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

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 m...

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Veröffentlicht in:The Journal of chemical physics 2013-12, Vol.139 (21), p.214107-214107
Hauptverfasser: Subotnik, Joseph E., Ouyang, Wenjun, Landry, Brian R.
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container_title The Journal of chemical physics
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creator Subotnik, Joseph E.
Ouyang, Wenjun
Landry, Brian R.
description 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.
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subjects Adiabatic flow
ALGORITHMS
BOLTZMANN-VLASOV EQUATION
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Couplings
Liouville equations
LIOUVILLE THEOREM
MATHEMATICAL METHODS AND COMPUTING
MATRIX ELEMENTS
SEMICLASSICAL APPROXIMATION
Switches
Trajectories
Wave packets
title Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence
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