Nonadiabatic Dynamics of Condensed Phase Rate Processes

The study of quantum rate processes occurring in condensed phase environments is difficult because of the large number of degrees of freedom involved. Since a full quantum mechanical treatment is not computationally feasible, one is motivated to use mixed quantum-classical dynamical methods. This type of dynamics is applicable when one can single out a few degrees of freedom to be quantum in nature while treating the remainder classically. We describe a method that is based on the quantum-classical Liouville equation, which clearly prescribes the details of the coupling between the quantum and classical degrees of freedom. With the aid of this machinery, we show how to compute rate constants of reactions involving quantum particles immersed in a classical bath. We illustrate the use of this method on a model for proton transfer in a molecular complex dissolved in a polar solvent. I