Semiclassical evaluation of nonadiabatic rates in condensed phases

Abstract

A procedure for calculating nonadiabatic transition rates in the semiclassical limit is implemented and tested for models relevant for condensed phase processes. The method is based on evaluating the golden rule rate expression using a quantum description for the electronic subsystem and a semiclassical propagation for the nuclear degrees of freedom, similar to Heller’s calculation of absorption and Raman spectra. In condensed phase processes, the short lifetimes of the relevant correlation functions make it possible to implement the procedure within the frozen Gaussian method. Furthermore, because of the large density of states involved, which implies fast dephasing, incoherent superpositions of frozen Gaussian trajectories may be used for the evaluation of the rate. The method is tested using two simple exactly soluble models. One of them, consisting of two coupled electronic potential surfaces, harmonic and linear, is also used for testing and comparing a recently proposed algorithm by Tully. The other, the well-known displaced harmonic potentials model, is a prototype of many condensed phase processes. Finally, the method is applied for calculating the nonadiabatic radiationless relaxation of the solvated electron from its first excited state to the fully solvated ground state.