Extension of path integral quantum transition state theory to the case of nonadiabatic activated dynamics

In this paper, a methodology is introduced by which one may compute rates of nonadiabatic processes for arbitrary potential forms. This method augments the extant path-integral transition state theory approach in which information about the inherently dynamical rate process is obtained from a static analysis of a free energy surface. The present resulting formula reduces to previous single adiabatic surface results when the adiabatic surface are well separated. Numerical examples show that the method well approximates the exact results in the nonadiabatic limit and over a large range of temperatures for quadratic and for nonquadratic potentials. Corroborating these results, analysis of the rate formula for a single-oscillator spin-boson Hamiltonian in the nonadiabatic classical-limit reveals close agreement with the known exact result. (C) 1999 American Institute of Physics. [S0021-9606(99)50631-4].