1
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Huang C, Bai S, Shi Q. Simulation of the Pump-Probe Spectra and Excitation Energy Relaxation of the B850 Band of the LH2 Complex in Purple Bacteria. J Phys Chem B 2024; 128:7467-7475. [PMID: 39059418 DOI: 10.1021/acs.jpcb.4c02059] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/28/2024]
Abstract
Ultrafast spectroscopic techniques have been vital in studying excitation energy transfer (EET) in photosynthetic light harvesting complexes. In this paper, we simulate the pump-probe spectra of the B850 band of the light harvesting complex 2 (LH2) of purple bacteria, by using the hierarchical equation of motion method and the optical response function approach. The ground state bleach, stimulated emission, and excited state absorption components of the pump-probe spectra are analyzed in detail. The laser pulse-induced population dynamics are also simulated to help understand the main features of the pump-probe spectra and the EET process. It is shown that the excitation energy relaxation is an ultrafast process with multiple time scales. The first 40 fs of the pump-probe spectra is dominated by the relaxation of the k = ±1 states to both the k = 0 and higher energy states. Dynamics on a longer time scale around 200 fs reflects the relaxation of higher energy states to the k = 0 state.
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Affiliation(s)
- Chenghong Huang
- 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
- China University of Chinese Academy of Sciences, Beijing 100049, China
| | - Shuming Bai
- 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
- 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, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun,Beijing 100190, China
- China University of Chinese Academy of Sciences, Beijing 100049, China
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2
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Sayer T, Montoya-Castillo A. Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra. J Chem Phys 2024; 160:044108. [PMID: 38270238 DOI: 10.1063/5.0185578] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 12/26/2023] [Indexed: 01/26/2024] Open
Abstract
Modern 4-wave mixing spectroscopies are expensive to obtain experimentally and computationally. In certain cases, the unfavorable scaling of quantum dynamics problems can be improved using a generalized quantum master equation (GQME) approach. However, the inclusion of multiple (light-matter) interactions complicates the equation of motion and leads to seemingly unavoidable cubic scaling in time. In this paper, we present a formulation that greatly simplifies and reduces the computational cost of previous work that extended the GQME framework to treat arbitrary numbers of quantum measurements. Specifically, we remove the time derivatives of quantum correlation functions from the modified Mori-Nakajima-Zwanzig framework by switching to a discrete-convolution implementation inspired by the transfer tensor approach. We then demonstrate the method's capabilities by simulating 2D electronic spectra for the excitation-energy-transfer dimer model. In our method, the resolution of data can be arbitrarily coarsened, especially along the t2 axis, which mirrors how the data are obtained experimentally. Even in a modest case, this demands O(103) fewer data points. We are further able to decompose the spectra into one-, two-, and three-time correlations, showing how and when the system enters a Markovian regime where further measurements are unnecessary to predict future spectra and the scaling becomes quadratic. This offers the ability to generate long-time spectra using only short-time data, enabling access to timescales previously beyond the reach of standard methodologies.
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Affiliation(s)
- Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
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3
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Toutounji M. Homogeneous Dephasing in Photosynthetic Bacterial Reaction Centers: Time Correlation Function Approach. Chemphyschem 2024; 25:e202300335. [PMID: 37953408 DOI: 10.1002/cphc.202300335] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2023] [Revised: 11/06/2023] [Accepted: 11/07/2023] [Indexed: 11/14/2023]
Abstract
A new tractable linear electronic transition dipole moment time correlation function (ETDMTCF) that accurately accounts for electronic dephasing, asymmetry, and width of 1-phonon profile, which the zero-phonon line (ZPL) contributes to it, in Rhodopseudomonas viridis bacterial reaction center is derived. This time correlation function proves to be superior to other frequency-domain expressions in case of strong electron-phonon coupling (which is often the case in bacterial RCs and pigment-protein complexes), many vibrational modes involved, and high temperature, whereby more vibronic and electronic (sequence) transitions would arise. The Fourier transform of this ETDMTCF leads to asymmetric multiphonon profiles composed of Lorentzian distribution and Gaussian distribution on the high- and low-energy sides, respectively, whereby the overtone widths fold themselves with that of the one-phonon profile. This ETDMTCF also features expedient computation in large systems using asymmetric phonon profiles to account correctly for dephasing and pigment-protein interaction (electron-phonon coupling). The derived ETDMTCF allows computing all nonlinear optical signals in both time and frequency domains, through the nonlinear dipole moment time correlation functions (as guided by nonlinear optical response theory) in line with the eight Liouville space pathways. The linear transition dipole moment time correlation function is of a central value as the nonlinear transition dipole moment time correlation function is expressed in terms of the linear transition dipole moment time correlation function, derived herein. One of the great advantages of presenting this ETDMTCF is its applicability to nonlinear transition dipole moment time correlation functions in line with the eight Liouville space pathways needed in computing nonlinear signals. As such, there is more to the utility and applicability of the presented ETDMTCF besides computational expediency and efficiency. Results show good agreement with the reported literature. The intimate connection between a one-phonon profile and the corresponding bath spectral density in photosynthetic complexes is discussed.
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Affiliation(s)
- Mohamad Toutounji
- College of Science, Department of Chemistry, P. O. Box 15551, UAE University, Al-Ain, United Arab Emirate
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4
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Liu Z, Jha A, Liang XT, Duan HG. Transient chiral dynamics revealed by two-dimensional circular dichroism spectroscopy. Phys Rev E 2023; 107:054119. [PMID: 37329099 DOI: 10.1103/physreve.107.054119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2022] [Accepted: 05/05/2023] [Indexed: 06/18/2023]
Abstract
Chirality has been considered as one of the key factors in the evolution of life in nature. It is important to uncover how chiral potentials of molecular systems play vital role in fundamental photochemical processes. Here, we investigate the role of chirality in photoinduced energy transfer in a model dimeric system, where the monomers are excitonically coupled. To observe transient chiral dynamics and energy transfer, we employ circularly polarized laser pulses in two-dimensional electronic spectroscopy to construct the two-dimensional circular dichroism (2DCD) spectral maps. Tracking time-resolved peak magnitudes in 2DCD spectra allows one to identify chirality induced population dynamics. The dynamics of energy transfer is revealed by the time-resolved kinetics of cross peaks. However, the differential signal of 2DCD spectra shows the magnitude of cross peaks is dramatically reduced at initial waiting time, which indicates the weak chiral interactions between two monomers. The downhill energy transfer is resolved by presenting a strong magnitude of cross peak in 2DCD spectra after long waiting time. The chiral contribution towards coherent and incoherent energy-transfer pathways in the model dimer system is further examined via control of excitonic couplings between two monomers. Applications are made to study the energy-transfer process in the Fenna-Matthews-Olson complex. Our work uncovers the potential of 2DCD spectroscopy to resolve the chiral-induced interactions and population transfers in excitonically coupled systems.
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Affiliation(s)
- Zihui Liu
- Department of Physics, School of Physical Science and Technology, Ningbo University, Ningbo 315211, P.R. China
| | - Ajay Jha
- Rosalind Franklin Institute, Harwell, Oxfordshire OX11 0QX, United Kingdom
- Department of Pharmacology, University of Oxford, Oxford OX1 3QT, United Kingdom
- Research Complex at Harwell, Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom
| | - Xian-Ting Liang
- Department of Physics, School of Physical Science and Technology, Ningbo University, Ningbo 315211, P.R. China
| | - Hong-Guang Duan
- Department of Physics, School of Physical Science and Technology, Ningbo University, Ningbo 315211, P.R. China
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5
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Atsango AO, Montoya-Castillo A, Markland TE. An accurate and efficient Ehrenfest dynamics approach for calculating linear and nonlinear electronic spectra. J Chem Phys 2023; 158:074107. [PMID: 36813724 DOI: 10.1063/5.0138671] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
Linear and nonlinear electronic spectra provide an important tool to probe the absorption and transfer of electronic energy. Here, we introduce a pure state Ehrenfest approach to obtain accurate linear and nonlinear spectra that is applicable to systems with large numbers of excited states and complex chemical environments. We achieve this by representing the initial conditions as sums of pure states and unfolding multi-time correlation functions into the Schrödinger picture. By doing this, we show that one can obtain significant improvements in accuracy over the previously used projected Ehrenfest approach and that these benefits are particularly pronounced in cases where the initial condition is a coherence between excited states. While such initial conditions do not arise when calculating linear electronic spectra, they play a vital role in capturing multidimensional spectroscopies. We demonstrate the performance of our method by showing that it is able to quantitatively capture the exact linear, 2D electronic spectroscopy, and pump-probe spectra for a Frenkel exciton model in slow bath regimes and is even able to reproduce the main spectral features in fast bath regimes.
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Affiliation(s)
- Austin O Atsango
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | | | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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6
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Chen L, Bennett DIG, Eisfeld A. Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion. J Chem Phys 2022; 157:114104. [DOI: 10.1063/5.0107925] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a methodology for simulating multi-dimensional electronic spectra of molecular aggregates with coupling of electronic excitation to a structured environment using the stochastic non-Markovian quantum state diffusion (NMQSD) method in combination with perturbation theory for the response functions. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space, but with the same noise. We demonstrate that our approach shows fast convergence with respect to the number of stochastic trajectories, providing a promising technique for numerical calculation of two-dimensional electronic spectra of large molecular aggregates.
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Affiliation(s)
- Lipeng Chen
- Department of Chemistry, Max-Planck-Institute for the Physics of Complex Systems, Germany
| | - Doran I. G Bennett
- Chemistry, Southern Methodist University Department of Chemistry, United States of America
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7
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Fay TP. A simple improved low temperature correction for the hierarchical equations of motion. J Chem Phys 2022; 157:054108. [DOI: 10.1063/5.0100365] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The study of open system quantum dynamics has been transformed by the hierarchical equations of motion (HEOM) method, which gives the exact dynamics for a system coupled to a harmonic bath at arbitrary temperature and system-bath coupling strength. However in its standard form the method is only consistent with the weak-coupling quantum master equation at all temperatures when many auxiliary density operators are included in the hierarchy, even when low temperature corrections are included. Here we propose a new low temperature correction scheme for the termination of the hierarchy based on Zwanzig projection which alleviates this problem, and restores consistency with the weak-coupling master equation with a minimal hierarchy. The utility of the new correction scheme is demonstrated on a range of model systems, including the Fenna-Metthews-Olson complex. The new closure is found to improve convergence of the HEOM even beyond the weak-coupling limit and is very straightforward to implement in existing HEOM codes.
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Affiliation(s)
- Thomas Patrick Fay
- Department of Chemistry, University of California Berkeley Department of Chemistry, United States of America
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8
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Abstract
Multidimensional optical spectra are measured from the response of a material system to a sequence of laser pulses and have the capacity to elucidate specific molecular interactions and dynamics whose influences are absent or obscured in a conventional linear absorption spectrum. Interpretation of complex spectra is supported by theoretical modeling of the spectroscopic observable, requiring implementation of quantum dynamics for coupled electrons and nuclei. Performing numerically correct quantum dynamics in this context may pose computational challenges, particularly in the condensed phase. Semiclassical methods based on calculating classical trajectories offer a practical alternative. Here I review the recent application of some semiclassical, trajectory-based methods to nonlinear molecular vibrational and electronic spectra. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Roger F. Loring
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York, USA
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9
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Kim HW, Rhee YM. Two‐dimensional electronic spectrum simulation of simple photosynthetic complex models with semi‐classical Poisson bracket mapping equation. B KOREAN CHEM SOC 2022. [DOI: 10.1002/bkcs.12469] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Hyun Woo Kim
- Center for Molecular Modeling and Simulation, Korea Research Institute of Chemical Technology (KRICT) Daejeon South Korea
| | - Young Min Rhee
- Department of Chemistry Korea Advanced Institute of Science and Technology (KAIST) Daejeon South Korea
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10
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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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11
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Seibt J, Kühn O. Strong Exciton-Vibrational Coupling in Molecular Assemblies. Dynamics Using the Polaron Transformation in HEOM Space. J Phys Chem A 2021; 125:7052-7065. [PMID: 34353023 DOI: 10.1021/acs.jpca.1c02684] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In Frenkel exciton dynamics of aggregated molecules, the polaron transformation (PT) technique leads to decoupling of diagonal elements in the subspace of excited electronic states from vibrations. In this article we describe for the first time how PT becomes applicable in the framework of the "Hierarchical Equations of Motion" (HEOM) approach for treatment of open quantum systems. We extend the concept of formulating operators in HEOM space by deriving hierarchical equations of PT which lead to a shift in the excited state potential energy surface to compensate its displacement. While the assumption of thermal equilibration of the vibrational oscillators, introduced by PT, results in a stationary state in a monomer, in a dimer under the same assumption nonequilibrium dynamics appears because of the interplay of the transfer process and vibrational equilibration. Both vertical transitions generating a vibrationally hot state and initially equilibrated vibrational oscillators evolve toward the same stationary asymptotic state associated with polaron formation. The effect of PT on the dynamics of this process depends on initial excitation and basis representation of the electronic system. The developed approach facilitates a generic formulation of quantum master equations involving perturbative treatment of polaron dynamics.
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Affiliation(s)
- Joachim Seibt
- Institute of Physics, University of Rostock, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany.,Institute for Theoretical Physics, Johannes Kepler University Linz, Altenberger Str. 69, 4040 Linz, Austria
| | - Oliver Kühn
- Institute of Physics, University of Rostock, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
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12
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Polley K, Loring RF. Two-dimensional vibrational-electronic spectra with semiclassical mechanics. J Chem Phys 2021; 154:194110. [PMID: 34240897 DOI: 10.1063/5.0051667] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Two-dimensional vibrational-electronic (2DVE) spectra probe the effects on vibronic spectra of initial vibrational excitation in an electronic ground state. The optimized mean trajectory (OMT) approximation is a semiclassical method for computing nonlinear spectra from response functions. Ensembles of classical trajectories are subject to semiclassical quantization conditions, with the radiation-matter interaction inducing discontinuous transitions. This approach has been previously applied to two-dimensional infrared and electronic spectra and is extended here to 2DVE spectra. For a system including excitonic coupling, vibronic coupling, and interaction of a chromophore vibration with a resonant environment, the OMT method is shown to well approximate exact quantum dynamics.
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Affiliation(s)
- Kritanjan Polley
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
| | - Roger F Loring
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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13
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Wong MT, Cheng YC. A quantum Langevin equation approach for two-dimensional electronic spectra of coupled vibrational and electronic dynamics. J Chem Phys 2021; 154:154107. [PMID: 33887933 DOI: 10.1063/5.0042848] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We present an efficient method to simulate two-dimensional (2D) electronic spectra of condensed-phase systems with an emphasis on treating quantum nuclear wave packet dynamics explicitly. To this end, we combine a quantum Langevin equation (QLE) approach for dissipation and a perturbative scheme to calculate three-pulse photon-echo polarizations based on wave packet dynamics under the influence of external fields. The proposed dynamical approach provides a consistent description of nuclear quantum dynamics, pulse-overlap effects, and vibrational relaxation, enabling simulations of 2D electronic spectra with explicit and non-perturbative treatment of coupled electronic-nuclear dynamics. We apply the method to simulate 2D electronic spectra of a displaced-oscillator model in the condensed phase and discuss the spectral and temporal evolutions of 2D signals. Our results show that the proposed QLE approach is capable of describing vibrational relaxation, decoherence, and vibrational coherence transfer, as well as their manifestations in spectroscopic signals. Furthermore, vibrational quantum beats specific for excited-state vs ground-state nuclear wave packet dynamics can also be identified. We anticipate that this method will provide a useful tool to conduct theoretical studies of 2D spectroscopy for strong vibronically coupled systems and to elucidate intricate vibronic couplings in complex molecular systems.
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Affiliation(s)
- Man Tou Wong
- Department of Chemistry and Center for Quantum Science and Engineering, National Taiwan University, Taipei City 106, Taiwan
| | - Yuan-Chung Cheng
- Department of Chemistry and Center for Quantum Science and Engineering, National Taiwan University, Taipei City 106, Taiwan
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14
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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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15
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Polley K, Loring RF. Spectroscopic response theory with classical mapping Hamiltonians. J Chem Phys 2020; 153:204103. [PMID: 33261495 DOI: 10.1063/5.0029231] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Exact quantum dynamics with a time-independent Hamiltonian in a discrete state space can be computed using classical mechanics through the classical Meyer-Miller-Stock-Thoss mapping Hamiltonian. In order to compute quantum response functions from classical dynamics, we extend this mapping to a quantum Hamiltonian with time-dependence arising from a classical field. This generalization requires attention to time-ordering in quantum and classical propagators. Quantum response theory with the original quantum Hamiltonian is equivalent to classical response theory with the classical mapping Hamiltonian. We elucidate the structure of classical response theory with the mapping Hamiltonian, thereby generating classical versions of the two-sided quantum density operator diagrams conventionally used to describe spectroscopic processes. This formal development can provide a foundation for new semiclassical approximations to spectroscopic observables for models in which classical nuclear degrees of freedom are introduced into a mapping Hamiltonian describing electronic states. Calculations of the temperature-dependence of two-dimensional electronic spectra for an exciton dimer using two semiclassical approaches are compared with benchmark calculations using the hierarchical equations of motion method.
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Affiliation(s)
- Kritanjan Polley
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
| | - Roger F Loring
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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16
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Polley K, Loring RF. One and Two Dimensional Vibronic Spectra for an Exciton Dimer from Classical Trajectories. J Phys Chem B 2020; 124:9913-9920. [DOI: 10.1021/acs.jpcb.0c07078] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Kritanjan Polley
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, United States
| | - Roger F. Loring
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, United States
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17
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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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18
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Sánchez Muñoz C, Schlawin F. Photon Correlation Spectroscopy as a Witness for Quantum Coherence. PHYSICAL REVIEW LETTERS 2020; 124:203601. [PMID: 32501097 DOI: 10.1103/physrevlett.124.203601] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2020] [Accepted: 04/28/2020] [Indexed: 06/11/2023]
Abstract
The development of spectroscopic techniques able to detect and verify quantum coherence is a goal of increasing importance given the rapid progress of new quantum technologies, the advances in the field of quantum thermodynamics, and the emergence of new questions in chemistry and biology regarding the possible relevance of quantum coherence in biochemical processes. Ideally, these tools should be able to detect and verify the presence of quantum coherence in both the transient dynamics and the steady state of driven-dissipative systems, such as light-harvesting complexes driven by thermal photons in natural conditions. This requirement poses a challenge for standard laser spectroscopy methods. Here, we propose photon correlation measurements as a new tool to analyze quantum dynamics in molecular aggregates in driven-dissipative situations. We show that the photon correlation statistics of the light emitted in several models of molecular aggregates can signal the presence of coherent dynamics. Deviations from the counting statistics of independent emitters constitute a direct fingerprint of quantum coherence in the steady state. Furthermore, the analysis of frequency resolved photon correlations can signal the presence of coherent dynamics even in the absence of steady state coherence, providing direct spectroscopic access to the much sought-after site energies in molecular aggregates.
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Affiliation(s)
- Carlos Sánchez Muñoz
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Frank Schlawin
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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19
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Jain A, Petit AS, Anna JM, Subotnik JE. Simple and Efficient Theoretical Approach To Compute 2D Optical Spectra. J Phys Chem B 2019; 123:1602-1617. [DOI: 10.1021/acs.jpcb.8b08674] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Amber Jain
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai, 400076, India
| | - Andrew S. Petit
- Department of Chemistry and Biochemistry, California State University, Fullerton, California 92834, United States
| | - Jessica M. Anna
- Department of Chemistry, University of Pennsylvania, 231 South 34th Street, Philadelphia, Pennsylvania 19104, United States
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, 231 South 34th Street, Philadelphia, Pennsylvania 19104, United States
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20
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Treatment of Herzberg-Teller and non-Condon effects in optical spectra with Hierarchical Equations of Motion. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2018.08.026] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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21
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Ke Y, Zhao Y. Calculations of coherent two-dimensional electronic spectra using forward and backward stochastic wavefunctions. J Chem Phys 2018; 149:014104. [DOI: 10.1063/1.5037684] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
Affiliation(s)
- Yaling Ke
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
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22
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Han L, Zhang HD, Zheng X, Yan Y. On the exact truncation tier of fermionic hierarchical equations of motion. J Chem Phys 2018; 148:234108. [PMID: 29935503 DOI: 10.1063/1.5034776] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The hierarchical equations of motion (HEOM) theory is in principle exact for describing the dissipative dynamics of quantum systems linearly coupled to Gaussian environments. In practice, the hierarchy needs to be truncated at a finite tier. We demonstrate that, for general systems described by the fermionic HEOM, the (n+L̃)th-tier truncation with L̃=2NσNν yields the exact density operators up to the nth tier. Here, Nσ = 2 for fermionic systems and Nν is the system degrees of freedom. For noninteracting systems, L̃ is further reduced by half. Such an exact termination pattern originates from the Pauli exclusion principle for fermions, and it holds true regardless of the system-environment coupling strength, the number of coupling reservoirs, or the specific scheme employed to unravel the environment memory contents. The relatively small L̃ emphasizes the nonperturbative nature of the HEOM theory. We also propose a simplified HEOM approach to further reduce the memory cost for practical calculations.
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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
| | - 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
| | - 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
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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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Fetherolf JH, Berkelbach TC. Linear and nonlinear spectroscopy from quantum master equations. J Chem Phys 2018; 147:244109. [PMID: 29289132 DOI: 10.1063/1.5006824] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.
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Affiliation(s)
- Jonathan H Fetherolf
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| | - Timothy C Berkelbach
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
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25
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Leng X, Yan YM, Zhu RD, Song K, Weng YX, Shi Q. Simulation of the Two-Dimensional Electronic Spectroscopy and Energy Transfer Dynamics of Light-Harvesting Complex II at Ambient Temperature. J Phys Chem B 2018; 122:4642-4652. [DOI: 10.1021/acs.jpcb.8b00674] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Xuan Leng
- Beijing National Laboratory for Condensed Matter Physics, CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Ya-Ming 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
| | - Rui-Dan Zhu
- Beijing National Laboratory for Condensed Matter Physics, CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Kai Song
- 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
| | - Yu-Xiang Weng
- Beijing National Laboratory for Condensed Matter Physics, CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, 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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26
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Bircher MP, Liberatore E, Browning NJ, Brickel S, Hofmann C, Patoz A, Unke OT, Zimmermann T, Chergui M, Hamm P, Keller U, Meuwly M, Woerner HJ, Vaníček J, Rothlisberger U. Nonadiabatic effects in electronic and nuclear dynamics. STRUCTURAL DYNAMICS (MELVILLE, N.Y.) 2017; 4:061510. [PMID: 29376108 PMCID: PMC5760266 DOI: 10.1063/1.4996816] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2017] [Accepted: 10/19/2017] [Indexed: 05/25/2023]
Abstract
Due to their very nature, ultrafast phenomena are often accompanied by the occurrence of nonadiabatic effects. From a theoretical perspective, the treatment of nonadiabatic processes makes it necessary to go beyond the (quasi) static picture provided by the time-independent Schrödinger equation within the Born-Oppenheimer approximation and to find ways to tackle instead the full time-dependent electronic and nuclear quantum problem. In this review, we give an overview of different nonadiabatic processes that manifest themselves in electronic and nuclear dynamics ranging from the nonadiabatic phenomena taking place during tunnel ionization of atoms in strong laser fields to the radiationless relaxation through conical intersections and the nonadiabatic coupling of vibrational modes and discuss the computational approaches that have been developed to describe such phenomena. These methods range from the full solution of the combined nuclear-electronic quantum problem to a hierarchy of semiclassical approaches and even purely classical frameworks. The power of these simulation tools is illustrated by representative applications and the direct confrontation with experimental measurements performed in the National Centre of Competence for Molecular Ultrafast Science and Technology.
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Affiliation(s)
- Martin P Bircher
- Laboratory of Computational Chemistry and Biochemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Elisa Liberatore
- Laboratory of Computational Chemistry and Biochemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Nicholas J Browning
- Laboratory of Computational Chemistry and Biochemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Sebastian Brickel
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | | | - Aurélien Patoz
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Oliver T Unke
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Tomáš Zimmermann
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Majed Chergui
- Laboratoire de Spectroscopie Ultrarapide (LSU) and Lausanne Centre for Ultrafast Science (LACUS), Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Peter Hamm
- Department of Chemistry, University of Zurich, Zürich, Switzerland
| | - Ursula Keller
- Physics Department, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Markus Meuwly
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Hans-Jakob Woerner
- Laboratorium für Physikalische Chemie, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Jiří Vaníček
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Ursula Rothlisberger
- Laboratory of Computational Chemistry and Biochemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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27
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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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28
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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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29
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Liang XT. Long-Lived Coherence Originating from Electronic-Vibrational Couplings in Light-Harvesting Complexes. CHINESE J CHEM PHYS 2017. [DOI: 10.1063/1674-0068/30/cjcp1609188] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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30
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31
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Duan HG, Frey M, Thorwart M, Nalbach P. Two-dimensional photon echoes reveal non-Markovian energy transfer in an excitonic dimer. Phys Rev E 2016; 94:052146. [PMID: 27967015 DOI: 10.1103/physreve.94.052146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2016] [Indexed: 11/07/2022]
Abstract
We show that strong non-Markovian effects can be revealed by the steady-state two-dimensional (2D) photon echo spectra at asymptotic waiting times. For this, we use a simple dimer toy model that is strongly coupled to a harmonic bath with parameters typical for photoactive biomolecules. We calculate the 2D photon echo spectra employing both the numerically exact hierarchy equation of motion and the quasiadiabatic path integral approach and compare these results with approximate results from a time-nonlocal quantum master equation approach. While the latter correctly reproduces the exact population dynamics at long times, it fails at the same time to correctly describe the 2D photon echo spectra at long waiting times. The differences show that non-Markovian effects are much more important for the steady-state 2D photon echoes than for the equilibrium populations. Thus, accurate theoretical descriptions of the energy transfer dynamics in biomolecular complexes have to be based on numerically exact simulations of the environmental fluctuations when nonlinear response functions are analyzed.
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Affiliation(s)
- Hong-Guang Duan
- I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355 Hamburg, Germany.,The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany.,Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Moritz Frey
- I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355 Hamburg, Germany.,Physikalisches Institut, Universität Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Michael Thorwart
- I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355 Hamburg, Germany.,The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Peter Nalbach
- Westfälische Hochschule, Münsterstrasse 265, 46397 Bocholt, Germany
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32
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Chorošajev V, Gelzinis A, Valkunas L, Abramavicius D. Benchmarking the stochastic time-dependent variational approach for excitation dynamics in molecular aggregates. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.06.014] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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33
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Ding JJ, Zhang HD, Wang Y, Xu RX, Zheng X, Yan Y. Minimum-exponents ansatz for molecular dynamics and quantum dissipation. J Chem Phys 2016; 145:204110. [DOI: 10.1063/1.4967964] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jin-Jin Ding
- School of Chemistry and Chemical Engineering, Nantong University, Nantong, Jiangsu 226019, China
| | - Hou-Dao Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and iChEM and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and iChEM and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rui-Xue Xu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and iChEM 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 Department of Chemical Physics and iChEM 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 Department of Chemical Physics and iChEM and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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34
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Holdaway DIH, Collini E, Olaya-Castro A. Coherence specific signal detection via chiral pump-probe spectroscopy. J Chem Phys 2016; 144:194112. [DOI: 10.1063/1.4948943] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- David I. H. Holdaway
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Elisabetta Collini
- Department of Chemical Sciences, University of Padova, I-35131 Padova, Italy
| | - Alexandra Olaya-Castro
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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35
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Liang XT. Simulating signatures of two-dimensional electronic spectra of the Fenna-Matthews-Olson complex: By using a numerical path integral. J Chem Phys 2015; 141:044116. [PMID: 25084890 DOI: 10.1063/1.4890533] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
A framework for simulating electronic spectra from photon-echo experiments is constructed by using a numerical path integral technique. This method is non-Markovian and nonperturbative and, more importantly, is not limited by a fixed form of the spectral density functions of the environment. Next, a two-dimensional (2D) third-order electronic spectrum of a dimer system is simulated. The spectrum is in agreement with the experimental and theoretical results previously reported [for example, M. Khalil, N. Demirdöven, and A. Tokmakoff, Phys. Rev. Lett. 90, 047401 (2003)]. Finally, a 2D third-order electronic spectrum of the Fenna-Matthews-Olson (FMO) complex is simulated by using the Debye, Ohmic, and Adolphs and Renger spectral density functions. It is shown that this method can clearly produce the spectral signatures of the FMO complex by using only the Adolphs and Renger spectral density function. Plots of the evolution of the diagonal and cross-peaks show that they are oscillating with the population time.
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Affiliation(s)
- Xian-Ting Liang
- Department of Physics and Institute of Optics, Ningbo University, Ningbo 315211, China
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36
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Jing YY, Song K, Bai SM, Shi Q. Linear and Nonlinear Spectra in Photosynthetic Light Harvesting Complexes: Benchmark Tests of Modified Redfield Method. CHINESE J CHEM PHYS 2015. [DOI: 10.1063/1674-0068/28/cjcp1506126] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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37
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Yeh SH, Kais S. Simulated two-dimensional electronic spectroscopy of the eight-bacteriochlorophyll FMO complex. J Chem Phys 2015; 141:234105. [PMID: 25527917 DOI: 10.1063/1.4903546] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
The Fenna-Matthews-Olson (FMO) protein-pigment complex acts as a molecular wire conducting energy between the outer antenna system and the reaction center; it is an important photosynthetic system to study the transfer of excitonic energy. Recent crystallographic studies report the existence of an additional (eighth) bacteriochlorophyll a (BChl a) in some of the FMO monomers. To understand the functionality of this eighth BChl, we simulated the two-dimensional electronic spectra of both the 7-site (apo form) and the 8-site (holo form) variant of the FMO complex from green sulfur bacteria, Prosthecochloris aestuarii. By comparing the spectrum, it was found that the eighth BChl can affect two different excitonic energy transfer pathways: (1) it is directly involved in the first apo form pathway (6 → 3 → 1) by passing the excitonic energy to exciton 6; and (2) it facilitates an increase in the excitonic wave function overlap between excitons 4 and 5 in the second pathway (7 → 4,5 → 2 → 1) and thus increases the possible downward sampling routes across the BChls.
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Affiliation(s)
- Shu-Hao Yeh
- Department of Chemistry and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - Sabre Kais
- Department of Chemistry and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
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38
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Liu H, Zhu L, Bai S, Shi Q. Reduced quantum dynamics with arbitrary bath spectral densities: hierarchical equations of motion based on several different bath decomposition schemes. J Chem Phys 2015; 140:134106. [PMID: 24712779 DOI: 10.1063/1.4870035] [Citation(s) in RCA: 87] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigated applications of the hierarchical equation of motion (HEOM) method to perform high order perturbation calculations of reduced quantum dynamics for a harmonic bath with arbitrary spectral densities. Three different schemes are used to decompose the bath spectral density into analytical forms that are suitable to the HEOM treatment: (1) The multiple Lorentzian mode model that can be obtained by numerically fitting the model spectral density. (2) The combined Debye and oscillatory Debye modes model that can be constructed by fitting the corresponding classical bath correlation function. (3) A new method that uses undamped harmonic oscillator modes explicitly in the HEOM formalism. Methods to extract system-bath correlations were investigated for the above bath decomposition schemes. We also show that HEOM in the undamped harmonic oscillator modes can give detailed information on the partial Wigner transform of the total density operator. Theoretical analysis and numerical simulations of the spin-Boson dynamics and the absorption line shape of molecular dimers show that the HEOM formalism for high order perturbations can serve as an important tool in studying the quantum dissipative dynamics in the intermediate coupling regime.
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Affiliation(s)
- Hao 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, Zhongguancun, Beijing 100190, China
| | - Lili Zhu
- 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
| | - Shuming Bai
- 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
| | - 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
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39
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Leng X, Liang XT. Simulation of two-dimensional electronic spectra of phycoerythrin 545 at ambient temperature. J Phys Chem B 2014; 118:12366-70. [PMID: 25299464 DOI: 10.1021/jp506974r] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
By using a hierarchical equations-of-motion approach, we reproduce the two-dimensional electronic spectra of phycoerythrin 545 from Rhodomonas CS24 at ambient temperature (294 K). The simulated spectra are in agreement with the experimental results reported in Wong et al. (Nat. Chem. 2012, 4, 396). The evolutions of cross peaks for rephasing spectra and diagonal peaks for nonrephasing spectra have also been plotted. The peaks oscillate with the population times, with frequencies, phases, and amplitudes of the oscillating curves also being qualitatively consistent with the experimental results.
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Affiliation(s)
- Xuan Leng
- Department of Physics and Institute of Optics, Ningbo University , Ningbo 315211, China
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40
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Grossmann F. Quantum effects in intermediate-temperature dipole-dipole correlation-functions in the presence of an environment. J Chem Phys 2014; 141:144305. [DOI: 10.1063/1.4896835] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- F. Grossmann
- Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
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41
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42
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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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43
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Mineo H, Lin SH, Fujimura Y, Xu J, Xu RX, Yan YJ. Non-Markovian response of ultrafast coherent electronic ring currents in chiral aromatic molecules in a condensed phase. J Chem Phys 2013; 139:214306. [DOI: 10.1063/1.4834035] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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44
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Tempelaar R, van der Vegte CP, Knoester J, Jansen TLC. Surface hopping modeling of two-dimensional spectra. J Chem Phys 2013; 138:164106. [DOI: 10.1063/1.4801519] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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45
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van der Vegte CP, Dijkstra AG, Knoester J, Jansen TLC. Calculating Two-Dimensional Spectra with the Mixed Quantum-Classical Ehrenfest Method. J Phys Chem A 2013; 117:5970-80. [DOI: 10.1021/jp311668r] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- C. P. van der Vegte
- Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
| | - A. G. Dijkstra
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts
Avenue, Cambridge, Massachusetts 02139, United States
| | - J. Knoester
- Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
| | - T. L. C. Jansen
- Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
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46
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Jing Y, Chen L, Bai S, Shi Q. Equilibrium excited state and emission spectra of molecular aggregates from the hierarchical equations of motion approach. J Chem Phys 2013; 138:045101. [DOI: 10.1063/1.4775843] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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47
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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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Ding JJ, Xu RX, Yan Y. Optimizing hierarchical equations of motion for quantum dissipation and quantifying quantum bath effects on quantum transfer mechanisms. J Chem Phys 2012; 136:224103. [PMID: 22713032 DOI: 10.1063/1.4724193] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present an optimized hierarchical equations of motion theory for quantum dissipation in multiple Brownian oscillators bath environment, followed by a mechanistic study on a model donor-bridge-acceptor system. We show that the optimal hierarchy construction, via the memory-frequency decomposition for any specified Brownian oscillators bath, is generally achievable through a universal pre-screening search. The algorithm goes by identifying the candidates for the best be just some selected Padé spectrum decomposition based schemes, together with a priori accuracy control criterions on the sole approximation, the white-noise residue ansatz, involved in the hierarchical construction. Beside the universal screening search, we also analytically identify the best for the case of Drude dissipation and that for the Brownian oscillators environment without strongly underdamped bath vibrations. For the mechanistic study, we quantify the quantum nature of bath influence and further address the issue of localization versus delocalization. Proposed are a reduced system entropy measure and a state-resolved constructive versus destructive interference measure. Their performances on quantifying the correlated system-environment coherence are exemplified in conjunction with the optimized hierarchical equations of motion evaluation of the model system dynamics, at some representing bath parameters and temperatures. Analysis also reveals the localization to delocalization transition as temperature decreases.
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Affiliation(s)
- Jin-Jin Ding
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
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Bixner O, Lukeš V, Mančal T, Hauer J, Milota F, Fischer M, Pugliesi I, Bradler M, Schmid W, Riedle E, Kauffmann HF, Christensson N. Ultrafast photo-induced charge transfer unveiled by two-dimensional electronic spectroscopy. J Chem Phys 2012; 136:204503. [DOI: 10.1063/1.4720492] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
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Seibt J, Eisfeld A. Intermolecular torsional motion of a π-aggregated dimer probed by two-dimensional electronic spectroscopy. J Chem Phys 2012; 136:024109. [DOI: 10.1063/1.3674993] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
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