A justification for a nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation of the time evolution operator

• Published in: The Journal of chemical physics 2006-10, Vol.125 (15), p.154116-154116-12
• Main Authors: Wu, Yinghua, Herman, Michael F.
• Format: Article
• Language: English
• Subjects: Algorithms; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Computer Simulation; Models, Chemical; Phase Transition; PROPAGATOR; Quantum Theory; SCHROEDINGER EQUATION; SEMICLASSICAL APPROXIMATION; Surface Properties; SURFACES; TIME DEPENDENCE; Time Factors
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.2358352

A justification is given for the validity of a nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) method. The method is based on a propagator that combines the single surface HK SC-IVR method [ J. Chem. Phys. 84 , 326 ( 1986 ) ] and Herman's nonadiabatic semiclassical surface hopping theory [ J. Chem. Phys. 103 , 8081 ( 1995 ) ], which was originally developed using the primitive semiclassical Van Vleck propagator. We show that the nonadiabatic HK SC-IVR propagator satisfies the time-dependent Schrödinger equation to the first order of ℏ and the error is O ( ℏ 2 ) . As a required lemma, we show that the stationary phase approximation, under current assumptions, has an error term ℏ 1 order higher than the leading term. Our derivation suggests some changes to the previous development, and it is shown that the numerical accuracy in applications to Tully's three model systems in low energies is improved.