A NONEQUILIBRIUM GOLDEN-RULE FORMULA FOR ELECTRONIC-STATE POPULATIONSIN NONADIABATICALLY COUPLED SYSTEMS

A formula for computing approximate leakage of population from an init ially prepared electronic state with a nonequilibrium nuclear distribu tion to a second nonadiabatically coupled electronic state is derived and applied. The formula is a nonequilibrium generalization of the fam iliar golden rule, which applies when the initial nuclear state is a r ovibrational eigenstate of the potential energy surface associated wit h the initially populated electronic state. Here, more general initial nuclear states are considered. The resultant prescription, termed the nonequilibrium golden rule formula, can be evaluated via semiclassica l procedures and hence applied to multidimensional, e.g., condensed ph ase systems. To illustrate its accuracy, application is made to a spin -boson model of ''inner sphere'' electron transfer. This model, introd uced by Garg et al. [J. Chem. Phys. 83, 4491 (1985)] for the nonadiaba tic transition out of a thermal distribution of states in the initial (donor) electronic level, is extended to include nonequilibrium, nonst ationary initial nuclear states on the donor surface. The predictions of the nonequilibrium golden rule are found to agree well with numeric ally exact path integral results for a wide range of initial distortio ns of the initial nuclear wave packet from its equilibrium configurati on.