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Zhong K, Nguyen HL, Do TN, Tan HS, Knoester J, Jansen TLC. Coarse-Grained Approach to Simulate Signatures of Excitation Energy Transfer in Two-Dimensional Electronic Spectroscopy of Large Molecular Systems. J Chem Theory Comput 2024; 20:6111-6124. [PMID: 38996082 PMCID: PMC11270824 DOI: 10.1021/acs.jctc.4c00413] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2024] [Revised: 06/25/2024] [Accepted: 06/27/2024] [Indexed: 07/14/2024]
Abstract
Two-dimensional electronic spectroscopy (2DES) has proven to be a highly effective technique in studying the properties of excited states and the process of excitation energy transfer in complex molecular assemblies, particularly in biological light-harvesting systems. However, the accurate simulation of 2DES for large systems still poses a challenge because of the heavy computational demands it entails. In an effort to overcome this limitation, we devised a coarse-grained 2DES method. This method encompasses the treatment of the entire system by dividing it into distinct weakly coupled segments, which are assumed to communicate predominantly through incoherent exciton transfer. We first demonstrate the efficiency of this method through simulation on a model dimer system, which demonstrates a marked improvement in calculation efficiency, with results that exhibit good concordance with reference spectra calculated with less approximate methods. Additionally, the application of this method to the light-harvesting antenna 2 (LH2) complex of purple bacteria showcases its advantages, accuracy, and limitations. Furthermore, simulating the anisotropy decay in LH2 induced by energy transfer and its comparison with experiments confirm that the method is capable of accurately describing dynamical processes in a biologically relevant system. This method presented lends itself to an extension that accounts for the effect of intrasegment relaxation processes on the 2DES spectra, which for computational efficiency are ignored in the implementation reported here. It is envisioned that the method will be employed in the future to accurately and efficiently calculate 2D spectra of more extensive systems, such as photosynthetic supercomplexes.
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Affiliation(s)
- Kai Zhong
- Zernike
Institute for Advanced Materials, University
of Groningen, Nijenborgh 3, 9747 AG Groningen, The Netherlands
- School
of Chemistry, Chemical Engineering and Biotechnology, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore
| | - Hoang Long Nguyen
- Zernike
Institute for Advanced Materials, University
of Groningen, Nijenborgh 3, 9747 AG Groningen, The Netherlands
- School
of Chemistry, Chemical Engineering and Biotechnology, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore
| | - Thanh Nhut Do
- School
of Chemistry, Chemical Engineering and Biotechnology, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore
| | - Howe-Siang Tan
- School
of Chemistry, Chemical Engineering and Biotechnology, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore
| | - Jasper Knoester
- Zernike
Institute for Advanced Materials, University
of Groningen, Nijenborgh 3, 9747 AG Groningen, The Netherlands
- Faculty
of Science, Leiden University, Einsteinweg 55, 2300 RA Leiden, The Netherlands
| | - Thomas L. C. Jansen
- Zernike
Institute for Advanced Materials, University
of Groningen, Nijenborgh 3, 9747 AG Groningen, The Netherlands
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2
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Zhang S, Chen Y, Shi Q. Simulating the operation of a quantum computer in a dissipative environment. J Chem Phys 2024; 160:054101. [PMID: 38299625 DOI: 10.1063/5.0185263] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Accepted: 01/09/2024] [Indexed: 02/02/2024] Open
Abstract
The operations of current quantum computers are still significantly affected by decoherence caused by interaction with the environment. In this work, we employ the non-perturbative hierarchical equations of motion (HEOM) method to simulate the operation of model quantum computers and reveal the effects of dissipation on the entangled quantum states and on the performance of well-known quantum algorithms. Multi-qubit entangled states in Shor's factorizing algorithm are first generated and propagated using the HEOM. It is found that the failure of factorization is accompanied by a loss of fidelity and mutual information. An important challenge in using the HEOM to simulate quantum computers in a dissipative environment is how to efficiently treat systems with many qubits. We propose a two-dimensional tensor network scheme for this problem and demonstrate its capability by simulating a one-dimensional random circuit model with 21 qubits.
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Affiliation(s)
- Shuocang Zhang
- 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
| | - Yinjia Chen
- 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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3
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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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4
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Zhang J, Tanimura Y. Imaginary-time hierarchical equations of motion for thermodynamic variables. J Chem Phys 2022; 156:174112. [PMID: 35525645 DOI: 10.1063/5.0091468] [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
The partition function (PF) plays a key role in the calculation of quantum thermodynamic properties of a system that interacts with a heat bath. The imaginary-time hierarchical equations of motion (imHEOM) approach was developed to evaluate in a rigorous manner the PF of a system strongly coupled to a non-Markovian bath. In this paper, we present a numerically efficient scheme to evaluate the imHEOM utilizing the β-differentiated imHEOM (BD-imHEOM) that are obtained by differentiating the elements of the imHEOM with respect to the inverse temperature. This approach allows us to evaluate the system, system-bath interaction, and heat-bath parts of the PF efficiently. Moreover, we employ a polyharmonic decomposition method to construct a concise hierarchical structure with better convergence, thus reducing the cost of numerical integrations. We demonstrate the proposed approach by compute thermodynamic quantities of a spin-boson system and a 2 × 2 antiferromagnetic triangular spin lattice system with an Ohmic spectral distribution.
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Affiliation(s)
- Jiaji Zhang
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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5
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Chen L, Bennett DIG, Eisfeld A. Simulation of absorption spectra of molecular aggregates: A hierarchy of stochastic pure state approach. J Chem Phys 2022; 156:124109. [DOI: 10.1063/5.0078435] [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
Simulation of spectroscopic observables for molecular aggregates with strong and structured coupling of electronic excitation to vibrational degrees of freedom is an important but challenging task. The Hierarchy of Pure States (HOPS) provides a formally exact solution based on local, stochastic trajectories. Exploiting the localization of HOPS for the simulation of absorption spectra in large aggregates requires a formulation in terms of normalized trajectories. Here, we provide a normalized dyadic equation where the ket- and bra-states are propagated in different electronic Hilbert spaces. This work opens the door to applying adaptive HOPS methods for the simulation of absorption spectra.
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Affiliation(s)
- Lipeng Chen
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, Dresden, Germany
| | - Doran I. G. Bennett
- Department of Chemistry, Southern Methodist University, P.O. Box 750314, Dallas, Texas 75205, USA
| | - Alexander Eisfeld
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, Dresden, Germany
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6
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Abstract
Numerous linear and non-linear spectroscopic techniques have been developed to elucidate structural and functional information of complex systems ranging from natural systems, such as proteins and light-harvesting systems, to synthetic systems, such as solar cell materials and light-emitting diodes. The obtained experimental data can be challenging to interpret due to the complexity and potential overlapping spectral signatures. Therefore, computational spectroscopy plays a crucial role in the interpretation and understanding of spectral observables of complex systems. Computational modeling of various spectroscopic techniques has seen significant developments in the past decade, when it comes to the systems that can be addressed, the size and complexity of the sample types, the accuracy of the methods, and the spectroscopic techniques that can be addressed. In this Perspective, I will review the computational spectroscopy methods that have been developed and applied for infrared and visible spectroscopies in the condensed phase. I will discuss some of the questions that this has allowed answering. Finally, I will discuss current and future challenges and how these may be addressed.
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Affiliation(s)
- Thomas L C Jansen
- Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
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7
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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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8
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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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9
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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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10
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Sakamoto S, Tanimura Y. Numerically "exact" simulations of entropy production in the fully quantum regime: Boltzmann entropy vs von Neumann entropy. J Chem Phys 2020; 153:234107. [PMID: 33353341 DOI: 10.1063/5.0033664] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a scheme to evaluate thermodynamic variables for a system coupled to a heat bath under a time-dependent external force using the quasi-static Helmholtz energy from the numerically "exact" hierarchical equations of motion (HEOM). We computed the entropy produced by a spin system strongly coupled to a non-Markovian heat bath for various temperatures. We showed that when changes to the external perturbation occurred sufficiently slowly, the system always reached thermal equilibrium. Thus, we calculated the Boltzmann entropy and the von Neumann entropy for an isothermal process, as well as various thermodynamic variables, such as changes in internal energies, heat, and work, for a system in quasi-static equilibrium based on the HEOM. We found that although the characteristic features of the system entropies in the Boltzmann and von Neumann cases as a function of the system-bath coupling strength are similar, those for the total entropy production are completely different. The total entropy production in the Boltzmann case is always positive, whereas that in the von Neumann case becomes negative if we chose a thermal equilibrium state of the total system (an unfactorized thermal equilibrium state) as the initial state. This is because the total entropy production in the von Neumann case does not properly take into account the contribution of the entropy from the system-bath interaction. Thus, the Boltzmann entropy must be used to investigate entropy production in the fully quantum regime. Finally, we examined the applicability of the Jarzynski equality.
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Affiliation(s)
- Souichi Sakamoto
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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11
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Wang YC, Zhao Y. The hierarchical stochastic schrödinger equations: Theory and applications. CHINESE J CHEM PHYS 2020. [DOI: 10.1063/1674-0068/cjcp2009165] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Yu-Chen Wang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
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12
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Duan HG, Jha A, Li X, Tiwari V, Ye H, Nayak PK, Zhu XL, Li Z, Martinez TJ, Thorwart M, Miller RJD. Intermolecular vibrations mediate ultrafast singlet fission. SCIENCE ADVANCES 2020; 6:eabb0052. [PMID: 32948583 PMCID: PMC7500928 DOI: 10.1126/sciadv.abb0052] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2020] [Accepted: 07/31/2020] [Indexed: 05/20/2023]
Abstract
Singlet fission is a spin-allowed exciton multiplication process in organic semiconductors that converts one spin-singlet exciton to two triplet excitons. It offers the potential to enhance solar energy conversion by circumventing the Shockley-Queisser limit on efficiency. We study the primary steps of singlet fission in a pentacene film by using a combination of TG and 2D electronic spectroscopy complemented by quantum chemical and nonadiabatic dynamics calculations. We show that the coherent vibrational dynamics induces the ultrafast transition from the singlet excited electronic state to the triplet-pair state via a degeneracy of potential energy surfaces, i.e., a multidimensional conical intersection. Significant vibronic coupling of the electronic wave packet to a few key intermolecular rocking modes in the low-frequency region connect the excited singlet and triplet-pair states. Along with high-frequency local vibrations acting as tuning modes, they open a new channel for the ultrafast exciton transfer through the resulting conical intersection.
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Affiliation(s)
- Hong-Guang Duan
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
- I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355 Hamburg, Germany
- The Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Ajay Jha
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Xin Li
- Department of Chemistry and PULSE Institute, Stanford University, Stanford, CA 94305, USA
| | - Vandana Tiwari
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
- Department of Chemistry, University of Hamburg, Martin-Luther-King Platz 6, 20146 Hamburg, Germany
| | - Hanyang Ye
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - Pabitra K Nayak
- TIFR Centre for Interdisciplinary Sciences, 36/P, Gopanpally Village, Ranga Reddy District, Hyderabad 500107, India
| | - Xiao-Lei Zhu
- Department of Chemistry and PULSE Institute, Stanford University, Stanford, CA 94305, USA
| | - Zheng Li
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany.
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Todd J Martinez
- Department of Chemistry and PULSE Institute, Stanford University, Stanford, CA 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - Michael Thorwart
- I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355 Hamburg, Germany.
- The Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - R J Dwayne Miller
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany.
- The Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
- Departments of Chemistry and Physics, University of Toronto, 80 St. George Street, Toronto, ON M5S 3H6, Canada
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13
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Yan Y, Liu Y, Xing T, Shi Q. Theoretical study of excitation energy transfer and nonlinear spectroscopy of photosynthetic light‐harvesting complexes using the nonperturbative reduced dynamics method. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2020. [DOI: 10.1002/wcms.1498] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- 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 Beijing China
- University of Chinese Academy of Sciences Beijing China
- Physical Science Laboratory Huairou National Comprehensive Science Center Beijing China
| | - Yanying Liu
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species Institute of Chemistry, Chinese Academy of Sciences Beijing China
- University of Chinese Academy of Sciences Beijing China
- Physical Science Laboratory Huairou National Comprehensive Science Center Beijing China
| | - Tao Xing
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species Institute of Chemistry, Chinese Academy of Sciences Beijing China
- University of Chinese Academy of Sciences Beijing China
- Physical Science Laboratory Huairou National Comprehensive Science Center Beijing 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 Beijing China
- University of Chinese Academy of Sciences Beijing China
- Physical Science Laboratory Huairou National Comprehensive Science Center Beijing China
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14
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Ullah A, Han L, Yan YA, Zheng X, Yan Y, Chernyak V. Stochastic equation of motion approach to fermionic dissipative dynamics. II. Numerical implementation. J Chem Phys 2020; 152:204106. [DOI: 10.1063/1.5142166] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Arif Ullah
- Hefei National Laboratory 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
| | - Lu Han
- Hefei National Laboratory 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
| | - Yun-An Yan
- School of Physics and Optoelectronic Engineering, Ludong University, Shandong 264025, China
| | - Xiao Zheng
- Hefei National Laboratory 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 Laboratory for Physical Sciences at the Microscale and iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Vladimir Chernyak
- Hefei National Laboratory 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
- Department of Chemistry, Wayne State University, 5101 Cass Avenue, Detroit, Michigan 48202, USA
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15
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Han L, Ullah A, Yan YA, Zheng X, Yan Y, Chernyak V. Stochastic equation of motion approach to fermionic dissipative dynamics. I. Formalism. J Chem Phys 2020; 152:204105. [DOI: 10.1063/1.5142164] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Affiliation(s)
- Lu Han
- Hefei National Laboratory 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
| | - Arif Ullah
- Hefei National Laboratory 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
| | - Yun-An Yan
- School of Physics and Optoelectronic Engineering, Ludong University, Shandong 264025, China
| | - Xiao Zheng
- Hefei National Laboratory 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 Laboratory for Physical Sciences at the Microscale & iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Vladimir Chernyak
- Hefei National Laboratory 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
- Department of Chemistry, Wayne State University, 5101 Cass Avenue, Detroit, Michigan 48202, USA
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16
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Li W, Ren J, Shuai Z. Numerical assessment for accuracy and GPU acceleration of TD-DMRG time evolution schemes. J Chem Phys 2020; 152:024127. [PMID: 31941314 DOI: 10.1063/1.5135363] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
The time dependent density matrix renormalization group (TD-DMRG) has become one of the cutting edge methods of quantum dynamics for complex systems. In this paper, we comparatively study the accuracy of three time evolution schemes in the TD-DMRG, the global propagation and compression method with the Runge-Kutta algorithm (P&C-RK), the time dependent variational principle based methods with the matrix unfolding algorithm (TDVP-MU), and with the projector-splitting algorithm (TDVP-PS), by performing benchmarks on the exciton dynamics of the Fenna-Matthews-Olson complex. We show that TDVP-MU and TDVP-PS yield the same result when the time step size is converged and they are more accurate than P&C-RK4, while TDVP-PS tolerates a larger time step size than TDVP-MU. We further adopt the graphical processing units to accelerate the heavy tensor contractions in the TD-DMRG, and it is able to speed up the TDVP-MU and TDVP-PS schemes by up to 73 times.
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Affiliation(s)
- Weitang Li
- MOE Key Laboratory of Organic Optoelectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People's Republic of China
| | - Jiajun Ren
- MOE Key Laboratory of Organic Optoelectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People's Republic of China
| | - Zhigang Shuai
- MOE Key Laboratory of Organic Optoelectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People's Republic of China
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17
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Borrelli R. Density matrix dynamics in twin-formulation: An efficient methodology based on tensor-train representation of reduced equations of motion. J Chem Phys 2019; 150:234102. [PMID: 31228887 DOI: 10.1063/1.5099416] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
The twin-formulation of quantum statistical mechanics is employed to describe a new methodology for the solution of the equations of motion of the reduced density matrix in their hierarchical formulation. It is shown that the introduction of tilde operators and of their algebra in the dual space greatly simplifies the application of numerical techniques for the propagation of the density matrix. The application of tensor-train representation of a vector to solve complex quantum dynamical problems within the framework of the twin-formulation is discussed. Next, applications of the hierarchical equations of motion to a dissipative polaron model are presented showing the validity and accuracy of the new approach.
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18
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Kato A, Tanimura Y. Hierarchical Equations of Motion Approach to Quantum Thermodynamics. ACTA ACUST UNITED AC 2019. [DOI: 10.1007/978-3-319-99046-0_24] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/19/2023]
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19
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Axelrod S, Brumer P. An efficient approach to the quantum dynamics and rates of processes induced by natural incoherent light. J Chem Phys 2018; 149:114104. [PMID: 30243280 DOI: 10.1063/1.5041005] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
In many important cases, the rate of excitation of a system embedded in an environment is significantly smaller than the internal system relaxation rates. An important example is that of light-induced processes under natural conditions, in which the system is excited by weak, incoherent (e.g., solar) radiation. Simulating the dynamics on the time scale of the excitation source can thus be computationally intractable. Here we describe a method for obtaining the dynamics of quantum systems without directly solving the master equation. We present an algorithm for the numerical implementation of this method and, as an example, use it to reconstruct the internal conversion dynamics of pyrazine excited by sunlight. Significantly, this approach also allows us to assess the role of quantum coherence on biological time scales, which is a topic of ongoing interest.
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Affiliation(s)
- Simon Axelrod
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Paul Brumer
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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20
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Magazzù L, Denisov S, Hänggi P. Asymptotic Floquet states of a periodically driven spin-boson system in the nonperturbative coupling regime. Phys Rev E 2018; 98:022111. [PMID: 30253481 DOI: 10.1103/physreve.98.022111] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2018] [Indexed: 06/08/2023]
Abstract
Being an exemplary model of open quantum system, the spin-boson model is widely employed in theoretical and experimental studies. Beyond the weak coupling limit, the spin-boson dynamics can be described by a time-nonlocal generalized master equation with a memory kernel accounting for the dissipative effects induced by the bosonic environment. When the spin is in addition modulated by an external time-periodic electromagnetic field, the interplay between dissipation and forcing provides a spectrum of nontrivial asymptotic states, especially so in the regime of nonlinear response. Here we implement the method for evaluating the dissipative Floquet dynamics of non-Markovian systems introduced in Magazzù et al. [Phys. Rev. A 96, 042103 (2017)2469-992610.1103/PhysRevA.96.042103] to obtain these nonequilibrium asymptotic states.
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Affiliation(s)
- Luca Magazzù
- Institute of Physics, University of Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany
| | - Sergey Denisov
- Institute of Physics, University of Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany
- Department of Applied Mathematics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603950, Russia
- Sumy State University, Rimsky-Korsakov Street 2, 40007 Sumy, Ukraine
| | - Peter Hänggi
- Institute of Physics, University of Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany
- Nanosystems Initiative Munich, Schellingstraße 4, D-80799 München, Germany
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21
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Wang Y, Ke Y, Zhao Y. The hierarchical and perturbative forms of stochastic Schrödinger equations and their applications to carrier dynamics in organic materials. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2018. [DOI: 10.1002/wcms.1375] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- Yu‐Chen Wang
- State Key Laboratory for Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University Xiamen China
| | - Yaling Ke
- State Key Laboratory for Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University Xiamen China
| | - Yi Zhao
- State Key Laboratory for Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University Xiamen China
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22
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Hsieh CY, Cao J. A unified stochastic formulation of dissipative quantum dynamics. II. Beyond linear response of spin baths. J Chem Phys 2018; 148:014104. [PMID: 29306289 DOI: 10.1063/1.5018726] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We use the "generalized hierarchical equation of motion" proposed in Paper I [C.-Y. Hsieh and J. Cao, J. Chem. Phys. 148, 014103 (2018)] to study decoherence in a system coupled to a spin bath. The present methodology allows a systematic incorporation of higher-order anharmonic effects of the bath in dynamical calculations. We investigate the leading order corrections to the linear response approximations for spin bath models. Two kinds of spin-based environments are considered: (1) a bath of spins discretized from a continuous spectral density and (2) a bath of localized nuclear or electron spins. The main difference resides with how the bath frequency and the system-bath coupling parameters are distributed in an environment. When discretized from a continuous spectral density, the system-bath coupling typically scales as ∼1/NB where NB is the number of bath spins. This scaling suppresses the non-Gaussian characteristics of the spin bath and justifies the linear response approximations in the thermodynamic limit. For the nuclear/electron spin bath models, system-bath couplings are directly deduced from spin-spin interactions and do not necessarily obey the 1/NB scaling. It is not always possible to justify the linear response approximations in this case. Furthermore, if the spin-spin Hamiltonian is highly symmetrical, there exist additional constraints that generate highly non-Markovian and persistent dynamics that is beyond the linear response treatments.
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Affiliation(s)
- Chang-Yu Hsieh
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
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23
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Kramer T, Noack M, Reinefeld A, Rodríguez M, Zelinskyy Y. Efficient calculation of open quantum system dynamics and time-resolved spectroscopy with distributed memory HEOM (DM-HEOM). J Comput Chem 2018; 39:1779-1794. [DOI: 10.1002/jcc.25354] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2018] [Revised: 04/20/2018] [Accepted: 04/22/2018] [Indexed: 12/17/2022]
Affiliation(s)
- Tobias Kramer
- Zuse Institute Berlin (ZIB), Takustr. 7; 14195 Berlin Germany
- Department of Physics; Harvard University, 17 Oxford Street; Cambridge Massachusetts 02138
| | - Matthias Noack
- Zuse Institute Berlin (ZIB), Takustr. 7; 14195 Berlin Germany
| | | | - Mirta Rodríguez
- Zuse Institute Berlin (ZIB), Takustr. 7; 14195 Berlin Germany
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24
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Duan C, Wang Q, Tang Z, Wu J. The study of an extended hierarchy equation of motion in the spin-boson model: The cutoff function of the sub-Ohmic spectral density. J Chem Phys 2018; 147:164112. [PMID: 29096483 DOI: 10.1063/1.4997669] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
Following a recently proposed decomposition technique [C. R. Duan et al., Phys. Rev. B 95, 214308 (2017)], we inspect the zero-temperature spin-boson model for five different cutoff functions of the spectral density. With oscillatory and non-oscillatory exponentially decaying functions to decompose the bath correlation function, the hierarchy equation of motion is reliably extended to each spectral density under our investigation. The predicted spin dynamics is gradually converged with the increase of the hierarchic expansion order and the number of decomposing basis functions. Our systematic study of different cutoff functions expands previous results of the delocalized-localized phase transition with the exponential and sudden cutoffs in the spectral density.
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Affiliation(s)
- Chenru Duan
- Physics Department, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Qianlong Wang
- Physics Department, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Zhoufei Tang
- Physics Department, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Jianlan Wu
- Physics Department, Zhejiang University, Hangzhou, Zhejiang 310027, China
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25
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Ye L, Zhang HD, Wang Y, Zheng X, Yan Y. Low-frequency logarithmic discretization of the reservoir spectrum for improving the efficiency of hierarchical equations of motion approach. J Chem Phys 2017; 147:074111. [DOI: 10.1063/1.4999027] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- LvZhou Ye
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hou-Dao Zhang
- 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, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
- iChEM (Collaborative Innovation Center of Chemistry for Energy Materials), University of Science and Technology of China, Hefei, Anhui 230026, China
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26
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Ikeda T, Tanimura Y. Probing photoisomerization processes by means of multi-dimensional electronic spectroscopy: The multi-state quantum hierarchical Fokker-Planck equation approach. J Chem Phys 2017; 147:014102. [DOI: 10.1063/1.4989537] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- Tatsushi Ikeda
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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27
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Ke Y, Zhao Y. Hierarchy of stochastic Schrödinger equation towards the calculation of absorption and circular dichroism spectra. J Chem Phys 2017; 146:174105. [DOI: 10.1063/1.4982230] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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28
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Ye L, Wang X, Hou D, Xu RX, Zheng X, Yan Y. HEOM-QUICK: a program for accurate, efficient, and universal characterization of strongly correlated quantum impurity systems. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2016. [DOI: 10.1002/wcms.1269] [Citation(s) in RCA: 70] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- LvZhou Ye
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics; University of Science and Technology of China; Hefei China
| | - Xiaoli Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics; University of Science and Technology of China; Hefei China
| | - Dong Hou
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics; University of Science and Technology of China; Hefei China
| | - Rui-Xue Xu
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics; University of Science and Technology of China; Hefei China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics; University of Science and Technology of China; Hefei China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale and iChEM (Collaborative Innovation Center of Chemistry for Energy Materials); University of Science and Technology of China; Hefei China
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29
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Kato A, Tanimura Y. Quantum heat transport of a two-qubit system: Interplay between system-bath coherence and qubit-qubit coherence. J Chem Phys 2015; 143:064107. [DOI: 10.1063/1.4928192] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Akihito Kato
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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