Semiclassical (SC) Description of Electronically Non-AdiabaticDynamics via the Initial Value Representation (IVR)

The initial value representation (IVR) of semiclassical (SC) theory is used in conjunction with the Meyer-Miller/Stock-Thoss description of electronic degrees of freedom in order to treat electronically non-adiabatic processes. It is emphasized that the classical equations of motion for the nuclear and electronic degrees of freedom that emerge in this description are precisely the Ehrenfest equations of motion (the force on the nuclei is the force averaged over the electronic wavefunction), but that the trajectories given by these equations of motion do not have the usual shortcomings of the traditional Ehrenfest model when they are used within the SC-IVR framework. For example, in the traditional Ehrenfest model (a mixed quantum-classical approach) the nuclear motion emerges from a non-adiabatic encounter on an average potential energy surface (a weighted average according to the population in the various electronic states), while the SC-IVR describes the correct correlation between electronic and nuclear dynamics, i.e., the nuclear motion is on one potential energy surface or the other depending on the electronic state. Calculations using forward-backward versions of SC-IVR theory (FB-IVR) are presented to illustrate this behavior. An even more approximate version of the SC-IVR, the linearized approximation (LSC-IVR), is slightly better than the traditional Ehrenfest model, but since it cannot describe quantum coherence effects, the LSC-IVR is also not able to describe the correct correlation between nuclear and electronic dynamics