Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence

Journal Article · Sat Dec 07 04:00:00 EST 2013 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4829856· OSTI ID:22251285

Ouyang, Wenjun; Landry, Brian R. ^[1]

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1. Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States)

In this article, we demonstrate that Tully's fewest-switches surface hopping (FSSH) algorithm approximately obeys the mixed quantum-classical Liouville equation (QCLE), provided that several conditions are satisfied – some major conditions, and some minor. The major conditions are: (1) nuclei must be moving quickly with large momenta; (2) there cannot be explicit recoherences or interference effects between nuclear wave packets; (3) force-based decoherence must be added to the FSSH algorithm, and the trajectories can no longer rigorously be independent (though approximations for independent trajectories are possible). We furthermore expect that FSSH (with decoherence) will be most robust when nonadiabatic transitions in an adiabatic basis are dictated primarily by derivative couplings that are presumably localized to crossing regions, rather than by small but pervasive off-diagonal force matrix elements. In the end, our results emphasize the strengths of and possibilities for the FSSH algorithm when decoherence is included, while also demonstrating the limitations of the FSSH algorithm and its inherent inability to follow the QCLE exactly.

• OSTI ID: 22251285
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 21 Vol. 139; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
ALGORITHMS
BOLTZMANN-VLASOV EQUATION
LIOUVILLE THEOREM
MATRIX ELEMENTS
SEMICLASSICAL APPROXIMATION