The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.
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28 April 2009
Research Article|
April 29 2009
Electron transfer dynamics: Zusman equation versus exact theory
Qiang Shi;
Qiang Shi
a)
1Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry,
Chinese Academy of Sciences
, Zhongguancun, Beijing 100190, China
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Liping Chen;
Liping Chen
1Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry,
Chinese Academy of Sciences
, Zhongguancun, Beijing 100190, China
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Guangjun Nan;
Guangjun Nan
1Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry,
Chinese Academy of Sciences
, Zhongguancun, Beijing 100190, China
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Ruixue Xu;
Ruixue Xu
b)
2Hefei National Laboratory for Physical Sciences at Microscale,
University of Science and Technology of China
, Hefei, Anhui 230026, China
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YiJing Yan
YiJing Yan
c)
3Department of Chemistry,
Hong Kong University of Science and Technology
, Kowloon, Hong Kong
Search for other works by this author on:
Qiang Shi
1,a)
Liping Chen
1
Guangjun Nan
1
Ruixue Xu
2,b)
YiJing Yan
3,c)
1Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry,
Chinese Academy of Sciences
, Zhongguancun, Beijing 100190, China
2Hefei National Laboratory for Physical Sciences at Microscale,
University of Science and Technology of China
, Hefei, Anhui 230026, China
3Department of Chemistry,
Hong Kong University of Science and Technology
, Kowloon, Hong Kong
a)
Electronic mail: [email protected].
b)
Electronic mail: [email protected].
c)
Electronic mail: [email protected].
J. Chem. Phys. 130, 164518 (2009)
Article history
Received:
March 01 2009
Accepted:
April 03 2009
Citation
Qiang Shi, Liping Chen, Guangjun Nan, Ruixue Xu, YiJing Yan; Electron transfer dynamics: Zusman equation versus exact theory. J. Chem. Phys. 28 April 2009; 130 (16): 164518. https://doi.org/10.1063/1.3125003
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