title: On transition rates in surface hopping.
abstract: Trajectory surface hopping (TSH) is one of the most widely used quantum-classical algorithms for nonadiabatic 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 aim to elucidate the theoretical basis for the widely used hopping rules. Naturally, we concentrate thereby on the formal aspects of the TSH. Using a Gaussian wave packet limit, we derive the transition rates governing the hopping process at a simple avoided level 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 crossings; (ii) rescaling of the nuclear velocities to conserve total energy; (iii) electronic transition rates linear in the nonadiabatic coupling vectors. The well-known Landau-Zener model is then used for illustration.
authors.affiliation: Laboratoire de Physique Théorique-IRSAMC, CNRS, Université Paul Sabatier, F-31062 Toulouse Cedex 04, France.
authors.forename: J M
authors.initials: JM
authors.lastname: Escartín
authors.forename: P
authors.initials: P
authors.lastname: Romaniello
authors.forename: L
authors.initials: L
authors.lastname: Stella
authors.forename: P-G
authors.initials: PG
authors.lastname: Reinhard
authors.forename: E
authors.initials: E
authors.lastname: Suraud
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004583:Electrons; D008956:Models, Chemical; D056004:Molecular Dynamics Simulation; D044367:Phase Transition; D011789:Quantum Theory; D013499:Surface Properties