Surface hopping, transition state theory and decoherence. I. Scattering theory and time-reversibility

We provide an in-depth investigation of transmission coefficients as computed using the augmented-fewest switches surface hopping algorithm in the low energy regime. Empirically, microscopic reversibility is shown to hold approximately. Furthermore, we show that, in some circumstances, including decoherence on top of surface hopping calculations can help recover (as opposed to destroy) oscillations in the transmission coefficient as a function of energy; these oscillations can be studied analytically with semiclassical scattering theory. Finally, in the spirit of transition state theory, we also show that transmission coefficients can be calculated rather accurately starting from the curve crossing point and running trajectories forwards and backwards.