exact quantum evaluations of the Franck–Condon single channel amplitudes by performing calculations for the photodissociation of HCN, ICN, and CO2, thereby testing the range of validity of the semiclassical methods. Also, the wavelength dependence of the isotope effect for HCN dissociation is described.