1
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Guan W, Bao P, Peng J, Lan Z, Shi Q. mpsqd: A matrix product state based Python package to simulate closed and open system quantum dynamics. J Chem Phys 2024; 161:122501. [PMID: 39324531 DOI: 10.1063/5.0226214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2024] [Accepted: 09/06/2024] [Indexed: 09/27/2024] Open
Abstract
We introduce a Python package based on matrix product states (MPS) to simulate both the time-dependent Schrödinger equation (TDSE) and the hierarchical equations of motion (HEOM). The wave function in the TDSE or the reduced density operator/auxiliary density operators in the HEOM are represented using MPS. A matrix product operator (MPO) is then constructed to represent the Hamiltonian in the TDSE or the generalized Liouvillian in the HEOM. The fourth-order Runge-Kutta method and the time-dependent variational principle are used to propagate the MPS. Several examples, including the nonadiabatic interconversion dynamics of the pyrazine molecule, excitation energy transfer dynamics in molecular aggregates and photosynthetic light-harvesting complexes, the spin-boson model, a laser driven two-state model, the Holstein model, and charge transport in the Anderson impurity model, are presented to demonstrate the capability of the package.
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Affiliation(s)
- Weizhong Guan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Peng Bao
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
| | - Jiawei Peng
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety & MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, China and School of Environment, South China Normal University, Guangzhou 510006, China
- School of Chemistry, South China Normal University, Guangzhou 510006, China
| | - Zhenggang Lan
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety & MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, China and School of Environment, South China Normal University, Guangzhou 510006, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
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2
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Li G, Shi Z, Huang L, Wang L. Multiconfigurational Surface Hopping: a Time-Dependent Variational Approach with Momentum-Jump Trajectories. J Chem Theory Comput 2024. [PMID: 39215702 DOI: 10.1021/acs.jctc.4c00842] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/04/2024]
Abstract
The Ehrenfest mean field dynamics and trajectory surface hopping have been widely used in nonadiabatic dynamics simulations. Based on the time-dependent variational principle (TDVP), the multiconfigurational Ehrenfest (MCE) method has also been developed and can be regarded as a multiconfigurational extension of the traditional Ehrenfest dynamics. However, it is not straightforward to apply the TDVP to surface hopping trajectories because there exists momentum jump during surface hops. To solve this problem, we here propose a multiconfigurational surface hopping (MCSH) method, where continuous momenta are obtained by linear interpolation and the interpolated trajectories are used to construct the basis functions for TDVP in a postprocessing manner. As demonstrated in a series of representative spin-boson models, MCSH achieves high accuracy with only several hundred trajectory bases and can uniformly improve the performance of surface hopping. In principle, MCSH can be combined with all kinds of mixed quantum-classical trajectories and thus has the potential to properly describe general nonadiabatic dynamics.
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Affiliation(s)
- Guijie Li
- Zhejiang Key Laboratory of Excited-State Energy Conversion and Energy Storage, Department of Chemistry, Zhejiang University, Hangzhou 310058, China
| | - Zhecun Shi
- Zhejiang Key Laboratory of Excited-State Energy Conversion and Energy Storage, Department of Chemistry, Zhejiang University, Hangzhou 310058, China
| | - Lei Huang
- Zhejiang Key Laboratory of Excited-State Energy Conversion and Energy Storage, Department of Chemistry, Zhejiang University, Hangzhou 310058, China
| | - Linjun Wang
- Zhejiang Key Laboratory of Excited-State Energy Conversion and Energy Storage, Department of Chemistry, Zhejiang University, Hangzhou 310058, China
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3
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Liu L, Ren J, Fang W. Improved memory truncation scheme for quasi-adiabatic propagator path integral via influence functional renormalization. J Chem Phys 2024; 161:084101. [PMID: 39171703 DOI: 10.1063/5.0221916] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2024] [Accepted: 08/05/2024] [Indexed: 08/23/2024] Open
Abstract
Accurately simulating non-Markovian quantum dynamics in system-bath coupled problems remains challenging. In this work, we present a novel memory truncation scheme for the iterative quasi-adiabatic propagator path integral (iQuAPI) method to improve accuracy. Conventional memory truncation in iQuAPI discards all influence functional beyond a certain time interval, which is not effective for problems with a long memory time. Our proposed scheme selectively retains the most significant parts of the influence functional using the density matrix renormalization group algorithm. We validate the effectiveness of our scheme through simulations of the spin-boson model across various parameter sets, demonstrating faster convergence and improved accuracy compared to the conventional scheme. Our findings suggest that the new memory truncation scheme significantly advances the capabilities of iQuAPI for problems with a long memory time.
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Affiliation(s)
- Limin Liu
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, 100875 Beijing, People's Republic of China
| | - Jiajun Ren
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, 100875 Beijing, People's Republic of China
| | - Weihai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, 100875 Beijing, People's Republic of China
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4
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Hogg CR, Glatthard J, Cerisola F, Anders J. Tutorial on the stochastic simulation of dissipative quantum oscillators. J Chem Phys 2024; 161:071501. [PMID: 39166893 DOI: 10.1063/5.0222528] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2024] [Accepted: 07/22/2024] [Indexed: 08/23/2024] Open
Abstract
Generic open quantum systems are notoriously difficult to simulate unless one looks at specific regimes. In contrast, classical dissipative systems can often be effectively described by stochastic processes, which are generally less computationally expensive. Here, we use the paradigmatic case of a dissipative quantum oscillator to give a pedagogic introduction to the modeling of open quantum systems using quasiclassical methods, i.e., classical stochastic methods that use a "quantum" noise spectrum to capture the influence of the environment on the system. Such quasiclassical methods have the potential to offer insights into the impact of the quantum nature of the environment on the dynamics of the system of interest while still being computationally tractable.
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Affiliation(s)
- C R Hogg
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom
| | - J Glatthard
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom
| | - F Cerisola
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom
| | - J Anders
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom
- Institut für Physik und Astronomie, University of Potsdam, 14476 Potsdam, Germany
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5
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Nestmann K, Leijnse M, Wegewijs MR. RealTimeTransport: An open-source C++ library for quantum transport simulations in the strong coupling regime. J Chem Phys 2024; 161:064108. [PMID: 39132788 DOI: 10.1063/5.0220783] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2024] [Accepted: 07/19/2024] [Indexed: 08/13/2024] Open
Abstract
The description of quantum transport in the strong system-reservoir coupling regime poses a significant theoretical and computational challenge that demands specialized tools for accurate analysis. RealTimeTransport is a new open-source C++ library that enables the computation of both stationary and transient transport observables for generic quantum systems connected to metallic reservoirs. It computes the Nakajima-Zwanzig memory kernels for both dynamics and transport in real-time, going beyond traditional expansions in the bare system-reservoir couplings. Currently, several methods are available as follows: (i) A renormalized perturbation theory in leading and next-to-leading order, which avoids the low-temperature breakdown that limits the traditional theory. (ii) Starting from this well-behaved reference solution, a two- and three-loop, self-consistent renormalization-group transformation of the memory kernels is implemented. This allows refined quantitative predictions even in the presence of many body resonances, such as the Kondo enhancement of cotunneling. This paper provides an overview of the theory, the architecture of RealTimeTransport, and practical demonstrations of the currently implemented methods. In particular, we analyze the stationary transport through a serial double quantum dot and showcase for the T = 0 interacting Anderson model the complete time-development of single-electron tunneling (SET), cotunneling-assisted SET, and inelastic cotunneling resonances throughout the entire gate-bias stability diagram. We discuss the range of applicability of the implemented methods and benchmark them against other advanced approaches.
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Affiliation(s)
- Konstantin Nestmann
- Division of Solid State Physics and NanoLund, Lund University, S-22100 Lund, Sweden
| | - Martin Leijnse
- Division of Solid State Physics and NanoLund, Lund University, S-22100 Lund, Sweden
| | - Maarten R Wegewijs
- Institute for Theory of Statistical Physics, RWTH Aachen, 52056 Aachen, Germany
- JARA-FIT, 52056 Aachen, Germany
- Institut, Forschungszentrum Jülich, 52425 Jülich, Germany
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6
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Mäck M, Thoss M, Rudge SL. Nonadiabatic dynamics of molecules interacting with metal surfaces: Extending the hierarchical equations of motion and Langevin dynamics approach to position-dependent metal-molecule couplings. J Chem Phys 2024; 161:064106. [PMID: 39132787 DOI: 10.1063/5.0222076] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2024] [Accepted: 07/25/2024] [Indexed: 08/13/2024] Open
Abstract
Electronic friction and Langevin dynamics is a popular mixed quantum-classical method for simulating the nonadiabatic dynamics of molecules interacting with metal surfaces, as it can be computationally more efficient than fully quantum approaches. In this work, we extend the theory of electronic friction within the hierarchical equations of motion formalism to models with a position-dependent metal-molecule coupling. We show that the addition of a position-dependent metal-molecule coupling adds new contributions to the electronic friction and other forces, which are highly relevant for many physical processes. Our expressions for the electronic forces within the Langevin equation are valid both in and out of equilibrium and for molecular models containing strong interactions. We demonstrate the approach by applying it to different models of interest.
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Affiliation(s)
- Martin Mäck
- Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Michael Thoss
- Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Samuel L Rudge
- Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
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7
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Zuo L, Ye L, Li X, Xu RX, Yan Y, Zheng X. Unraveling the Nature of Spin Coupling in a Metal-Free Diradical: Theoretical Distinction of Ferromagnetic and Antiferromagnetic Interactions. J Phys Chem Lett 2024; 15:5761-5769. [PMID: 38776132 DOI: 10.1021/acs.jpclett.4c01063] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/31/2024]
Abstract
Metal-free diradicals based on polycyclic aromatic hydrocarbons are promising candidates for organic spintronics due to their stable magnetism and tunable spin coupling. However, distinguishing and elucidating the origins of ferromagnetic and antiferromagnetic interactions in these systems remain challenging. Here, we investigate the 2-OS diradical molecule sandwiched between gold electrodes using a combined density functional theory and hierarchical equations of motion approach. We find that the dihedral angle between the radical moieties controls the nature and strength of the intramolecular spin coupling, transitioning smoothly from antiferromagnetic to ferromagnetic as the angle increases. Distinct features in the inelastic electron tunneling spectra are identified that can discern the two coupling regimes, including spin excitation steps whose energies directly reveal the exchange coupling constant. Mechanical stretching of the junction is predicted to modulate the spectral line shapes by adjusting the hybridization of the molecular radicals with the electrodes. Our work elucidates the electronic origin of tunable spin interactions in 2-OS and provides spectroscopic fingerprints for characterizing magnetism in metal-free diradicals.
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Affiliation(s)
- Lijun Zuo
- Hefei National Research Center for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
| | - Lyuzhou Ye
- Hefei National Research Center for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
| | - Xiangyang Li
- Hefei National Research Center for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
| | - Rui-Xue Xu
- Hefei National Research Center for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
| | - YiJing Yan
- Hefei National Research Center for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
| | - Xiao Zheng
- Department of Chemistry, Fudan University, Shanghai 200433, P. R. China
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8
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Gu B. Diagrammatic representation and nonperturbative approximations of the exact time-convolutionless master equation. J Chem Phys 2024; 160:204113. [PMID: 38787536 DOI: 10.1063/5.0187191] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2023] [Accepted: 04/30/2024] [Indexed: 05/25/2024] Open
Abstract
The time-convolutionless master equation provides a general framework to model the non-Markovian dynamics of an open quantum system with a time-local generator. A diagrammatic representation is developed and proven for the perturbative expansion of the exact time-local generator for an open quantum system interacting with arbitrary environments. A truncation of the perturbation expansion leads to perturbative time-convolutionless quantum master equations. We further introduce a general iterative approach to construct nonperturbative approximations for the time-local generator as nested time-ordered exponential operators.
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Affiliation(s)
- Bing Gu
- Department of Chemistry and Department of Physics, Westlake University, Hangzhou, Zhejiang 310030, China and Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
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9
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Kang M, Nuomin H, Chowdhury SN, Yuly JL, Sun K, Whitlow J, Valdiviezo J, Zhang Z, Zhang P, Beratan DN, Brown KR. Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics. Nat Rev Chem 2024; 8:340-358. [PMID: 38641733 DOI: 10.1038/s41570-024-00595-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 03/07/2024] [Indexed: 04/21/2024]
Abstract
Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond the reach of current classical-digital simulation. To identify a 'quantum advantage' for these simulations, performance analysis of both analog-quantum simulation on noisy hardware and classical-digital algorithms is needed. In this Review, we make a comparison between a noisy analog trapped-ion simulator and a few choice classical-digital methods on simulating the dynamics of a model molecular Hamiltonian with linear vibronic coupling. We describe several simple Hamiltonians that are commonly used to model molecular systems, which can be simulated with existing or emerging trapped-ion hardware. These Hamiltonians may serve as stepping stones towards the use of trapped-ion simulators for systems beyond the reach of classical-digital methods. Finally, we identify dynamical regimes in which classical-digital simulations seem to have the weakest performance with respect to analog-quantum simulations. These regimes may provide the lowest hanging fruit to make the most of potential quantum advantages.
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Affiliation(s)
- Mingyu Kang
- Duke Quantum Center, Duke University, Durham, NC, USA.
- Department of Physics, Duke University, Durham, NC, USA.
| | - Hanggai Nuomin
- Department of Chemistry, Duke University, Durham, NC, USA
| | | | - Jonathon L Yuly
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
| | - Ke Sun
- Duke Quantum Center, Duke University, Durham, NC, USA
- Department of Physics, Duke University, Durham, NC, USA
| | - Jacob Whitlow
- Duke Quantum Center, Duke University, Durham, NC, USA
- Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA
| | - Jesús Valdiviezo
- Kenneth S. Pitzer Theory Center, University of California, Berkeley, CA, USA
- Department of Chemistry, University of California, Berkeley, CA, USA
- Departamento de Ciencias, Sección Química, Pontificia Universidad Católica del Perú, Lima, Peru
| | - Zhendian Zhang
- Department of Chemistry, Duke University, Durham, NC, USA
| | - Peng Zhang
- Department of Chemistry, Duke University, Durham, NC, USA
| | - David N Beratan
- Department of Physics, Duke University, Durham, NC, USA.
- Department of Chemistry, Duke University, Durham, NC, USA.
- Department of Biochemistry, Duke University, Durham, NC, USA.
| | - Kenneth R Brown
- Duke Quantum Center, Duke University, Durham, NC, USA.
- Department of Physics, Duke University, Durham, NC, USA.
- Department of Chemistry, Duke University, Durham, NC, USA.
- Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA.
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10
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Li T, Yan Y, Shi Q. Is there a finite mobility for the one vibrational mode Holstein model? Implications from real time simulations. J Chem Phys 2024; 160:111102. [PMID: 38501468 DOI: 10.1063/5.0198107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2024] [Accepted: 03/02/2024] [Indexed: 03/20/2024] Open
Abstract
The question of whether there exists a finite mobility in the standard Holstein model with one vibrational mode on each site remains unclear. In this Communication, we approach this problem by employing the hierarchical equation of motion method to simulate model systems where the vibrational modes are dissipative. It is found that, as the friction becomes smaller, the charge carrier mobility increases significantly and a friction-free limit cannot be obtained. The current autocorrelation functions are also calculated for the friction-free Holstein model, and converged results cannot be obtained with an increase in the number of sites. Based on these observations, we conclude that a finite mobility cannot be defined for the standard Holstein model in the parameter regime explored in this work.
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Affiliation(s)
- Tianchu Li
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yaming Yan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
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11
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Zhang YL, Liu XJ, An Z. Effects of Soliton Creation on Transient Transport through a Polymer Chain. J Phys Chem B 2024; 128:1812-1817. [PMID: 38324304 DOI: 10.1021/acs.jpcb.3c08121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2024]
Abstract
By using a nonadiabatic molecular dynamics method combined with the hierarchical equations of motion, we have investigated the nonequilibrium transient transport through a conjugated polymer chain. The polymer chain is described by the Su-Schrieffer-Heeger model, and its two ends are coupled with metal electrodes of different chemical potentials. In order to present the evolutions of the electronic injection and transport in the real-time domain, we have mainly discussed the dynamic relaxation processes of the excited states and transient transport currents. It is found that due to the existence of electron-phonon couplings in the conjugated polymers, creation of solitons not only affects the time of the system achieving the steady state but also leads to periodical oscillations of the steady-state transport currents with time in our simulations. Furthermore, with increasing applied bias voltage, the steady-state transport electronic current increases, which proved that the creation of the solitons can assist the electronic transport. These results have shown that the creation of the excited states is important in understanding the transport properties in organic nanostructures.
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Affiliation(s)
- Y L Zhang
- Hebei Key Laboratory of Photoelectric Control on Surface and Interface, College of Science, Hebei University of Science and Technology, Shijiazhuang 050018, China
| | - X J Liu
- College of Physics, Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang 050024, China
| | - Z An
- College of Physics, Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang 050024, China
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12
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Erpenbeck A, Gull E, Cohen G. Shaping Electronic Flows with Strongly Correlated Physics. NANO LETTERS 2023; 23:10480-10489. [PMID: 37955307 DOI: 10.1021/acs.nanolett.3c03067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/14/2023]
Abstract
Nonequilibrium quantum transport is of central importance in nanotechnology. Its description requires the understanding of strong electronic correlations that couple atomic-scale phenomena to the nanoscale. So far, research in correlated transport has focused predominantly on few-channel transport, precluding the investigation of cross-scale effects. Recent theoretical advances enable the solution of models that capture the interplay between quantum correlations and confinement beyond a few channels. This problem is the focus of this study. We consider an atomic impurity embedded in a metallic nanosheet spanning two leads, showing that transport is significantly altered by tuning only the phase of a single local hopping parameter. Furthermore─depending on this phase─correlations reshape the electronic flow throughout the sheet, either funneling it through the impurity or scattering it away from a much larger region. This demonstrates the potential for quantum correlations to bridge length scales in the design of nanoelectronic devices and sensors.
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Affiliation(s)
- Andre Erpenbeck
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Emanuel Gull
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Guy Cohen
- The Raymond and Beverley Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
- School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
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13
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Li G, Shi Z, Guo X, Wang L. What is Missing in the Mean Field Description of Spatial Distribution of Population? Important Role of Auxiliary Wave Packets in Trajectory Branching. J Phys Chem Lett 2023; 14:9855-9863. [PMID: 37890155 DOI: 10.1021/acs.jpclett.3c02690] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/29/2023]
Abstract
When the traditional Ehrenfest mean field approach is employed to simulate nonadiabatic dynamics, an effective wave packet (WP) on the average potential energy surface (PES) is utilized to describe the nuclear motion. In the fully quantum picture, however, the WP components on different adiabatic PESs gradually separate in space because they evolve under different velocities and forces. Due to trajectory branching of the WP components, proper decoherence needs to be taken into account, and the spatial distribution of population cannot be described by a single effective WP. Here, we propose an auxiliary branching corrected mean field (A-BCMF) method, where trajectories of auxiliary WPs on adiabatic PESs are introduced. As benchmarked in the three standard Tully models, A-BCMF not only gives correct channel populations but also captures an accurate time-dependent spatial distribution of population. Thereby, we reveal the important role of auxiliary WPs in solving intrinsic problems of the widely used mean field description of nonadiabatic dynamics.
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Affiliation(s)
- Guijie Li
- Key Laboratory of Excited-State Materials of Zhejiang Province, Department of Chemistry, Zhejiang University, Hangzhou 310058, China
| | - Zhecun Shi
- Key Laboratory of Excited-State Materials of Zhejiang Province, Department of Chemistry, Zhejiang University, Hangzhou 310058, China
| | - Xin Guo
- Key Laboratory of Excited-State Materials of Zhejiang Province, Department of Chemistry, Zhejiang University, Hangzhou 310058, China
| | - Linjun Wang
- Key Laboratory of Excited-State Materials of Zhejiang Province, Department of Chemistry, Zhejiang University, Hangzhou 310058, China
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14
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Erpenbeck A, Ke Y, Peskin U, Thoss M. How an electrical current can stabilize a molecular nanojunction. NANOSCALE 2023; 15:16333-16343. [PMID: 37766513 DOI: 10.1039/d3nr02176a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/29/2023]
Abstract
The stability of molecular junctions under transport is of the utmost importance for the field of molecular electronics. This question is often addressed within the paradigm of current-induced heating of nuclear degrees of freedom or current-induced forces acting upon the nuclei. At the same time, an essential characteristic of the failure of a molecular electronic device is its changing conductance - typically from a finite value for the intact device to zero for a device that lost its functionality. In this publication, we focus on the current-induced changes in the molecular conductance, which are inherent to molecular junctions at the limit of mechanical stability. We employ a numerically exact framework based on the hierarchical equations of motion approach, which treats both electronic and nuclear degrees of freedom on an equal footing and does not impose additional assumptions. Studying generic model systems for molecular junctions with dissociative potentials for a wide range of parameters spanning the adiabatic and the nonadiabatic regime, we find that molecular junctions that exhibit a decrease in conductance upon dissociation are more stable than junctions that are more conducting in their dissociated state. This represents a new mechanism that stabilizes molecular junctions under current. Moreover, we identify characteristic signatures in the current of breaking junctions related to the interplay between changes in the conductance and the nuclear configuration and show how these are related to properties of the leads rather than characteristics of the molecule itself.
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Affiliation(s)
- André Erpenbeck
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.
| | - Yaling Ke
- Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Uri Peskin
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Michael Thoss
- Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
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15
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Liu W, Chen ZH, Su Y, Wang Y, Dou W. Predicting rate kernels via dynamic mode decomposition. J Chem Phys 2023; 159:144110. [PMID: 37823462 DOI: 10.1063/5.0170512] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Accepted: 09/25/2023] [Indexed: 10/13/2023] Open
Abstract
Simulating dynamics of open quantum systems is sometimes a significant challenge, despite the availability of various exact or approximate methods. Particularly when dealing with complex systems, the huge computational cost will largely limit the applicability of these methods. In this work, we investigate the usage of dynamic mode decomposition (DMD) to evaluate the rate kernels in quantum rate processes. DMD is a data-driven model reduction technique that characterizes the rate kernels using snapshots collected from a small time window, allowing us to predict the long-term behaviors with only a limited number of samples. Our investigations show that whether the external field is involved or not, the DMD can give accurate prediction of the result compared with the traditional propagations, and simultaneously reduce the required computational cost.
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Affiliation(s)
- Wei Liu
- Department of Chemistry, School of Science, Westlake University, Hangzhou 310024 Zhejiang, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024 Zhejiang, China
| | - Zi-Hao Chen
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yu Su
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Wenjie Dou
- Department of Chemistry, School of Science, Westlake University, Hangzhou 310024 Zhejiang, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024 Zhejiang, China
- Department of Physics, School of Science, Westlake University, Hangzhou 310024, Zhejiang, China
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16
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Dan X, Shi Q. Theoretical study of nonadiabatic hydrogen atom scattering dynamics on metal surfaces using the hierarchical equations of motion method. J Chem Phys 2023; 159:044101. [PMID: 37486050 DOI: 10.1063/5.0155172] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2023] [Accepted: 06/30/2023] [Indexed: 07/25/2023] Open
Abstract
Hydrogen atom scattering on metal surfaces is investigated based on a simplified Newns-Anderson model. Both the nuclear and electronic degrees of freedom are treated quantum mechanically. By partitioning all the surface electronic states as the bath, the hierarchical equations of motion method for the fermionic bath is employed to simulate the scattering dynamics. It is found that, with a reasonable set of parameters, the main features of the recent experimental studies of hydrogen atom scattering on metal surfaces can be reproduced. Vibrational states on the chemisorption state whose energies are close to the incident energy are found to play an important role, and the scattering process is dominated by a single-pass electronic transition forth and back between the diabatic physisorption and chemisorption states. Further study on the effects of the atom-surface coupling strength reveals that, upon increasing the atom-surface coupling strength, the scattering mechanism changes from typical nonadiabatic transitions to dynamics in the electronic friction regime.
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Affiliation(s)
- Xiaohan Dan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, 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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17
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Wang Y, Dou W. Nonadiabatic dynamics near metal surface with periodic drivings: A Floquet surface hopping algorithm. J Chem Phys 2023; 158:2895265. [PMID: 37290089 DOI: 10.1063/5.0148418] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2023] [Accepted: 05/23/2023] [Indexed: 06/10/2023] Open
Abstract
We develop a Floquet surface hopping approach to deal with nonadiabatic dynamics of molecules near metal surfaces subjected to time-periodic drivings from strong light-matter interactions. The method is based on a Floquet classical master equation (FCME) derived from a Floquet quantum master equation (FQME), followed by a Wigner transformation to treat nuclear motion classically. We then propose different trajectory surface hopping algorithms to solve the FCME. We find that a Floquet averaged surface hopping with electron density (FaSH-density) algorithm works the best as benchmarked with the FQME, capturing both the fast oscillations due to the driving and the correct steady-state observables. This method will be very useful to study strong light-matter interactions with a manifold of electronic states.
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Affiliation(s)
- Yu Wang
- Department of Chemistry, School of Science, Westlake University, Hangzhou 310024, Zhejiang, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024, Zhejiang, China
| | - Wenjie Dou
- Department of Chemistry, School of Science, Westlake University, Hangzhou 310024, Zhejiang, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024, Zhejiang, China
- Department of Physics, School of Science, Westlake University, Hangzhou 310024, Zhejiang, China
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18
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Erpenbeck A, Gull E, Cohen G. Quantum Monte Carlo Method in the Steady State. PHYSICAL REVIEW LETTERS 2023; 130:186301. [PMID: 37204908 DOI: 10.1103/physrevlett.130.186301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Revised: 12/07/2022] [Accepted: 04/07/2023] [Indexed: 05/21/2023]
Abstract
We present a numerically exact steady-state inchworm Monte Carlo method for nonequilibrium quantum impurity models. Rather than propagating an initial state to long times, the method is directly formulated in the steady state. This eliminates any need to traverse the transient dynamics and grants access to a much larger range of parameter regimes at vastly reduced computational costs. We benchmark the method on equilibrium Green's functions of quantum dots in the noninteracting limit and in the unitary limit of the Kondo regime. We then consider correlated materials described with dynamical mean field theory and driven away from equilibrium by a bias voltage. We show that the response of a correlated material to a bias voltage differs qualitatively from the splitting of the Kondo resonance observed in bias-driven quantum dots.
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Affiliation(s)
- A Erpenbeck
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - E Gull
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - G Cohen
- The Raymond and Beverley Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
- School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
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19
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Lyu N, Mulvihill E, Soley MB, Geva E, Batista VS. Tensor-Train Thermo-Field Memory Kernels for Generalized Quantum Master Equations. J Chem Theory Comput 2023; 19:1111-1129. [PMID: 36719350 DOI: 10.1021/acs.jctc.2c00892] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
The generalized quantum master equation (GQME) approach provides a rigorous framework for deriving the exact equation of motion for any subset of electronic reduced density matrix elements (e.g., the diagonal elements). In the context of electronic dynamics, the memory kernel and inhomogeneous term of the GQME introduce the implicit coupling to nuclear motion and dynamics of electronic density matrix elements that are projected out (e.g., the off-diagonal elements), allowing for efficient quantum dynamics simulations. Here, we focus on benchmark quantum simulations of electronic dynamics in a spin-boson model system described by various types of GQMEs. Exact memory kernels and inhomogeneous terms are obtained from short-time quantum-mechanically exact tensor-train thermo-field dynamics (TT-TFD) simulations and are compared with those obtained from an approximate linearized semiclassical method, allowing for assessment of the accuracy of these approximate memory kernels and inhomogeneous terms. Moreover, we have analyzed the computational cost of the full and reduced-dimensionality GQMEs. The scaling of the computational cost is dependent on several factors, sometimes with opposite scaling trends. The TT-TFD memory kernels can provide insights on the main sources of inaccuracies of GQME approaches when combined with approximate input methods and pave the road for the development of quantum circuits that implement GQMEs on digital quantum computers.
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Affiliation(s)
- Ningyi Lyu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Ellen Mulvihill
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Micheline B Soley
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States.,Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States.,Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States.,Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
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20
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Chen ZH, Wang Y, Xu RX, Yan Y. Open quantum systems with nonlinear environmental backactions: Extended dissipaton theory vs core-system hierarchy construction. J Chem Phys 2023; 158:074102. [PMID: 36813728 DOI: 10.1063/5.0134700] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
In this paper, we present a comprehensive account of quantum dissipation theories with the quadratic environment couplings. The theoretical development includes the Brownian solvation mode embedded hierarchical quantum master equations, a core-system hierarchy construction that verifies the extended dissipaton equation of motion (DEOM) formalism [R. X. Xu et al., J. Chem. Phys. 148, 114103 (2018)]. Developed are also the quadratic imaginary-time DEOM for equilibrium and the λ(t)-DEOM for nonequilibrium thermodynamics problems. Both the celebrated Jarzynski equality and Crooks relation are accurately reproduced, which, in turn, confirms the rigorousness of the extended DEOM theories. While the extended DEOM is more numerically efficient, the core-system hierarchy quantum master equation is favorable for "visualizing" the correlated solvation dynamics.
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Affiliation(s)
- Zi-Hao Chen
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rui-Xue Xu
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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21
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Zhang D, Zuo L, Ye L, Chen ZH, Wang Y, Xu RX, Zheng X, Yan Y. Hierarchical equations of motion approach for accurate characterization of spin excitations in quantum impurity systems. J Chem Phys 2023; 158:014106. [PMID: 36610957 DOI: 10.1063/5.0131739] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Recent technological advancement in scanning tunneling microscopes has enabled the measurement of spin-field and spin-spin interactions in single atomic or molecular junctions with an unprecedentedly high resolution. Theoretically, although the fermionic hierarchical equations of motion (HEOM) method has been widely applied to investigate the strongly correlated Kondo states in these junctions, the existence of low-energy spin excitations presents new challenges to numerical simulations. These include the quest for a more accurate and efficient decomposition for the non-Markovian memory of low-temperature environments and a more careful handling of errors caused by the truncation of the hierarchy. In this work, we propose several new algorithms, which significantly enhance the performance of the HEOM method, as exemplified by the calculations on systems involving various types of low-energy spin excitations. Being able to characterize both the Kondo effect and spin excitation accurately, the HEOM method offers a sophisticated and versatile theoretical tool, which is valuable for the understanding and even prediction of the fascinating quantum phenomena explored in cutting-edge experiments.
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Affiliation(s)
- Daochi Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lijun Zuo
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lyuzhou Ye
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zi-Hao Chen
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rui-Xue Xu
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao Zheng
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Hefei National Research Center for Physical Sciences at the Microscale and iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
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22
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Sindhu A, Jain A. Coherence and Efficient Energy Transfer in Molecular Wires: Insights from Surface Hopping Simulations. Chemphyschem 2022; 23:e202200392. [PMID: 35944188 DOI: 10.1002/cphc.202200392] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2022] [Revised: 08/09/2022] [Indexed: 01/04/2023]
Abstract
Understanding the dynamics of electronic energy transfer through a molecular wire is essential to understand the working of natural processes like photosynthesis. We investigate simpler 2 and 3-site model Hamiltonians in this work to understand the importance of coherence to efficient energy transfer. We compare the results of surface hopping simulation with that of numerically exact results and rate theories. Different parameters are analyzed, motivated by a photosynthetic molecular wire - the FMO complex. A comparison of results from different theories shows that coherence can play an important role towards efficient energy transfer for certain parameters. When these coherences are important, even small couplings (of the order of 5 cm-1 ) in the Hamiltonian can significantly affect rates. Surface hopping simulations capture all the results correctly qualitatively. Rate theories, on the other hand, can differ significantly from numerically exact results when coherences become important. The results of this work should provide design guidelines for efficient energy transfer in molecular wires.
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23
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Zuo L, Zhuang Q, Ye L, Yan Y, Zheng X. Unveiling the Decisive Factor for the Sharp Transition in the Scanning Tunneling Spectroscopy of a Single Nickelocene Molecule. J Phys Chem Lett 2022; 13:11262-11270. [PMID: 36448930 DOI: 10.1021/acs.jpclett.2c03168] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Scanning tunneling microscopy (STM) has been utilized to realize the precise measurement and control of local spin states. Experiments have demonstrated that when a nickelocene (Nc) molecule is attached to the apex of an STM tip, the dI/dV spectra exhibit a sharp or a smooth transition when the tip is displaced toward the substrate. However, what leads to the two distinct types of transitions remains unclear, and more intriguingly, the physical origin of the abrupt change in the line shape of dI/dV spectra remains unclear. To clarify these intriguing issues, we perform first-principles-based simulations on the STM tip control process for the Cu tip/Nc/Cu(100) junction. In particular, we find that the suddenly enhanced hybridization between the d orbitals on the Ni ion and the metallic bands in the substrate leads to Kondo correlation overwhelming spin excitation, which is the main cause of the sharp transition in the dI/dV spectra observed experimentally.
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Affiliation(s)
- Lijun Zuo
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Qingfeng Zhuang
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lyuzhou Ye
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Hefei National Research Center for Physical Sciences at the Microscale and iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao Zheng
- Department of Chemistry, Fudan University, Shanghai 200433, China
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24
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Xu Y, Jin J, Wang S, Yan Y. Memory-effect-preserving quantum master equation approach to noise spectrum of transport current. Phys Rev E 2022; 106:064130. [PMID: 36671117 DOI: 10.1103/physreve.106.064130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2022] [Accepted: 11/28/2022] [Indexed: 06/17/2023]
Abstract
Within the time-nonlocal quantum master equation description, we develop an efficient method for calculating the noise spectrum of transport current through interacting mesoscopic systems. By introducing proper current-related density operators, we propose a practical and very efficient time-local equation of motion implementation to compute the noise spectrum, which contains the full information of emission and absorption. We obtain an analytical expression to characterize the nonequilibrium transport including Coulomb interaction and memory effect. We demonstrate the proposed method with double quantum dots systems and find good agreement with the exact results, whenever the system-reservoir coupling is smaller than the temperature.
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Affiliation(s)
- Yishan Xu
- School of Physics, Hangzhou Normal University, Hangzhou, Zhejiang 311121, China
| | - Jinshuang Jin
- School of Physics, Hangzhou Normal University, Hangzhou, Zhejiang 311121, China
| | - Shikuan Wang
- Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
| | - YiJing Yan
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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25
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Tong K, Dou W. Numerical study of non-adiabatic quantum thermodynamics of the driven resonant level model: non-equilibrium entropy production and higher order corrections. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:495703. [PMID: 36223783 DOI: 10.1088/1361-648x/ac99c8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2022] [Accepted: 10/12/2022] [Indexed: 06/16/2023]
Abstract
We present our numerical study on quantum thermodynamics of the resonant level model subjected to non-equilibrium condition as well as external driving. Following our previous work on non-equilibrium quantum thermodynamics (Douet al2020Phys. Rev.B101184304), we expand the density operator into a series of power in the driving speed, where we can determine the non-adiabatic thermodynamic quantities. Particularly, we calculate the non-equilibrium entropy production rate as well as higher order non-adiabatic corrections to the energy and/or population, which is not determined previously in Douet al(2020Phys. Rev.B101184304). In the limit of weak system-bath coupling, our results reduce to the one from the quantum master equation.
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Affiliation(s)
- Kaiyi Tong
- School of Science, Westlake University, Hangzhou, Zhejiang 310024, People's Republic of China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, People's Republic of China
| | - Wenjie Dou
- School of Science, Westlake University, Hangzhou, Zhejiang 310024, People's Republic of China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, People's Republic of China
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26
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Mitrić P, Janković V, Vukmirović N, Tanasković D. Spectral Functions of the Holstein Polaron: Exact and Approximate Solutions. PHYSICAL REVIEW LETTERS 2022; 129:096401. [PMID: 36083668 DOI: 10.1103/physrevlett.129.096401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2022] [Revised: 05/02/2022] [Accepted: 08/05/2022] [Indexed: 06/15/2023]
Abstract
It is generally accepted that the dynamical mean field theory gives a good solution of the Holstein model, but only in dimensions greater than two. Here, we show that this theory, which becomes exact in the weak coupling and in the atomic limit, provides an excellent, numerically cheap, approximate solution for the spectral function of the Holstein model in the whole range of parameters, even in one dimension. To establish this, we make a detailed comparison with the spectral functions that we obtain using the newly developed momentum-space numerically exact hierarchical equations of motion method, which yields electronic correlation functions directly in real time. We crosscheck these conclusions with our path integral quantum Monte Carlo and exact diagonalization results, as well as with the available numerically exact results from the literature.
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Affiliation(s)
- Petar Mitrić
- Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
| | - Veljko Janković
- Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
| | - Nenad Vukmirović
- Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
| | - Darko Tanasković
- Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
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27
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Su Y, Chen ZH, Zhu H, Wang Y, Han L, Xu RX, Yan Y. Electron Transfer under the Floquet Modulation in Donor-Bridge-Acceptor Systems. J Phys Chem A 2022; 126:4554-4561. [PMID: 35786902 DOI: 10.1021/acs.jpca.2c03308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Electron transfer (ET) processes are of broad interest in modern chemistry. With the advancements of experimental techniques, one may modulate the ET via such events as light-matter interactions. In this work, we study the ET under a Floquet modulation occurring in the donor-bridge-acceptor systems, with the rate kernels projected out from the exact dissipaton equation of motion formalism. This together with the Floquet theorem enables us to investigate the interplay between the intrinsic non-Markovianity and the driving periodicity. The observed rate kernel exhibits a Herzberg-Teller-like mechanism induced by the bridge fluctuation subject to effective modulation.
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Affiliation(s)
- Yu Su
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zi-Hao Chen
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Haojie Zhu
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lu Han
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rui-Xue Xu
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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28
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Wang Y, Chen ZH, Xu RX, Zheng X, Yan Y. A statistical quasi-particles thermofield theory with Gaussian environments: System-bath entanglement theorem for nonequilibrium correlation functions. J Chem Phys 2022; 157:044102. [DOI: 10.1063/5.0094875] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
For open quantum systems, environmental dissipative effect can be represented by statistical quasi-particles, namely dissipatons. We exploit this fact to establish the dissipaton thermofield theory. The resulting generalized Langevin dynamics of absorptive and emissive thermofield operators are effectively noise-resolved. The system-bath entanglement theorem is then readily followed between a important class of nonequilibrium steady-state correlation functions. All these relations are validated numerically. A simple corollary is the transport current expression, which exactly recovers the result obtained from the nonequilibrium Green's function formalism.
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Affiliation(s)
- Yao Wang
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, China
| | - Zi-Hao Chen
- University of Science and Technology of China, China
| | - Rui-Xue Xu
- University of Science and Technology of China, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, China
| | - YiJing Yan
- Department of Chemical Physics, USTC, China
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29
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Ke Y, Kaspar C, Erpenbeck A, Peskin U, Thoss M. Nonequilibrium reaction rate theory: Formulation and implementation within the hierarchical equations of motion approach. J Chem Phys 2022; 157:034103. [DOI: 10.1063/5.0098545] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The study of chemical reactions in environments under nonequilibrium conditions has been of interest recently in a variety of contexts, including current-induced reactions in molecular junctions and scanning tunneling microscopy experiments. In this work, we outline a fully quantum mechanical, numerically exact approach to describe chemical reaction rates in such nonequilibrium situations. The approach is based on an extension of the flux correlation function formalism to nonequilibrium conditions and uses a mixed real and imaginary time hierarchical equations of motion approach for the calculation of rate constants. As a specific example, we investigate current-induced intramolecular proton transfer reactions in a molecular junction for different applied bias voltages and molecule-lead coupling strengths.
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Affiliation(s)
- Yaling Ke
- Institute of Physics, Albert-Ludwigs-Universität Freiburg, Germany
| | | | | | - Uri Peskin
- Chemistry, Technion Israel Institute of Technology, Israel
| | - Michael Thoss
- University of Freiburg Institute of Physics, Germany
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30
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Chen ZH, Wang Y, Zheng X, Xu RX, Yan Y. Universal time-domain Prony fitting decomposition for optimized hierarchical quantum master equations. J Chem Phys 2022; 156:221102. [DOI: 10.1063/5.0095961] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, we propose the time-domain Prony fitting decomposition (t-PFD) as an accurate and effcient exponential series method, applicable to arbitrary bath correlation functions. The resulting numerical effciency of hierarchical equations of motion (HEOM) formalism is greatly optimized, especially in low temperature regimes that would be inaccessible with other methods. For demonstration, we calibrate the present t-PFD against the celebrated Padé spectrum decomposition (PSD) method, followed by converged HEOM evaluations on the single-impurity Anderson model system.
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Affiliation(s)
- Zi-Hao Chen
- University of Science and Technology of China, China
| | - Yao Wang
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, China
| | - Rui-Xue Xu
- University of Science and Technology of China, China
| | - YiJing Yan
- Department of Chemical Physics, USTC, China
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31
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Ke Y, Borrelli R, Thoss M. Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space. J Chem Phys 2022; 156:194102. [DOI: 10.1063/5.0088947] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We extend the twin-space formulation of the hierarchical equations of motion approach in combination with the matrix product state representation (introduced in J. Chem. Phys. 150, 234102, [2019]) to nonequilibrium scenarios where the open quantum system is coupled to a hybrid fermionic and bosonic environment. The key ideas used in the extension are a reformulation of the hierarchical equations of motion for the auxiliary density matrices into a time-dependent Schrödinger-like equation for an augmented multi-dimensional wave function as well as a tensor decomposition into a product of low-rank matrices. The new approach facilitates accurate simulations of non-equilibrium quantum dynamics in larger and more complex open quantum systems. The performance of the method is demonstrated for a model of a molecular junction exhibiting current-induced mode-selective vibrational excitation.
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Affiliation(s)
- Yaling Ke
- Institute of Physics, Albert-Ludwigs-Universität Freiburg, Germany
| | - Raffaele Borrelli
- Department of Agricoltural Science, Università degli Studi di Torino, Italy
| | - Michael Thoss
- University of Freiburg Institute of Physics, Germany
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32
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Li Z, Cheng Y, Zheng X, Wei J, Yan Y, Luo HG. Study the mixed valence problem in asymmetric Anderson model: Fano-Kondo resonance around Fermi level. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:255601. [PMID: 35378517 DOI: 10.1088/1361-648x/ac640a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2021] [Accepted: 04/04/2022] [Indexed: 06/14/2023]
Abstract
We numerically calculate the local density of states (LDOS) in asymmetric Anderson model in mixed valence regime using hierarchical equations of motion approach. Based on the idea that the asymmetric line shape of LDOS around Fermi level stems from the interference between the single particle resonance and the Kondo resonance, we perform a fitting. From the fitting results, we obtain the Kondo temperatures and the Fano factors with changing the single particle energy. The tendency of Kondo temperature agrees with the previous analytic expressions and the Fano factors are in an expected variation of Fano resonance. Our study shows that the Fano-Kondo resonance can reasonably explain the asymmetric line shape of the LDOS around the Fermi level.
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Affiliation(s)
- ZhenHua Li
- School of Physical Science and Technology & Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, People's Republic of China
- Beijing Computational Science Research Center, Beijing 100193, People's Republic of China
| | - YongXi Cheng
- Beijing Computational Science Research Center, Beijing 100193, People's Republic of China
- Department of Science, Taiyuan Institute of Technology, Taiyuan 030008, People's Republic of China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics & CAS Center for Excellence in Nanoscience, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - JianHua Wei
- Department of Physics, Renmin University of China, Beijing 100872, People's Republic of China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Hong-Gang Luo
- School of Physical Science and Technology & Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, People's Republic of China
- Beijing Computational Science Research Center, Beijing 100193, People's Republic of China
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33
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Dan X, Xu M, Yan Y, Shi Q. Generalized master equation for charge transport in a molecular junction: Exact memory kernels and their high order expansion. J Chem Phys 2022; 156:134114. [PMID: 35395901 DOI: 10.1063/5.0086663] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
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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Affiliation(s)
- 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
| | - 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
| | - 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
| | - Qiang Shi
- 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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34
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Mulvihill E, Geva E. Simulating the dynamics of electronic observables via reduced-dimensionality generalized quantum master equations. J Chem Phys 2022; 156:044119. [DOI: 10.1063/5.0078040] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Affiliation(s)
- Ellen Mulvihill
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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35
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Li T, Yan Y, Shi Q. A low-temperature quantum Fokker-Planck equation that improvesthe numerical stability of the hierarchical equations of motion for the Brownian oscillator spectral density. J Chem Phys 2022; 156:064107. [DOI: 10.1063/5.0082108] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Tianchu Li
- Institute of Chemistry Chinese Academy of Sciences, China
| | | | - Qiang Shi
- State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry Chinese Academy of Sciences, China
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36
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Computational Characterization of Nanosystems. CHINESE J CHEM PHYS 2022. [DOI: 10.1063/1674-0068/cjcp2111233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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37
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Zhang D, Ding X, Zhang HD, Zheng X, Yan Y. Adiabatic terminator for fermionic hierarchical equations of motion. CHINESE J CHEM PHYS 2021. [DOI: 10.1063/1674-0068/cjcp2110212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Affiliation(s)
- Daochi Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics & CAS Center for Excellence in Nanoscience, University of Science and Technology of China, Hefei 230026, China
| | - Xu Ding
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics & CAS Center for Excellence in Nanoscience, University of Science and Technology of China, Hefei 230026, China
| | - Hou-Dao Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics & CAS Center for Excellence in Nanoscience, University of Science and Technology of China, Hefei 230026, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics & CAS Center for Excellence in Nanoscience, University of Science and Technology of China, Hefei 230026, China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale & iChEM, University of Science and Technology of China, Hefei 230026, China
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38
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Medvedev IG. Classical master equations and broadened classical master equations: Some analytical results. J Chem Phys 2021; 155:114116. [PMID: 34551549 DOI: 10.1063/5.0064325] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Some analytical results for the steady-state properties of the single-molecule tunneling junction are obtained with the use of the broadened classical master equations and classical master equations. The case of the one electronic level of the bridge molecule coupled to a single classical harmonic oscillator is considered within the spin-less model. Based on these equations, we establish some relations between different average values of interest, considering the large bias limit and the limit of the weak electron-oscillator coupling. We derive the analytical expressions for a number of characteristic properties of the tunneling junction in these limiting cases, compare our results with those obtained by the numerically exact calculations, and find that our expressions work very well. In the diabatic regime, the approximate solutions of the classical master equations are suggested, which permit us to introduce the effective temperature Teff and perform rather simple calculations of the average vibrational excitations N and the tunnel current I. It is shown that in the adiabatic regime, the properties of the tunneling junction depend essentially on the effective temperature Teff ad. We obtain the analytical expressions for Teff ad using different approaches for the treatment of the adiabatic regime. For both the diabatic and adiabatic regimes, we calculate Teff, Teff ad, N, and I, compare our results with those available in the literature, and confirm well agreement. The dependence of N and I on the reorganization energy and the position of the electronic level of the bridge molecule is discussed.
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Affiliation(s)
- Igor G Medvedev
- A. N. Frumkin Institute of Physical Chemistry and Electrochemistry of Russian Academy of Sciences, Leninsky Prospect 31, 119071 Moscow, Russian Federation
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39
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Mulvihill E, Geva E. A Road Map to Various Pathways for Calculating the Memory Kernel of the Generalized Quantum Master Equation. J Phys Chem B 2021; 125:9834-9852. [PMID: 34424700 DOI: 10.1021/acs.jpcb.1c05719] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The generalized quantum master equation (GQME) provides a powerful framework for simulating electronic energy, charge, and coherence transfer dynamics in molecular systems. Within this framework, the effect of the nuclear degrees of freedom on the time evolution of the electronic reduced density matrix is fully captured by a memory kernel superoperator. However, the actual memory kernel depends on the choice of projection operator and is therefore not unique. Furthermore, calculating the memory kernel can be done in multiple ways that use different forms of projection-free inputs. Although the electronic dynamics is invariant to those choices when quantum-mechanically exact projection-free inputs are used, this is not the case when they are obtained via more feasible semiclassical or mixed quantum-classical approximate methods. Furthermore, the accuracy and numerical stability of the resulting electronic dynamics has been observed to be sensitive to the above-mentioned choices when approximate methods are used to calculate the projection-free inputs. In this article, we provide a systematic road map to 30 possible pathways for calculating the memory kernel and highlight how they are related as well as the ways in which they differ. We also compare the performance of different pathways in the context of the spin-boson benchmark model, with the projection-free inputs obtained via a mapping Hamiltonian linearized semiclassical method. In this case, we find that expressing the memory kernel with an exponential operator where the projection operator precedes the Liouvillian yields the most accurate and most numerically stable results.
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Affiliation(s)
- Ellen Mulvihill
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan48109, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan48109, United States
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40
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Mao H, Jin J, Wang S, Yan Y. Nonequilibrium Kondo regime current noise spectrum of quantum dot systems with the single impurity Anderson model. J Chem Phys 2021; 155:014104. [PMID: 34241380 DOI: 10.1063/5.0045346] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the nonequilibrium current noise spectrum of single impurity Anderson model quantum dot systems on the basis of the accurate dissipation equation of motion evaluations. By comparing between the equilibrium and nonequilibrium cases and between the non-Kondo and Kondo regimes, we identify the current noise spectrum of the nonequilibrium Kondo features that actually appear in the entire region of ω ∈ [-eV, eV]. It is well known that the primary Kondo characteristics at ω = ±eV = ±(μL - μR) display asymmetrical upturns and remarkable peaks in S(ω) and dS(ω)/dω, respectively. These features are originated from the Rabi interference of the transport current dynamics, with the Kondo oscillation frequency of |eV|. Moreover, we also identify the minor but very distinguishable inflections, crossing over from ω = -eV to ω = +eV. This uncovered feature would be related to the interference between two Kondo resonance channels.
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Affiliation(s)
- Hong Mao
- Department of Physics, Hangzhou Normal University, Hangzhou, Zhejiang 311121, China
| | - Jinshuang Jin
- Department of Physics, Hangzhou Normal University, Hangzhou, Zhejiang 311121, China
| | - Shikuan Wang
- Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale & i ChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
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41
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Chen ZH, Wang Y, Xu RX, Yan Y. Correlated vibration-solvent effects on the non-Condon exciton spectroscopy. J Chem Phys 2021; 154:244105. [PMID: 34241336 DOI: 10.1063/5.0053169] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Excitation energy transfer is crucially involved in a variety of systems. During the process, the non-Condon vibronic coupling and the surrounding solvent interaction may synergetically play important roles. In this work, we study the correlated vibration-solvent influences on the non-Condon exciton spectroscopy. Statistical analysis is elaborated for the overall vibration-plus-solvent environmental effects. Analytic solutions are derived for the linear absorption of monomer systems. General simulations are accurately carried out via the dissipaton-equation-of-motion approach. The resulted spectra in either the linear absorption or strong field regime clearly demonstrate the coherence enhancement due to the synergetic vibration-solvent correlation.
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Affiliation(s)
- Zi-Hao Chen
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and iChEM and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rui-Xue Xu
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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42
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Ke Y, Erpenbeck A, Peskin U, Thoss M. Unraveling current-induced dissociation mechanisms in single-molecule junctions. J Chem Phys 2021; 154:234702. [PMID: 34241274 DOI: 10.1063/5.0053828] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Understanding current-induced bond rupture in single-molecule junctions is both of fundamental interest and a prerequisite for the design of molecular junctions, which are stable at higher-bias voltages. In this work, we use a fully quantum mechanical method based on the hierarchical quantum master equation approach to analyze the dissociation mechanisms in molecular junctions. Considering a wide range of transport regimes, from off-resonant to resonant, non-adiabatic to adiabatic transport, and weak to strong vibronic coupling, our systematic study identifies three dissociation mechanisms. In the weak and intermediate vibronic coupling regime, the dominant dissociation mechanism is stepwise vibrational ladder climbing. For strong vibronic coupling, dissociation is induced via multi-quantum vibrational excitations triggered either by a single electronic transition at high bias voltages or by multiple electronic transitions at low biases. Furthermore, the influence of vibrational relaxation on the dissociation dynamics is analyzed and strategies for improving the stability of molecular junctions are discussed.
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Affiliation(s)
- Yaling Ke
- Institute of Physics, Albert-Ludwig University Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - André Erpenbeck
- School of Chemistry, The Raymond and Beverley Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Uri Peskin
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Michael Thoss
- Institute of Physics, Albert-Ludwig University Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
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43
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Kaspar C, Thoss M. Efficient Steady-State Solver for the Hierarchical Equations of Motion Approach: Formulation and Application to Charge Transport through Nanosystems. J Phys Chem A 2021; 125:5190-5200. [PMID: 34102055 DOI: 10.1021/acs.jpca.1c02863] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
An iterative approach is introduced, which allows the efficient solution of the hierarchical equations of motion (HEOM) for the steady-state of open quantum systems. The approach combines the method of matrix equations with an efficient preconditioning technique to reduce the numerical effort of solving the HEOM. Illustrative applications to simulate nonequilibrium charge transport in single-molecule junctions demonstrate the performance of the method.
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Affiliation(s)
- C Kaspar
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany
| | - M Thoss
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany.,EUCOR Centre for Quantum Science and Quantum Computing, University of Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany
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44
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Mulvihill E, Lenn KM, Gao X, Schubert A, Dunietz BD, Geva E. Simulating energy transfer dynamics in the Fenna-Matthews-Olson complex via the modified generalized quantum master equation. J Chem Phys 2021; 154:204109. [PMID: 34241158 DOI: 10.1063/5.0051101] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The generalized quantum master equation (GQME) provides a general and formally exact framework for simulating the reduced dynamics of open quantum systems. The recently introduced modified approach to the GQME (M-GQME) corresponds to a specific implementation of the GQME that is geared toward simulating the dynamics of the electronic reduced density matrix in systems governed by an excitonic Hamiltonian. Such a Hamiltonian, which is often used for describing energy and charge transfer dynamics in complex molecular systems, is given in terms of diabatic electronic states that are coupled to each other and correspond to different nuclear Hamiltonians. Within the M-GQME approach, the effect of the nuclear degrees of freedom on the time evolution of the electronic density matrix is fully captured by a memory kernel superoperator, which can be obtained from short-lived (compared to the time scale of energy/charge transfer) projection-free inputs. In this paper, we test the ability of the M-GQME to predict the energy transfer dynamics within a seven-state benchmark model of the Fenna-Matthews-Olson (FMO) complex, with the short-lived projection-free inputs obtained via the Ehrenfest method. The M-GQME with Ehrenfest-based inputs is shown to yield accurate results across a wide parameter range. It is also found to dramatically outperform the direct application of the Ehrenfest method and to provide better-behaved convergence with respect to memory time in comparison to an alternative implementation of the GQME approach previously applied to the same FMO model.
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Affiliation(s)
- Ellen Mulvihill
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Kristina M Lenn
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Xing Gao
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Alexander Schubert
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Barry D Dunietz
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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45
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Yan Y, Xu M, Li T, Shi Q. Efficient propagation of the hierarchical equations of motion using the Tucker and hierarchical Tucker tensors. J Chem Phys 2021; 154:194104. [PMID: 34240893 DOI: 10.1063/5.0050720] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We develop new methods to efficiently propagate the hierarchical equations of motion (HEOM) by using the Tucker and hierarchical Tucker (HT) tensors to represent the reduced density operator and auxiliary density operators. We first show that by employing the split operator method, the specific structure of the HEOM allows a simple propagation scheme using the Tucker tensor. When the number of effective modes in the HEOM increases and the Tucker representation becomes intractable, the split operator method is extended to the binary tree structure of the HT representation. It is found that to update the binary tree nodes related to a specific effective mode, we only need to propagate a short matrix product state constructed from these nodes. Numerical results show that by further employing the mode combination technique commonly used in the multi-configuration time-dependent Hartree approaches, the binary tree representation can be applied to study excitation energy transfer dynamics in a fairly large system including over 104 effective modes. The new methods may thus provide a promising tool in simulating quantum dynamics in condensed phases.
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Affiliation(s)
- Yaming Yan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
| | - Meng Xu
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
| | - Tianchu Li
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
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46
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Brian D, Liu Z, Dunietz BD, Geva E, Sun X. Three-state harmonic models for photoinduced charge transfer. J Chem Phys 2021; 154:174105. [PMID: 34241055 DOI: 10.1063/5.0050289] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
A widely used strategy for simulating the charge transfer between donor and acceptor electronic states in an all-atom anharmonic condensed-phase system is based on invoking linear response theory to describe the system in terms of an effective spin-boson model Hamiltonian. Extending this strategy to photoinduced charge transfer processes requires also taking into consideration the ground electronic state in addition to the excited donor and acceptor electronic states. In this paper, we revisit the problem of describing such nonequilibrium processes in terms of an effective three-state harmonic model. We do so within the framework of nonequilibrium Fermi's golden rule (NE-FGR) in the context of photoinduced charge transfer in the carotenoid-porphyrin-C60 (CPC60) molecular triad dissolved in explicit tetrahydrofuran (THF). To this end, we consider different ways for obtaining a three-state harmonic model from the equilibrium autocorrelation functions of the donor-acceptor, donor-ground, and acceptor-ground energy gaps, as obtained from all-atom molecular dynamics simulations of the CPC60/THF system. The quantum-mechanically exact time-dependent NE-FGR rate coefficients for two different charge transfer processes in two different triad conformations are then calculated using the effective three-state model Hamiltonians as well as a hierarchy of more approximate expressions that lead to the instantaneous Marcus theory limit. Our results show that the photoinduced charge transfer in CPC60/THF can be described accurately by the effective harmonic three-state models and that nuclear quantum effects are small in this system.
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Affiliation(s)
- Dominikus Brian
- Division of Arts and Sciences, NYU Shanghai, 1555 Century Avenue, Shanghai 200122, China
| | - Zengkui Liu
- Division of Arts and Sciences, NYU Shanghai, 1555 Century Avenue, Shanghai 200122, China
| | - Barry D Dunietz
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Xiang Sun
- Division of Arts and Sciences, NYU Shanghai, 1555 Century Avenue, Shanghai 200122, China
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47
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Wu W, Zhang ZZ. Controllable dynamics of a dissipative two-level system. Sci Rep 2021; 11:7188. [PMID: 33785788 PMCID: PMC8010078 DOI: 10.1038/s41598-021-86553-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2021] [Accepted: 03/12/2021] [Indexed: 11/09/2022] Open
Abstract
We propose a strategy to modulate the decoherence dynamics of a two-level system, which interacts with a dissipative bosonic environment, by introducing an ancillary degree of freedom. It is revealed that the decay rate of the two-level system can be significantly suppressed under suitable steers of the assisted degree of freedom. Our result provides an alternative way to fight against decoherence and realize a controllable quantum dissipative dynamics.
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Affiliation(s)
- Wei Wu
- Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, 730000, Gansu, China.
| | - Ze-Zhou Zhang
- Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, 730000, Gansu, China
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48
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Cheng X, Zhao H, Xie H. Non-equilibrium charge transport in a conjugated polymer. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:135502. [PMID: 33395677 DOI: 10.1088/1361-648x/abd811] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2020] [Accepted: 01/04/2021] [Indexed: 06/12/2023]
Abstract
To address the non-equilibrium transport mechanism in a conjugated polymer, we investigate the dynamics of the lattice deformation and the charge transport in a polymer chain coupled with the reservoirs by the time-dependent non-equilibrium Green's function formulism. We find that the delocalized soliton lattice wave (SLW) forms in the polymer, rather than the well-known localized excitations such as polarons and solitons. The source reservoir drives an electron-like transient dynamic SLW while the drain reservoir drives the hole-like one. These transient SLWs propagate in opposite directions and then merge and relax to a steady SLW. These results are confirmed by our analytical derivation based on the continuum model. When the bias voltages are symmetric (μL= -μR), the dynamic SLW subsides to the stationary soliton lattice (SL). In the energy domain, the sandwich-structured non-full filled SL bands form in the original gap, which can provide the conduction channels. Especially, in the case of the symmetric bias voltages (μL= -μR), the SL band is half-filled. The transmission current is the major part of the total current and the rest minor part is the effective current induced by the charge density waves accompanied by the SLW.
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Affiliation(s)
- Xiao Cheng
- Department of Physics, Chongqing University, Chongqing 401331, People's Republic of China
| | - Hui Zhao
- School of Physical Science and Engineering, Tongji University, 20092, People's Republic of China
| | - Hang Xie
- Department of Physics, Chongqing University, Chongqing 401331, People's Republic of China
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Tanimura Y. Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM). J Chem Phys 2021; 153:020901. [PMID: 32668942 DOI: 10.1063/5.0011599] [Citation(s) in RCA: 163] [Impact Index Per Article: 54.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
An open quantum system refers to a system that is further coupled to a bath system consisting of surrounding radiation fields, atoms, molecules, or proteins. The bath system is typically modeled by an infinite number of harmonic oscillators. This system-bath model can describe the time-irreversible dynamics through which the system evolves toward a thermal equilibrium state at finite temperature. In nuclear magnetic resonance and atomic spectroscopy, dynamics can be studied easily by using simple quantum master equations under the assumption that the system-bath interaction is weak (perturbative approximation) and the bath fluctuations are very fast (Markovian approximation). However, such approximations cannot be applied in chemical physics and biochemical physics problems, where environmental materials are complex and strongly coupled with environments. The hierarchical equations of motion (HEOM) can describe the numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system-bath interactions, which has been verified on the basis of exact analytical solutions (non-Markovian tests) with any desired numerical accuracy. The HEOM theory has been used to treat systems of practical interest, in particular, to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories. This article presents an overview of the HEOM theory, focusing on its theoretical background and applications, to help further the development of the study of open quantum dynamics.
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Affiliation(s)
- Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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Gong H, Wang Y, Zhang HD, Xu RX, Zheng X, Yan Y. Thermodynamic free-energy spectrum theory for open quantum systems. J Chem Phys 2020; 153:214115. [DOI: 10.1063/5.0028429] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Hong Gong
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM) and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM) and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hou-Dao Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM) and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rui-Xue Xu
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM) and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM) and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM) and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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