Semiclassical reaction rate constant of non-adiabatic system by means of initial value representation

We applied the semiclassical initial value representation (SC-IVR) method with the classical electron analog to deal with electronically non-adiabatic reactive barriers and calculated the thermal reaction rate constant. The symmetric form of the flux-flux correlation function is used, and the matrix element of the Boltzmannized flux operator is derived using imaginary-time path integral techniques. This combined use of non-adiabatic SC-IVR and non-adiabatic path-integral sampling (NA-IVR&PI) is beyond the treatment of mean-field, and we analyze its performance in comparison with some existing mean-field methods for different scenarios of potential energy surface. We found a systematically better performance. One exception is the deep tunneling regime, where the mean-field ring-polymer instanton is superior. In the golden rule limit, where all these mean-field methods break down, the significant advantage of NA-IVR&PI is shown by using the electronic states for description of the dividing surface.