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

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.