Semiclassical theory of electronically nonadiabatic dynamics: Results of a linearized approximation to the initial value representation

A linearized approximation to the semiclassical initial value representation ~SC-IVR!, referred to herein as the LSC-IVR, was used by us in a recent paper @J. Chem. Phys. 108, 9726 ~1998!# to calculate reactive flux correlation functions for a model of a chemical reaction on a single potential energy surface. This paper shows how the LSC-IVR—which is much easier to apply than the full SC-IVR because it linearizes the phase difference between interfering classical trajectories—can be applied to electronically nonadiabatic processes, i.e., those involving transitions between different potential-energy surfaces. Applications to several model problems are presented to show its usefulness: These are the nonadiabatic scattering problems used by Tully to test surface-hopping models, and also the spin–boson model of coupled electronic states in a condensed phase environment. Though not as accurate as the full SC-IVR, the LSC-IVR does a reasonably good job for all these applications, even describing correctly Stuckelberg oscillations ~interference between nonadiabatic transitions! and the transition between coherent and incoherent behavior in the spin– boson example. © 1998 American Institute of Physics. @S0021-9606~98!02041-8#