On transition rates in surface hopping

J. M. Escartin*, P. Romaniello, L. Stella, P. -G. Reinhard, E. Suraud

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Citations (Scopus)

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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770280]

Original languageEnglish
Article number234113
Number of pages6
JournalJournal of Chemical Physics
Volume137
Issue number23
DOIs
Publication statusPublished - 21 Dec 2012

Keywords

  • energy level crossing
  • molecular dynamics method
  • potential energy surfaces
  • quantum theory
  • total energy
  • wave functions
  • NONADIABATIC MOLECULAR-DYNAMICS
  • QUANTUM DECOHERENCE
  • BORN-OPPENHEIMER
  • SYSTEMS
  • APPROXIMATION
  • SIMULATIONS
  • SCATTERING
  • EVOLUTION

Cite this

Escartin, J. M., Romaniello, P., Stella, L., Reinhard, P. -G., & Suraud, E. (2012). On transition rates in surface hopping. Journal of Chemical Physics, 137(23), [234113]. https://doi.org/10.1063/1.4770280