Numerical comparison of generalized surface hopping, classical analog, and self-consistent eikonal approximations for nonadiabatic scattering

Three recently proposed semiclassical methods for nonadiabatic scattering are numerically compared for a one-dimensional curve crossing model. The generalized surface hopping approach has been found to be in excellent agreement with quantum results over a wide range of energies. The simpler variant of the self-consistent eikonal method follows the quantum results well at low energies. At higher energies it still follows the correct overall trend of decreasing transition probability, but it does not quantitatively reproduce the oscillations in the transition probability. The classical analog technique provides relatively good agreement with the quantum results over the entire range of energies examined. It is found in the application of this last method that there are typically four to eight stationary phase contributions at each energy and it is crucial to correctly describe the interference between these terms. It is also necessary to include uniform and analytically continued contributions at many energies, complicating the application of the method.