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-TVR 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. (C) 1998 American Institute of Physics. [S0021-9606(98)02041-8].