The semiclassical calculation of nonadiabatic tunneling rates

In this paper semiclassical low-temperature rate theory is extended to treat nonadiabatic transitions which are typically important in electron transfer reactions. This theory is appropriate for arbitrary coupling strength between electronic states. As in adiabatic semiclassical tunneling theory, it is found that the leading order contribution to the tunneling rate is due to periodic orbits which exist in the barrier region of configuration space between reactant and product. In the current case, these orbits move on effective potentials generated from upside-down (nuclear) potentials of the coupled electronic states. A stable method of finding these mixed quantum/classical “trajectories” is developed using a Newton–Raphson method. Examples employing model systems demonstrate that the current nonadiabatic theory well-reproduces the known adiabatic and Golden Rule limits and that the theory can indeed be applied to systems with more than one degree of freedom.