Short-time dynamics on several electronic states: formalism and computational study of I₂ in rare gas solvents

A computationally tractable approximation for both interstate and intrastate dynamics is derived and applied. The correlation between the electronic and nuclear degrees of freedom is explicitly allowed for in that there is an equation of motion for the nuclear dynamics on each electronic state. These equations for the intrastate dynamics are coupled due to the interstate interaction. The exact equations are derived from a quantum mechanical Hamiltonian and are then simplified by assuming that the coupling between the different electronic states is localized and that, in the absence of interstate coupling, the nuclear motion on each electronic state is classical-like. Equations for the populations and the phases of the different electronic states are also derived. Coupling of the nuclear modes to a classical solvent is included in the formalism and the main computational effort is in the mechanical description of the solvent. As a computational example, a simulation of a fast pump-fast probe for an iodine X → B (bound) transition, in rare gas solvents, is presented and discussed. Despite the long range of the B state potential of iodine, which enhances the effect of the solvent on the excited state dynamics, there is a finite delay before the coupling to the solvent is manifested. The delocalization of the optically prepared state markedly slows down as the density is lowered. At longer times there is considerable energy exchange with the solvent. As a result many molecules either gain enough energy to dissociate or are cooled down, depending on the temperature and density of the solvent. At the higher densities, many molecules which attempt to dissociate are caged.