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Journal of Chemical Physics / Volume 112 / Issue 15 / THEORETICAL METHODS AND ALGORITHMS

J. Chem. Phys. 112, 6543 (2000); http://dx.doi.org/10.1063/1.481225 (11 pages)

Mixed quantum-classical surface hopping dynamics

Steve Nielsen1, Raymond Kapral1, and Giovanni Ciccotti2

1Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, ON M5S 3H6, Canada
2INFM and Dipartimento di Fisica, Università “La Sapienza,” Piazzale Aldo Moro, 2, 00185 Roma, Italy

(Received 20 December 1999; accepted 24 January 2000)

An algorithm is presented for the exact solution of the evolution of the density matrix of a mixed quantum-classical system in terms of an ensemble of surface hopping trajectories. The system comprises a quantum subsystem coupled to a classical bath whose evolution is governed by a mixed quantum-classical Liouville equation. The integral solution of the evolution equation is formulated in terms of a concatenation of classical evolution segments for the bath phase space coordinates separated by operators that change the quantum state and bath momenta. A hybrid Molecular Dynamics–Monte Carlo scheme which follows a branching tree of trajectories arising from the action of momentum derivatives is constructed to solve the integral equation. We also consider a simpler scheme where changes in the bath momenta are approximated by momentum jumps. These schemes are illustrated by considering the computation of the evolution of the density matrix for a two-level system coupled to a low dimensional classical bath. © 2000 American Institute of Physics.

© 2000 American Institute of Physics

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KEYWORDS and PACS

Keywords

Liouville equation, Monte Carlo methods, molecular dynamics method, integral equations, matrix algebra, quantum theory, reaction kinetics theory

PACS

  • 82.20.Wt

    Computational modeling; simulation

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.481225

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
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    R. Kapral and G. Ciccotti, J. Chem. Phys. 110, 8919 (1999)JCPSA6000110000018008919000001.

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    K. Imre, E. Özizmir, M. Rosenbaum, and P. F. Zwiefel, J. Math. Phys. 5, 1097 (1967)JMAPAQ000008000005001097000001.

    Systems with low-dimensional classical baths have been used to test the validity of mixed quantum-classical schemes. See, for instance, D. Kohen, F. H. Stillinger, and J. C. Tully, J. Chem. Phys. 109, 4713 (1998)JCPSA6000109000012004713000001.

    E. R. Bittner and P. J. Rossky, J. Chem. Phys. 103, 8130 (1995)JCPSA6000103000018008130000001;, O. V. Prezhdo and P. J. Rossky, Phys. Rev. Lett. 81, 5294 (1998).


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