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Takahashi H, Tanimura Y. Discretized hierarchical equations of motion in mixed Liouville-Wigner space for two-dimensional vibrational spectroscopies of liquid water. J Chem Phys 2023; 158:044115. [PMID: 36725520 DOI: 10.1063/5.0135725] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
A model of a bulk water system describing the vibrational motion of intramolecular and intermolecular modes is constructed, enabling analysis of its linear and nonlinear vibrational spectra as well as the energy transfer processes between the vibrational modes. The model is described as a system of four interacting anharmonic oscillators nonlinearly coupled to their respective heat baths. To perform a rigorous numerical investigation of the non-Markovian and nonperturbative quantum dissipative dynamics of the model, we derive discretized hierarchical equations of motion in mixed Liouville-Wigner space, with Lagrange-Hermite mesh discretization being employed in the Liouville space of the intramolecular modes and Lagrange-Hermite mesh discretization and Hermite discretization in the Wigner space of the intermolecular modes. One-dimensional infrared and Raman spectra and two-dimensional terahertz-infrared-visible and infrared-infrared-Raman spectra are computed as demonstrations of the quantum dissipative description provided by our model.
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Affiliation(s)
- Hideaki Takahashi
- 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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2
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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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3
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Jo JY, Tanimura Y. Full molecular dynamics simulations of molecular liquids for single-beam spectrally controlled two-dimensional Raman spectroscopy. J Chem Phys 2021; 154:124115. [PMID: 33810650 DOI: 10.1063/5.0044661] [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
Single-beam spectrally controlled (SBSC) two-dimensional (2D) Raman spectroscopy is a unique 2D vibrational measurement technique utilizing trains of short pulses that are generated from a single broadband pulse by pulse shaping. This approach overcomes the difficulty of 2D Raman spectroscopy in dealing with small-signal extraction and avoids complicated low-order cascading effects, thus providing a new possibility for measuring the intramolecular and intermolecular modes of molecular liquids using fifth-order 2D Raman spectroscopy. Recently, for quantitatively investigating the mode-mode coupling mechanism, Hurwitz et al. [Opt. Express 28, 3803 (2020)] have developed a new pulse design for this measurement to separate the contributions of the fifth- and third-order polarizations, which are often overlapped in the original single-beam measurements. Here, we describe a method for simulating these original measurements and the new 2D Raman measurements on the basis of a second-order response function approach. We carry out full molecular dynamics simulations for carbon tetrachloride and liquid water using an equilibrium-nonequilibrium hybrid algorithm, with the aim of explaining the key features of the SBSC 2D Raman spectroscopic method from a theoretical point of view. The predicted signal profiles and intensities provide valuable information that can be applied to 2D spectroscopy experiments, allowing them to be carried out more efficiently.
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Affiliation(s)
- Ju-Yeon Jo
- 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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4
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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: 140] [Impact Index Per Article: 46.7] [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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5
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Yan Y, Xing T, Shi Q. A new method to improve the numerical stability of the hierarchical equations of motion for discrete harmonic oscillator modes. J Chem Phys 2020; 153:204109. [DOI: 10.1063/5.0027962] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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, 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
| | - 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, 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, 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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6
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Zhang J, Borrelli R, Tanimura Y. Proton tunneling in a two-dimensional potential energy surface with a non-linear system–bath interaction: Thermal suppression of reaction rate. J Chem Phys 2020; 152:214114. [DOI: 10.1063/5.0010580] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Affiliation(s)
- Jiaji Zhang
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Raffaele Borrelli
- DISAFA, University of Torino, Largo Paolo Braccini 2, I-10095 Grugliasco, Italy
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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7
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Ueno S, Tanimura Y. Modeling Intermolecular and Intramolecular Modes of Liquid Water Using Multiple Heat Baths: Machine Learning Approach. J Chem Theory Comput 2020; 16:2099-2108. [DOI: 10.1021/acs.jctc.9b01288] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Seiji Ueno
- HPC Systems Inc., Nakagyoku, Kyoto 604, Japan
- Department of Chemistry, Kyoto University, Kyoto 606-8502, Japan
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8
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Zhang HD, Cui L, Gong H, Xu RX, Zheng X, Yan Y. Hierarchical equations of motion method based on Fano spectrum decomposition for low temperature environments. J Chem Phys 2020; 152:064107. [PMID: 32061227 DOI: 10.1063/1.5136093] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The hierarchical equations of motion (HEOM) method has become one of the most popular methods for the studies of the open quantum system. However, its applicability to systems at ultra-low temperatures is largely restrained by the enormous computational cost, which is caused by the numerous exponential functions required to accurately characterize the non-Markovian memory of the reservoir environment. To overcome this problem, a Fano spectrum decomposition (FSD) scheme has been proposed recently [Cui et al., J. Chem. Phys. 151, 024110 (2019)], which expands the reservoir correlation functions using polynomial-exponential functions and hence greatly reduces the size of the memory basis set. In this work, we explicitly establish the FSD-based HEOM formalisms for both bosonic and fermionic environments. The accuracy and efficiency of the FSD-based HEOM are exemplified by the calculated low-temperature dissipative dynamics of a spin-boson model and the dynamic and static properties of a single-orbital Anderson impurity model in the Kondo regime. The encouraging numerical results highlight the practicality and usefulness of the FSD-based HEOM method for general open systems at ultra-low temperatures.
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Affiliation(s)
- Hou-Dao Zhang
- 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
| | - Lei Cui
- 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
| | - Hong Gong
- 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
| | - 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, Anhui 230026, 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
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9
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Jansen TLC, Saito S, Jeon J, Cho M. Theory of coherent two-dimensional vibrational spectroscopy. J Chem Phys 2019; 150:100901. [DOI: 10.1063/1.5083966] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Thomas la Cour Jansen
- University of Groningen, Zernike Institute for Advanced Materials, Nijenborgh 4, 9747 AG Groningen, The Netherlands
| | - Shinji Saito
- Institute for Molecular Science, Myodaiji, Okazaki, Aichi 444-8585, Japan and The Graduate University for Advanced Studies, Myodaiji, Okazaki, Aichi 444-8585, Japan
| | - Jonggu Jeon
- Center for Molecular Spectroscopy and Dynamics, Institute for Basic Science (IBS), Seoul 02841, South Korea
| | - Minhaeng Cho
- Center for Molecular Spectroscopy and Dynamics, Institute for Basic Science (IBS), Seoul 02841, South Korea
- Department of Chemistry, Korea University, Seoul 02841, South Korea
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10
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Shi Q, Xu Y, Yan Y, Xu M. Efficient propagation of the hierarchical equations of motion using the matrix product state method. J Chem Phys 2018; 148:174102. [DOI: 10.1063/1.5026753] [Citation(s) in RCA: 41] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- 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
| | - Yang 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 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, 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
| | - 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 and University of Chinese Academy of Sciences, Beijing 100049, China
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11
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Ritschel G, Strunz WT, Eisfeld A. Closures of the functional expansion hierarchy in the non-Markovian quantum state diffusion approach. J Chem Phys 2017; 147:064113. [DOI: 10.1063/1.4986251] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
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12
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Zhang HD, Qiao Q, Xu RX, Yan Y. Solvent-induced polarization dynamics and coherent two-dimensional spectroscopy: Dissipaton equation of motion approach. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.07.005] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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13
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Full molecular dynamics simulations of liquid water and carbon tetrachloride for two-dimensional Raman spectroscopy in the frequency domain. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.07.002] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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14
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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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15
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Ito H, Tanimura Y. Simulating two-dimensional infrared-Raman and Raman spectroscopies for intermolecular and intramolecular modes of liquid water. J Chem Phys 2016; 144:074201. [DOI: 10.1063/1.4941842] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
Affiliation(s)
- Hironobu Ito
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyoku, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyoku, Kyoto 606-8502, Japan
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16
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Ito H, Jo JY, Tanimura Y. Notes on simulating two-dimensional Raman and terahertz-Raman signals with a full molecular dynamics simulation approach. STRUCTURAL DYNAMICS (MELVILLE, N.Y.) 2015; 2:054102. [PMID: 26798823 PMCID: PMC4711663 DOI: 10.1063/1.4932597] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/29/2015] [Accepted: 09/25/2015] [Indexed: 06/05/2023]
Abstract
Recent developments in two-dimensional (2D) THz-Raman and 2D Raman spectroscopies have created the possibility for quantitatively investigating the role of many dynamic and structural aspects of the molecular system. We explain the significant points for properly simulating 2D vibrational spectroscopic studies of intermolecular modes using the full molecular dynamics approach, in particular, regarding the system size, the treatment of the thermostat, and inclusion of an Ewald summation for the induced polarizability. Moreover, using the simulation results for water employing various polarization functions, we elucidate the roles of permanent and induced optical properties in determining the 2D profiles of the signal.
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Affiliation(s)
- Hironobu Ito
- Department of Chemistry, Graduate School of Science, Kyoto University , Sakyoku, Kyoto 606-8502, Japan
| | - Ju-Yeon Jo
- Department of Chemistry, Graduate School of Science, Kyoto University , Sakyoku, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University , Sakyoku, Kyoto 606-8502, Japan
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17
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Wilkins DM, Dattani NS. Why Quantum Coherence Is Not Important in the Fenna–Matthews–Olsen Complex. J Chem Theory Comput 2015; 11:3411-9. [DOI: 10.1021/ct501066k] [Citation(s) in RCA: 74] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- David M. Wilkins
- Physical and Theoretical
Chemistry Laboratory, Oxford University, South Parks Road, Oxford, OX1 3QZ, United Kingdom
| | - Nikesh S. Dattani
- Quantum
Chemistry Laboratory,
Department of Chemistry, Kyoto University, 606-8502, Kyoto, Japan
- School of Materials Science
and Engineering, Nanyang Technological University, Block N4.1, Nanyang Avenue, Singapore 639798
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18
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Ikeda T, Ito H, Tanimura Y. Analysis of 2D THz-Raman spectroscopy using a non-Markovian Brownian oscillator model with nonlinear system-bath interactions. J Chem Phys 2015; 142:212421. [DOI: 10.1063/1.4917033] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tatsushi Ikeda
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Hironobu Ito
- 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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19
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Tanimura Y. Real-time and imaginary-time quantum hierarchal Fokker-Planck equations. J Chem Phys 2015; 142:144110. [DOI: 10.1063/1.4916647] [Citation(s) in RCA: 94] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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20
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Ito H, Hasegawa T, Tanimura Y. Calculating two-dimensional THz-Raman-THz and Raman-THz-THz signals for various molecular liquids: The samplers. J Chem Phys 2014; 141:124503. [PMID: 25273447 DOI: 10.1063/1.4895908] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hironobu Ito
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyoku, Kyoto 606-8502, Japan
| | - Taisuke Hasegawa
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyoku, Kyoto 606-8502, Japan
- Department of Physics, University of Hamburg, Centre for Free Electron Laser Science, DESY, Notkestrasse 85, D-22607 Hamburg, Germany
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyoku, Kyoto 606-8502, Japan
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21
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Tanimura Y. Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities. J Chem Phys 2014; 141:044114. [DOI: 10.1063/1.4890441] [Citation(s) in RCA: 121] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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22
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Tanimura Y. Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two-dimensional correlation spectroscopy. J Chem Phys 2012; 137:22A550. [DOI: 10.1063/1.4766931] [Citation(s) in RCA: 100] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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23
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Zhu L, Liu H, Xie W, Shi Q. Explicit system-bath correlation calculated using the hierarchical equations of motion method. J Chem Phys 2012. [DOI: 10.1063/1.4766358] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
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24
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Song J, Gao F, Cui RZ, Shuang F, Liang W, Huang X, Zhuang W. Investigating the structural origin of trpzip2 temperature dependent unfolding fluorescence line shape based on a Markov state model simulation. J Phys Chem B 2012; 116:12669-76. [PMID: 22994891 DOI: 10.1021/jp304714q] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Vibrationally resolved fluorescence spectra of the β-hairpin trpzip2 peptide at two temperatures as well as during a T-jump unfolding process are simulated on the basis of a combination of Markov state models and quantum chemistry schemes. The broad asymmetric spectral line shape feature is reproduced by considering the exciton-phonon couplings. The temperature dependent red shift observed in the experiment has been attributed to the state population changes of specific chromophores. Through further theoretical study, it is found that both the environment's electric field and the chromophores' geometry distortions are responsible for tryptophan fluorescence shift.
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Affiliation(s)
- Jian Song
- State Key Lab of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Dalian, 116023, China
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25
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Shit A, Chattopadhyay S, Ray Chaudhuri J. Towards an understanding of escape rate and state dependent diffusion for a quantum dissipative system. Chem Phys 2011. [DOI: 10.1016/j.chemphys.2011.06.002] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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26
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Chen L, Zheng R, Jing Y, Shi Q. Simulation of the two-dimensional electronic spectra of the Fenna-Matthews-Olson complex using the hierarchical equations of motion method. J Chem Phys 2011; 134:194508. [DOI: 10.1063/1.3589982] [Citation(s) in RCA: 87] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
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27
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Sakurai A, Tanimura Y. Does ℏ Play a Role in Multidimensional Spectroscopy? Reduced Hierarchy Equations of Motion Approach to Molecular Vibrations. J Phys Chem A 2011; 115:4009-22. [DOI: 10.1021/jp1095618] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Atsunori Sakurai
- Department of Chemistry, Graduate School of Science, Kyoto Universiy, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto Universiy, Kyoto 606-8502, Japan
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Ghosh P, Shit A, Chattopadhyay S, Chaudhuri JR. Realization of a Brownian engine to study transport phenomena: a semiclassical approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:061112. [PMID: 20866383 DOI: 10.1103/physreve.81.061112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2010] [Revised: 04/21/2010] [Indexed: 05/29/2023]
Abstract
Brownian particles moving in a periodic potential with or without external load are often used as good theoretical models for the phenomenological studies of microscopic heat engines. The model that we propose here, assumes the particle to be moving in a nonequilibrium medium and we have obtained the exact expression for the stationary current density. We have restricted our consideration to the overdamped motion of the Brownian particle. We present here a self-consistent theory based on the system-reservoir coupling model, within a microscopic approach, of fluctuation induced transport in the semiclassical limit for a general system coupled with two heat baths kept at different temperatures. This essentially puts forth an approach to semiclassical state-dependent diffusion. We also explore the possibility of observing a current when the temperature of the two baths are different, and also envisage that our system may act as a Carnot engine even when the bath temperatures are the same. The condition for such a construction has been elucidated.
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Affiliation(s)
- Pradipta Ghosh
- Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India
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29
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Hanna G, Geva E. Computational study of the signature of hydrogen-bond strength on the infrared spectra of a hydrogen-bonded complex dissolved in a polar liquid. Chem Phys 2010. [DOI: 10.1016/j.chemphys.2010.01.013] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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30
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Sahrapour MM, Makri N. Multitime response functions and nonlinear spectra for model quantum dissipative systems. J Chem Phys 2010; 132:134506. [DOI: 10.1063/1.3336463] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
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31
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Ghosh P, Chattopadhyay S, Chaudhuri JR. Stochastic resonance in a generalized quantum Kubo oscillator. J Phys Chem B 2010; 114:1368-79. [PMID: 20041674 DOI: 10.1021/jp909858c] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We discuss stochastic resonance in a biased linear quantum system that is subject to multiplicative and additive noises. Starting from a microscopic system-reservoir Hamiltonian, we derive a c-number analogue of the generalized Langevin equation. The developed approach puts forth a quantum mechanical generalization of the "Kubo type" oscillator which is a linear system. Such a system is often used in the literature to study various phenomena in nonequilibrium systems via a particular interaction between system and the external noise. Our analytical results proposed here have the ability to reveal the role of external noise and vis-a-vis the mechanisms and detection of subtle underlying signatures of the stochastic resonance behavior in a linear system. In our development, we show that only when the external noise possesses a "finite correlation time" the quantum effect begins to appear. We observe that the quantum effect enhances the resonance in comparison to the classical one.
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Affiliation(s)
- Pradipta Ghosh
- Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India
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32
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Chen L, Zheng R, Shi Q, Yan Y. Two-dimensional electronic spectra from the hierarchical equations of motion method: Application to model dimers. J Chem Phys 2010; 132:024505. [DOI: 10.1063/1.3293039] [Citation(s) in RCA: 59] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Bhattacharya S, Chaudhury P, Chattopadhyay S, Chaudhuri JR. Quantum transport in a periodic symmetric potential of a driven quantum system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:041127. [PMID: 19905293 DOI: 10.1103/physreve.80.041127] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2009] [Indexed: 05/28/2023]
Abstract
A system-reservoir nonlinear coupling model has been proposed to the situation when the system is driven externally by a random force and the associated bath is kept in thermal equilibrium, in an attempt to put forth a microscopic approach to quantum state-dependent diffusion and multiplicative noises in terms of a quantum Langevin equation in the overdamped limit (quantum Smoluchowski equation). We then obtain the analytical expression for phase induced quantum current in a periodic potential when the external noise has finite correlation time and explore the dependence of the current on various parameters related to the external noise, for example, the noise strength.
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Affiliation(s)
- Satyabrata Bhattacharya
- Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India
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34
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Tanimura Y, Ishizaki A. Modeling, calculating, and analyzing multidimensional vibrational spectroscopies. Acc Chem Res 2009; 42:1270-9. [PMID: 19441802 DOI: 10.1021/ar9000444] [Citation(s) in RCA: 77] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Spectral line shapes in a condensed phase contain information from various dynamic processes that modulate the transition energy, such as microscopic dynamics, inter- and intramolecular couplings, and solvent dynamics. Because nonlinear response functions are sensitive to the complex dynamics of chemical processes, multidimensional vibrational spectroscopies can separate these processes. In multidimensional vibrational spectroscopy, the nonlinear response functions of a molecular dipole or polarizability are measured using ultrashort pulses to monitor inter- and intramolecular vibrational motions. Because a complex profile of such signals depends on the many dynamic and structural aspects of a molecular system, researchers would like to have a theoretical understanding of these phenomena. In this Account, we explore and describe the roles of different physical phenomena that arise from the peculiarities of the system-bath coupling in multidimensional spectra. We also present simple analytical expressions for a weakly coupled multimode Brownian system, which we use to analyze the results obtained by the experiments and simulations. To calculate the nonlinear optical response, researchers commonly use a particular form of a system Hamiltonian fit to the experimental results. The optical responses of molecular vibrational motions have been studied in either an oscillator model or a vibration energy state model. In principle, both models should give the same results as long as the energy states are chosen to be the eigenstates of the oscillator model. The energy state model can provide a simple description of nonlinear optical processes because the diagrammatic Liouville space theory that developed in the electronically resonant spectroscopies can easily handle three or four energy states involved in high-frequency vibrations. However, the energy state model breaks down if we include the thermal excitation and relaxation processes in the dynamics to put the system in a thermal equilibrium state. The roles of these excitation and relaxation processes are different and complicated compared with those in the resonant spectroscopy. Observing the effects of such thermal processes is more intuitive with the oscillator model because the bath modes, which cause the fluctuation and dissipation processes, are also described in the coordinate space. This coordinate space system-bath approach complements a realistic full molecular dynamics simulation approach. By comparing the calculated 2D spectra from the coordinate space model and the energy state model, we can examine the role of thermal processes and anharmonic mode-mode couplings in the energy state model. For this purpose, we employed the Brownian oscillator model with the nonlinear system-bath interaction. Using the hierarchy formalism, we could precisely calculate multidimensional spectra for a single and multimode anharmonic system for inter- and intramolecular vibrational modes.
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Affiliation(s)
- Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University Kitashirakawa, Sakyoku, Kyoto 606-8502, Japan
| | - Akihito Ishizaki
- Department of Chemistry, Graduate School of Science, Kyoto University Kitashirakawa, Sakyoku, Kyoto 606-8502, Japan
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35
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Hanna G, Geva E. Multidimensional Spectra via the Mixed Quantum-Classical Liouville Method: Signatures of Nonequilibrium Dynamics. J Phys Chem B 2009; 113:9278-88. [DOI: 10.1021/jp902797z] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Gabriel Hanna
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
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36
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Chen L, Zheng R, Shi Q, Yan Y. Optical line shapes of molecular aggregates: Hierarchical equations of motion method. J Chem Phys 2009; 131:094502. [DOI: 10.1063/1.3213013] [Citation(s) in RCA: 111] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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37
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Bhattacharya S, Chaudhury P, Chattopadhyay S, Chaudhuri JR. Phase induced current in presence of nonequilibrium bath: A quantum approach. J Chem Phys 2008; 129:124708. [PMID: 19045049 DOI: 10.1063/1.2981053] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
Based on a system-reservoir nonlinear coupling model, where the associated bath is externally driven by a fluctuating force, we present a microscopic approach to quantum state-dependent diffusion and multiplicative noises in terms of a quantum (Markovian) Langevin equation in overdamped limit when the associated bath is in nonequilibrium state. We then explore the possibility of observing a quantum current when the bath is modulated by white noise, the phenomena which is absent in the classical regime.
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Affiliation(s)
- Satyabrata Bhattacharya
- Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India
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38
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Hanna G, Geva E. Computational Study of the One and Two Dimensional Infrared Spectra of a Vibrational Mode Strongly Coupled to Its Environment: Beyond the Cumulant and Condon Approximations. J Phys Chem B 2008; 112:12991-3004. [DOI: 10.1021/jp804120v] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Gabriel Hanna
- Department of Chemistry and FOCUS center, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Eitan Geva
- Department of Chemistry and FOCUS center, University of Michigan, Ann Arbor, Michigan 48109-1055
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39
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Bhattacharya S, Chaudhury P, Chattopadhyay S, Chaudhuri JR. Directed motion in a periodic potential of a quantum system coupled to a heat bath driven by a colored noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:021123. [PMID: 18850802 DOI: 10.1103/physreve.78.021123] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2008] [Indexed: 05/26/2023]
Abstract
A system-reservoir nonlinear coupling model is proposed for a quantum system when the associated bath is not in thermal equilibrium but is modulated by an external colored noise, to present a microscopic approach to quantum state-dependent diffusion and multiplicative noise in terms of a quantum Langevin description. Consequently, the Fokker-Planck equation in position space, valid in the overdamped limit, for multiplicative colored noise is constructed to explore the possibility of observing a quantum current and dependence of the current on various parameters of external noise is examined.
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Affiliation(s)
- Satyabrata Bhattacharya
- Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India
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40
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Li YL, Huang L, Dwayne Miller RJ, Hasegawa T, Tanimura Y. Two-dimensional fifth-order Raman spectroscopy of liquid formamide: Experiment and Theory. J Chem Phys 2008; 128:234507. [DOI: 10.1063/1.2927311] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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41
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Ishizaki A, Tanimura Y. Nonperturbative non-Markovian quantum master equation: Validity and limitation to calculate nonlinear response functions. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2007.10.037] [Citation(s) in RCA: 92] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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42
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Suzuki Y, Tanimura Y. Exploring a free energy landscape by means of multidimensional infrared and terahertz spectroscopies. J Chem Phys 2008; 128:164501. [PMID: 18447453 DOI: 10.1063/1.2897982] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
A model for the dipolar crystal system is employed to explore a role of free energy landscape (FEL), in which dipolar molecules are posted on two-dimensional lattice sites with two-state libratinal dynamics. All dipole-dipole interactions are included to have frustrated interactions among the dipoles. For the regular and distorted lattice cases, the FEL is calculated from the interaction energies and the total polarizations for all possible dipolar states at various temperatures. At high temperatures, the shape of the calculated FEL is smooth and parabolic, while it becomes bumpy at low temperatures exhibiting multiple local minima. To study dynamical aspects of the system, the single flip dynamics and the single-double mixed flips dynamics of dipoles are examined from a master equation approach. As the observables of linear absorption and two-dimensional (2D) infrared, far infrared, and terahertz spectroscopies, the first- and third-order response functions of polarization are calculated for different physical conditions characterized by the FEL. While the linear absorption signals decay in time in a similar manner regardless of the FEL profiles, the 2D signals exhibit prominent differences for those profiles. This indicates that we may differentiate the FEL profiles by changing two-time valuables in 2D spectroscopy. As illustrated in the single-double flips case, the FEL study by means of 2D spectroscopy, however, relies on the dynamics which is set independently from the FEL. The Smoluchowski equation is applied to examine the description of the collective dynamics on the microscopically calculated FEL. We found that the one-dimensional and 2D signals calculated from the Smoluchowski equation agree with those from master equation only at temperatures where the FEL becomes parabolic shape.
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Affiliation(s)
- Yohichi Suzuki
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa, Sakyoku, Kyoto 606-8502, Japan.
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43
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Chaudhuri JR, Chattopadhyay S, Banik SK. Multiplicative cross-correlated noise induced escape rate from a metastable state. J Chem Phys 2008; 128:154513. [PMID: 18433241 DOI: 10.1063/1.2901044] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. By starting from a phenomenological stationary Langevin description with multiplicative noise processes, we have investigated the Kramers theory for activated rate processes in a nonequilibrium open system (one dimensional in nature) driven by two external cross-correlated noise processes which are Gaussian, stationary, and delta correlated. Based on the Fokker-Planck description in phase space, we then derive the escape rate from a metastable state in the moderate to large friction limit to study the effect of degree of correlation on the same. By employing numerical simulation in the presence of external cross-correlated additive and multiplicative noises, we check the validity of our analytical formalism for constant dissipation, which shows a satisfactory agreement between both the approaches for the specific choice of noise processes. It is evident both from analytical development and the corresponding numerical simulation that the enhancement of rate is possible by increasing the degree of correlation of the external fluctuations.
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44
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Hasegawa T, Tanimura Y. Nonequilibrium molecular dynamics simulations with a backward-forward trajectories sampling for multidimensional infrared spectroscopy of molecular vibrational modes. J Chem Phys 2008; 128:064511. [DOI: 10.1063/1.2828189] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
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45
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Ishizaki A, Tanimura Y. Dynamics of a Multimode System Coupled to Multiple Heat Baths Probed by Two-Dimensional Infrared Spectroscopy. J Phys Chem A 2007; 111:9269-76. [PMID: 17880172 DOI: 10.1021/jp072880a] [Citation(s) in RCA: 76] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Reduced equation of motion for a multimode system coupled to multiple heat baths is constructed by extending the quantum Fokker-Planck equation with low-temperature correction terms (J. Phys. Soc. Jpn. 2005, 74, 3131). Unlike such common approaches used to describe intramolecular multimode vibration as a Bloch-Redfield theory and a stochastic theory, the present formalism is defined by the molecular coordinates. To explore the correlation among different modes through baths, we consider two cases of system-bath couplings. One is a correlated case in which two modes are coupled to a single bath, and the other is an uncorrelated case in which each mode is coupled to a different bath. We further classify the correlated case into two cases, the plus- and minus-correlated cases, according to distinct correlation manners. For these, one-dimensional and two-dimensional infrared (2D-IR) spectra are calculated numerically by solving the equation of motion. It is demonstrated that 2D-IR spectroscopy has the ability to analyze the correlation of fluctuation-dissipation processes among different modes.
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Affiliation(s)
- Akihito Ishizaki
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
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46
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Hayashi T, Mukamel S. Vibrational-exciton couplings for the amide I, II, III, and A modes of peptides. J Phys Chem B 2007; 111:11032-46. [PMID: 17725341 DOI: 10.1021/jp070369b] [Citation(s) in RCA: 74] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
The couplings between all amide fundamentals and their overtones and combination vibrational states are calculated. Combined with the level energies reported previously (Hayashi, T.; Zhuang, W.; Mukamel, S. J. Phys. Chem. A 2005, 109, 9747), we obtain a complete effective vibrational Hamiltonian for the entire amide system. Couplings between neighboring peptide units are obtained using the anharmonic vibrational Hamiltonian of glycine dipeptide (GLDP) at the BPW91/6-31G(d,p) level. Electrostatic couplings between non-neighboring units are calculated by the fourth rank transition multipole coupling (TMC) expansion, including 1/R3 (dipole-dipole), 1/R4 (quadrupole-dipole), and 1/R5 (quadrupole-quadrupole and octapole-dipole) interactions. Exciton delocalization length and its variation with frequency in the various amide bands are calculated. The simulated infrared amide I and II absorptions and CD spectra of 24 residue alpha-helical motifs (SPE3) are in good agreement with experiment.
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Affiliation(s)
- Tomoyuki Hayashi
- Department of Chemistry, University of California, Irvine, California 92697-2025, USA
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47
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Hahn S, Lee H, Cho M. Theoretical calculations of infrared absorption, vibrational circular dichroism, and two-dimensional vibrational spectra of acetylproline in liquids water and chloroform. J Chem Phys 2006; 121:1849-65. [PMID: 15260736 DOI: 10.1063/1.1763889] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
Infrared absorption, vibrational circular dichroism, and two-dimensional infrared pump-probe and photon echo spectra of acetylproline solutions are theoretically calculated and directly compared with experiments. In order to quantitatively determine interpeptide interaction-induced amide I mode frequency shifts, high-level quantum chemistry calculations were performed. The solvatochromic amide I mode frequency shift and fluctuation were taken into account by carrying out molecular dynamics simulations of acetylproline dissolved in liquids water and chloroform and by using the extrapolation method developed recently. We first studied correlation time scales of the two amide I vibrational frequency fluctuations, cross correlation between the two fluctuating local mode frequencies, ensemble averaged conformations of the acetylproline molecule in liquids water and chloroform. The corresponding conformations of the acetylproline in liquids water and chloroform are close to the ideal 3(10) helix and the C(7) structure, respectively. A few methods proposed to determine the angle between the two transition dipoles associated with the amide I vibrations were tested and their limitations are discussed.
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Affiliation(s)
- Seungsoo Hahn
- Department of Chemistry and Center for Multidimensional Spectroscopy, Korea University, Seoul 136-701, Korea
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48
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Saito S, Ohmine I. Fifth-order two-dimensional Raman spectroscopy of liquid water, crystalline ice Ih and amorphous ices: Sensitivity to anharmonic dynamics and local hydrogen bond network structure. J Chem Phys 2006; 125:084506. [PMID: 16965028 DOI: 10.1063/1.2232254] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
The theoretical study of off-resonant fifth-order two-dimensional (2D)-Raman spectroscopy is made to analyze the intermolecular dynamics of liquid and solid water. The 2D-Raman spectroscopy is susceptible to the nonlinear anharmonic dynamics and local hydrogen bond structure in water. It is found that the distinct 2D-Raman response appears as the negative signal near the t(2) axis. The origin of this negative signal for t(2)<15 fs is from the nonlinear polarizability in the librational motions, whereas that for 30 fs<t(2)<150 fs is attributed to the anharmonic translational motions. It is found that the mechanical anharmonicity and nonlinear polarizability couplings among modes clearly can be observed as the sum- and difference-frequency peaks in the 2D-Raman spectrum (i.e., Fourier transforms of the response). The 2D-Raman spectroscopies of ice Ih and amorphous ices, i.e., low density, high density, and very high density amorphous ices, are also investigated. It is found that the 2D-Raman spectroscopy is very sensitive to the anisotropy of the structure of ice Ih. The strong hydrogen bond stretching band is seen in the 2D-Raman spectroscopy of the polarization directions parallel to the c axis, whereas the contributions of the librational motion can be also seen in the spectrum with the polarization directions parallel to the a axis. The 2D-Raman spectroscopy is also found to be also very sensitive to the differences in local hydrogen bond network structures in various amorphous phases.
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Affiliation(s)
- Shinji Saito
- Department of Computational Molecular Science, Institute for Molecular Science, Myodaiji, Okazaki, Aichi 444-8585, Japan.
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49
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Ishizaki A, Tanimura Y. Modeling vibrational dephasing and energy relaxation of intramolecular anharmonic modes for multidimensional infrared spectroscopies. J Chem Phys 2006; 125:084501. [PMID: 16965023 DOI: 10.1063/1.2244558] [Citation(s) in RCA: 100] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Starting from a system-bath Hamiltonian in a molecular coordinate representation, we examine an applicability of a stochastic multilevel model for vibrational dephasing and energy relaxation in multidimensional infrared spectroscopy. We consider an intramolecular anharmonic mode nonlinearly coupled to a colored noise bath at finite temperature. The system-bath interaction is assumed linear plus square in the system coordinate, but linear in the bath coordinates. The square-linear system-bath interaction leads to dephasing due to the frequency fluctuation of system vibration, while the linear-linear interaction contributes to energy relaxation and a part of dephasing arises from anharmonicity. To clarify the role and origin of vibrational dephasing and energy relaxation in the stochastic model, the system part is then transformed into an energy eigenstate representation without using the rotating wave approximation. Two-dimensional (2D) infrared spectra are then calculated by solving a low-temperature corrected quantum Fokker-Planck (LTC-QFP) equation for a colored noise bath and by the stochastic theory. In motional narrowing regime, the spectra from the stochastic model are quite different from those from the LTC-QFP. In spectral diffusion regime, however, the 2D line shapes from the stochastic model resemble those from the LTC-QFP besides the blueshifts caused by the dissipation from the colored noise bath. The preconditions for validity of the stochastic theory for molecular vibrational motion are also discussed.
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Affiliation(s)
- Akihito Ishizaki
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
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50
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Hasegawa T, Tanimura Y. Calculating fifth-order Raman signals for various molecular liquids by equilibrium and nonequilibrium hybrid molecular dynamics simulation algorithms. J Chem Phys 2006; 125:074512. [PMID: 16942356 DOI: 10.1063/1.2217947] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
The fifth-order two-dimensional (2D) Raman signals have been calculated from the equilibrium and nonequilibrium (finite field) molecular dynamics simulations. The equilibrium method evaluates response functions with equilibrium trajectories, while the nonequilibrium method calculates a molecular polarizability from nonequilibrium trajectories for different pulse configurations and sequences. In this paper, we introduce an efficient algorithm which hybridizes the existing two methods to avoid the time-consuming calculations of the stability matrices which are inherent in the equilibrium method. Using nonequilibrium trajectories for a single laser excitation, we are able to dramatically simplify the sampling process. With this approach, the 2D Raman signals for liquid xenon, carbon disulfide, water, acetonitrile, and formamide are calculated and discussed. Intensities of 2D Raman signals are also estimated and the peak strength of formamide is found to be only five times smaller than that of carbon disulfide.
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Affiliation(s)
- Taisuke Hasegawa
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyo, Kyoto 606-8502, Japan.
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