A surface-hopping method for semiclassical calculations of cross sections for radiative association with electronic transitions.

A semiclassical method based on surface-hopping techniques is developed to model the dynamics of radiative association with electronic transitions. It can be proven that this method is an extension of the established semiclassical formula used in the characterization of diatomic molecule-formation. Our method is tested for diatomic molecules. It gives the same cross sections as the former semiclassical formula but, contrary to the former method, it allows us to follow the fate of the trajectories after the emission of a photon. This means that we can characterize the rovibrational states of the stabilized molecules. Using semiclassical quantization, we can obtain quantum state-resolved cross sections or emission spectra for the radiative association process. The calculated semiclassical state-resolved spectra show general agreement with the result of quantum mechanical perturbation theory. Furthermore, our surface-hopping model is not only applicable for the description of radiative association but it can be used for semiclassical characterization of any molecular process where spontaneous emission occurs.