Insight into the surface hopping approach from a wave packet limit
Journal of Chemical Physics 137, 234113 (2012)
Insight into the surface hopping approach from a wave packet limit
Trajectory surface hopping (TSH) is one of the most widely used quantum-classical algorithms for non-adiabatic molecular dynamics. Despite its empirical effectiveness and popularity, a rigorous derivation of TSH as the classical limit of a combined quantum electron-nuclear dynamics is still missing. In this work we elucidate some aspects of this algorithm by deriving, by means of a Gaussian wave packet limit, the transition rates governing the hopping process at a simple avoided crossing. In this derivation, which gives insight into the physics underlying the hopping process, some essential features of the standard TSH algorithm are retrieved, namely i) non-zero electronic transition rate ("hopping probability") at avoided level crossings; ii) rescaling of the nuclear velocities to conserve total energy; iii) electronic transition rates linear in the non-adiabatic coupling vectors. The well-known Landau-Zener model is then used for illustration.