We derive a set of generalized master equations (GMEs) to study charge transport dynamics in molecular junctions using the Nakajima–Zwanzig–Mori projection operator approach. In the new GME, time derivatives of population on each quantum state of the molecule, as well as the tunneling current, are calculated as the convolution of time non-local memory kernels with populations on all system states. The non-Markovian memory kernels are obtained by combining the hierarchical equations of motion (HEOM) method and a previous derived Dyson relation for the exact kernel. A perturbative expansion of these memory kernels is then calculated using the extended HEOM developed in our previous work [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. By using the resonant level model and the Anderson impurity model, we study properties of the exact memory kernels and analyze convergence properties of their perturbative expansions with respect to the system–bath coupling strength and the electron–electron repulsive energy. It is found that exact memory kernels calculated from HEOM exhibit short memory times and decay faster than the population and current dynamics. The high order perturbation expansion of the memory kernels can give converged results in certain parameter regimes. The Padé and Landau–Zener resummation schemes are also found to give improved results over low order perturbation theory.
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7 April 2022
Research Article|
April 07 2022
Generalized master equation for charge transport in a molecular junction: Exact memory kernels and their high order expansion
Xiaohan Dan
;
Xiaohan Dan
Beijing 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
and University of Chinese Academy of Sciences
, Beijing 100049, China
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Meng Xu
;
Meng Xu
Beijing 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
and University of Chinese Academy of Sciences
, Beijing 100049, China
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Yaming Yan
;
Yaming Yan
Beijing 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
and University of Chinese Academy of Sciences
, Beijing 100049, China
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Qiang Shi
Qiang Shi
a)
Beijing 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
and University of Chinese Academy of Sciences
, Beijing 100049, China
a)Author to whom correspondence should be addressed: qshi@iccas.ac.cn
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a)Author to whom correspondence should be addressed: qshi@iccas.ac.cn
J. Chem. Phys. 156, 134114 (2022)
Article history
Received:
January 27 2022
Accepted:
March 16 2022
Citation
Xiaohan Dan, Meng Xu, Yaming Yan, Qiang Shi; Generalized master equation for charge transport in a molecular junction: Exact memory kernels and their high order expansion. J. Chem. Phys. 7 April 2022; 156 (13): 134114. https://doi.org/10.1063/5.0086663
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