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

Journal Article · Sat Oct 21 04:00:00 EDT 2006 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.2358352· OSTI ID:20864318

Yinghua, Wu; Herman, Michael F ^[1]

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1. Department of Chemistry, Tulane University, 6400 Freret Street, New Orleans, Louisiana 70118 (United States)

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 Schroedinger equation to the first order of ({Dirac_h}/2{pi}) and the error is O(({Dirac_h}/2{pi}){sup 2}). As a required lemma, we show that the stationary phase approximation, under current assumptions, has an error term ({Dirac_h}/2{pi}){sup 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.

• OSTI ID: 20864318
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 15 Vol. 125; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
PROPAGATOR
SCHROEDINGER EQUATION
SEMICLASSICAL APPROXIMATION
SURFACES
TIME DEPENDENCE