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Frozen Gaussian approximation with surface hopping for mixed quantum-classical dynamics: A mathematical justification of fewest switches surface hopping algorithms


Authors: Jianfeng Lu and Zhennan Zhou
Journal: Math. Comp.
MSC (2010): Primary 65C05, 65M99, 81Q20
DOI: https://doi.org/10.1090/mcom/3310
Published electronically: November 22, 2017
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Abstract: We develop a surface hopping algorithm based on frozen Gaussian approximation for semiclassical matrix Schrödinger equations, in the spirit of Tully's fewest switches surface hopping method. The algorithm is asymptotically derived from the Schrödinger equation with rigorous approximation error analysis. The resulting algorithm can be viewed as a path integral stochastic representation of the semiclassical matrix Schrödinger equations. Our results provide mathematical understanding to and shed new light on the important class of surface hopping methods in theoretical and computational chemistry.


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Additional Information

Jianfeng Lu
Affiliation: Department of Mathematics, Department of Physics, and Department of Chemistry, Duke University, Box 90320, Durham, North Carolina 27708
Email: jianfeng@math.duke.edu

Zhennan Zhou
Affiliation: Department of Mathematics, Duke University, Box 90320, Durham, North Carolina 27708
Address at time of publication: Beijing International Center for Mathematical Research, Peking University, No. 5 Yiheyuan Road, Haidian District, Beijing, People’s Republic of China 100871
Email: zhennan@bicmr.pku.edu.cn

DOI: https://doi.org/10.1090/mcom/3310
Received by editor(s): June 9, 2016
Received by editor(s) in revised form: March 22, 2017
Published electronically: November 22, 2017
Additional Notes: This work was partially supported by the National Science Foundation under grants DMS-1312659, DMS-1454939 and RNMS11-07444 (KI-Net). The first author was also partially supported by the Alfred P. Sloan Foundation.
Article copyright: © Copyright 2017 American Mathematical Society

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