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Gelin MF, Chen L, Domcke W. Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals. Chem Rev 2022; 122:17339-17396. [PMID: 36278801 DOI: 10.1021/acs.chemrev.2c00329] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.
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Affiliation(s)
- Maxim F Gelin
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Lipeng Chen
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technical University of Munich, D-85747 Garching,Germany
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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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3
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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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4
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Sala M, Egorova D. Two-dimensional photon-echo spectroscopy at a conical intersection: A two-mode pyrazine model with dissipation. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.08.034] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
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Duan HG, Dijkstra AG, Nalbach P, Thorwart M. Efficient tool to calculate two-dimensional optical spectra for photoactive molecular complexes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042708. [PMID: 26565273 DOI: 10.1103/physreve.92.042708] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2015] [Indexed: 06/05/2023]
Abstract
We combine the coherent modified Redfield theory (CMRT) with the equation of motion-phase matching approach (PMA) to calculate two-dimensional photon-echo spectra for photoactive molecular complexes with an intermediate strength of the coupling to their environment. Both techniques are highly efficient, yet they involve approximations at different levels. By explicitly comparing with the numerically exact quasiadiabatic path integral approach, we show for the Fenna-Matthews-Olson complex that the CMRT describes the decay rates in the population dynamics well, but final stationary populations and the oscillation frequencies differ slightly. In addition, we use the combined CMRT+PMA to calculate two-dimensional photon-echo spectra for a simple dimer model. We find excellent agreement with the exact path integral calculations at short waiting times where the dynamics is still coherent. For long waiting times, differences occur due to different final stationary states, specifically for strong system-bath coupling. For weak to intermediate system-bath couplings, which is most important for natural photosynthetic complexes, the combined CMRT+PMA gives reasonable results with acceptable computational efforts.
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Affiliation(s)
- Hong-Guang Duan
- I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355 Hamburg, Germany
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Arend G Dijkstra
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Peter Nalbach
- I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, 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
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Yan TM, Fresch B, Levine RD, Remacle F. Information processing in parallel through directionally resolved molecular polarization components in coherent multidimensional spectroscopy. J Chem Phys 2015; 143:064106. [DOI: 10.1063/1.4928066] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tian-Min Yan
- Department de Chimie, B6c, Université de Liège, B4000 Liège, Belgium
| | - Barbara Fresch
- Department de Chimie, B6c, Université de Liège, B4000 Liège, Belgium
| | - R. D. Levine
- The Fritz Haber Research Center for Molecular Dynamics, The Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
- Crump Institute for Molecular Imaging and Department of Molecular and Medical Pharmacology, David Geffen School of Medicine and Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
| | - F. Remacle
- Department de Chimie, B6c, Université de Liège, B4000 Liège, Belgium
- The Fritz Haber Research Center for Molecular Dynamics, The Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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Jeske J, Ing DJ, Plenio MB, Huelga SF, Cole JH. Bloch-Redfield equations for modeling light-harvesting complexes. J Chem Phys 2015; 142:064104. [DOI: 10.1063/1.4907370] [Citation(s) in RCA: 56] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Affiliation(s)
- Jan Jeske
- Chemical and Quantum Physics, School of Applied Sciences, RMIT University, Melbourne 3001, Australia
| | - David J. Ing
- Chemical and Quantum Physics, School of Applied Sciences, RMIT University, Melbourne 3001, Australia
| | - Martin B. Plenio
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, D-89069 Ulm, Germany
| | - Susana F. Huelga
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, D-89069 Ulm, Germany
| | - Jared H. Cole
- Chemical and Quantum Physics, School of Applied Sciences, RMIT University, Melbourne 3001, Australia
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Seibt J, Pullerits T. Combined treatment of relaxation and fluctuation dynamics in the calculation of two-dimensional electronic spectra. J Chem Phys 2014; 141:114106. [DOI: 10.1063/1.4895401] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Affiliation(s)
- Joachim Seibt
- Department of Chemical Physics, Lund University, Box 124, SE-2100 Lund, Sweden
| | - Tõnu Pullerits
- Department of Chemical Physics, Lund University, Box 124, SE-2100 Lund, Sweden
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Egorova D. Oscillations in two-dimensional photon-echo signals of excitonic and vibronic systems: Stick-spectrum analysis and its computational verification. J Chem Phys 2014; 140:034314. [DOI: 10.1063/1.4861634] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Abstract
The outcome of a light-matter interaction depends on both the state of matter and the state of light. It is thus a natural setting for implementing bilinear classical logic. A description of the state of a time-varying system requires measuring an (ideally complete) set of time-dependent observables. Typically, this is prohibitive, but in weak-field spectroscopy we can move toward this goal because only a finite number of levels are accessible. Recent progress in nonlinear spectroscopies means that nontrivial measurements can be implemented and thereby give rise to interesting logic schemes where the outputs are functions of the observables. Lie algebra offers a natural tool for generating the outcome of the bilinear light-matter interaction. We show how to synthesize these ideas by explicitly discussing three-photon spectroscopy of a bichromophoric molecule for which there are four accessible states. Switching logic would use the on-off occupancies of these four states as outcomes. Here, we explore the use of all 16 observables that define the time-evolving state of the bichromophoric system. The bilinear laser-system interaction with the three pulses of the setup of a 2D photon echo spectroscopy experiment can be used to generate a rich parallel logic that corresponds to the implementation of a molecular decision tree. Our simulations allow relaxation by weak coupling to the environment, which adds to the complexity of the logic operations.
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Krčmář J, Gelin MF, Domcke W. Calculation of third-order signals via driven Schrödinger equations: General results and application to electronic 2D photon echo spectroscopy. Chem Phys 2013. [DOI: 10.1016/j.chemphys.2013.01.002] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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12
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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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13
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Parkhill JA, Tempel DG, Aspuru-Guzik A. Exciton coherence lifetimes from electronic structure. J Chem Phys 2012; 136:104510. [DOI: 10.1063/1.3689858] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Polyutov S, Kühn O, Pullerits T. Exciton-vibrational coupling in molecular aggregates: Electronic versus vibronic dimer. Chem Phys 2012. [DOI: 10.1016/j.chemphys.2011.12.006] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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15
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Yuen-Zhou J, Aspuru-Guzik A. Quantum process tomography of excitonic dimers from two-dimensional electronic spectroscopy. I. General theory and application to homodimers. J Chem Phys 2011; 134:134505. [PMID: 21476762 DOI: 10.1063/1.3569694] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Is it possible to infer the time evolving quantum state of a multichromophoric system from a sequence of two-dimensional electronic spectra (2D-ES) as a function of waiting time? Here we provide a positive answer for a tractable model system: a coupled dimer. After exhaustively enumerating the Liouville pathways associated to each peak in the 2D-ES, we argue that by judiciously combining the information from a series of experiments varying the polarization and frequency components of the pulses, detailed information at the amplitude level about the input and output quantum states at the waiting time can be obtained. This possibility yields a quantum process tomography (QPT) of the single-exciton manifold, which completely characterizes the open quantum system dynamics through the reconstruction of the process matrix. In this manuscript, we present the general theory as well as specific and numerical results for a homodimer, for which we prove that signals stemming from coherence to population transfer and vice versa vanish upon isotropic averaging, therefore, only allowing for a partial QPT in such case. However, this fact simplifies the spectra, and it follows that only two polarization controlled experiments (and no pulse-shaping requirements) suffice to yield the elements of the process matrix, which survive under isotropic averaging. Redundancies in the 2D-ES amplitudes allow for the angle between the two site transition dipole moments to be self-consistently obtained, hence simultaneously yielding structural and dynamical information of the dimer. Model calculations are presented, as well as an error analysis in terms of the angle between the dipoles and peak amplitude extraction. In the second article accompanying this study, we numerically exemplify the theory for heterodimers and carry out a detailed error analysis for such case. This investigation reveals an exciting quantum information processing (QIP) approach to spectroscopic experiments of excitonic systems, and hence, bridges an important gap between theoretical studies on excitation energy transfer from the QIP standpoint and experimental methods to study such systems in the chemical physics community.
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Affiliation(s)
- Joel Yuen-Zhou
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
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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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17
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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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Renger T. Theory of excitation energy transfer: from structure to function. PHOTOSYNTHESIS RESEARCH 2009; 102:471-485. [PMID: 19653118 DOI: 10.1007/s11120-009-9472-9] [Citation(s) in RCA: 132] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2008] [Accepted: 07/09/2009] [Indexed: 05/28/2023]
Abstract
This mini-review summarizes our current theoretical knowledge about excitation energy transfer in pigment-protein complexes. The challenge for theory lies in the complexity of these systems and in the fact that the pigment-pigment and the pigment-protein interactions are of equal magnitude. The first part of this review contains an introduction to the theory of light harvesting and to structure- based calculations of the parameters of the theory. The second part provides a discussion of the standard Förster and Redfield theories of excitation energy transfer, which are valid in the limit of weak and strong pigment-pigment coupling, respectively. Afterward, we provide a description of recent extensions of the standard theories and discuss challenging problems to be solved in the future.
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Affiliation(s)
- Thomas Renger
- Institut für Chemie und Biochemie, Freie Universität Berlin, Fabeckstrasse 36a, 14195 Berlin, Germany.
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19
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Gelin MF, Egorova D, Domcke W. Efficient calculation of time- and frequency-resolved four-wave-mixing signals. Acc Chem Res 2009; 42:1290-8. [PMID: 19449854 DOI: 10.1021/ar900045d] [Citation(s) in RCA: 72] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
"Four-wave-mixing" is the generic name for a family of nonlinear electronic and vibrational spectroscopies. These techniques are widely used to explore dissipation, dephasing, solvation, and interstate coupling mechanisms in various material systems. Four-wave-mixing spectroscopy needs a firm theoretical support, because it delivers information on material systems indirectly, through certain transients, which are measured as functions of carrier frequencies, durations, and relative time delays of the laser pulses. The observed transients are uniquely determined by the three-pulse-induced third-order polarization. There exist two conceptually different approaches to the calculation of the nonlinear polarization. In the standard perturbative approach to nonlinear spectroscopy, the third-order polarization is expressed in terms of the nonlinear response functions. As the material systems become more complex, the evaluation of the response functions becomes cumbersome and the calculation of the signals necessitates a number of approximations. Herein, we review alternative methods for the calculation of four-wave-mixing signals, in which the relevant laser pulses are incorporated into the system Hamiltonian and the driven system dynamics is simulated numerically exactly. The emphasis is on the recently developed equation-of-motion phase-matching approach (EOM-PMA), which allows us to calculate the three-pulse-induced third-order polarization in any phase-matching direction by performing three (with the rotating wave approximation) or seven (without the rotating wave approximation) independent propagations of the density matrix. The EOM-PMA is limited to weak laser fields (its domain of validity is equivalent to the approach based on the third-order response functions) but allows for arbitrary pulse durations and automatically accounts for pulse-overlap effects. As an illustration, we apply the EOM-PMA to the calculation of optical three-pulse photon-echo two-dimensional (2D) signals for a generic model system, which represents a characteristic photophysical dynamics of large molecules or chromophores in condensed phases. The EOM-PMA is easy to implement and can straightforwardly be incorporated into any computational scheme, which provides the time-dependent density matrix or wave function of the material system of interest. In particular, EOM-PMA-based computer codes can efficiently be implemented on parallel computers. The EOM-PMA facilitates considerably the computation of four-wave-mixing signals and 2D spectra, in both vibrational and electronic spectroscopy. The EOM-PMA can be extended to higher order optical responses, e.g., heterodyned 3D IR, transient 2D IR, and other six-wave-mixing techniques.
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Affiliation(s)
- Maxim F. Gelin
- Department of Chemistry, Technical University of Munich, D-85747 Garching, Germany
| | - Dassia Egorova
- Department of Chemistry, Technical University of Munich, D-85747 Garching, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technical University of Munich, D-85747 Garching, Germany
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Seibt J, Renziehausen K, Voronine DV, Engel V. Probing the geometry dependence of molecular dimers with two-dimensional-vibronic spectroscopy. J Chem Phys 2009; 130:134318. [DOI: 10.1063/1.3086935] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
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Sperling J, Nemeth A, Baum P, Šanda F, Riedle E, Kauffmann H, Mukamel S, Milota F. Exciton dynamics in a disordered conjugated polymer: Three-pulse photon-echo and transient grating experiments. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2008.02.046] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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22
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Egorova D. Detection of electronic and vibrational coherences in molecular systems by 2D electronic photon echo spectroscopy. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2007.12.019] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Brüggemann B, Persson P, Meyer HD, May V. Frequency dispersed transient absorption spectra of dissolved perylene: A case study using the density matrix version of the MCTDH method. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2007.11.001] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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25
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Analysis of vibrational coherences in homodyne and two-dimensional heterodyne photon-echo spectra of Nile Blue. Chem Phys 2007. [DOI: 10.1016/j.chemphys.2007.07.010] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Cheng YC, Lee H, Fleming GR. Efficient Simulation of Three-Pulse Photon-Echo Signals with Application to the Determination of Electronic Coupling in a Bacterial Photosynthetic Reaction Center. J Phys Chem A 2007; 111:9499-508. [PMID: 17696328 DOI: 10.1021/jp0735177] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A time-nonlocal quantum master equation coupled with a perturbative scheme to evaluate the third-order polarization in the phase-matching direction k(s) = -k(1) + k(2) + k(3) is used to efficiently simulate three-pulse photon-echo signals. The present method is capable of describing photon-echo peak shifts including pulse overlap and bath memory effects. In addition, the method treats the non-Markovian evolution of the density matrix and the third-order polarization in a consistent manner, thus is expected to be useful in systems with rapid and complex dynamics. We apply the theoretical method to describe one- and two-color three-pulse photon-echo peak shift experiments performed on a bacterial photosynthetic reaction center and demonstrate that, by properly incorporating the pulse overlap effects, the method can be used to describe simultaneously all peak shift experiments and determine the electronic coupling between the localized Q(y) excitations on the bacteriopheophytin (BPhy) and accessory bateriochlorophyll (BChl) in the reaction center. A value of J = 250 cm(-1) is found for the coupling between BPhy and BChl.
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Affiliation(s)
- Yuan-Chung Cheng
- Department of Chemistry and QB3 Institute, University of California Berkeley, Berkeley, California 94720, USA
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Non-perturbative calculation of 2D spectra in heterogeneous systems: Exciton relaxation in the FMO complex. Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2007.07.002] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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28
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Egorova D, Gelin MF, Domcke W. Analysis of cross peaks in two-dimensional electronic photon-echo spectroscopy for simple models with vibrations and dissipation. J Chem Phys 2007; 126:074314. [PMID: 17328612 DOI: 10.1063/1.2435353] [Citation(s) in RCA: 74] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
Abstract
The recently developed efficient method for the calculation of four-wave mixing signals [M. F. Gelin et al., J. Chem. Phys. 123, 164112 (2005)] is employed for the calculation of two-dimensional electronic photon-echo spectra. The effect of the explicit treatment of vibrations coupled to the electronic transitions is systematically analyzed. The impact of pulse durations, optical dephasing, and temperature on the spectra is investigated. The study aims at an understanding of the mechanisms which may give rise to cross peaks in the two-dimensional electronic spectra and at clarifying the conditions of their detection.
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Affiliation(s)
- Dassia Egorova
- Department of Chemistry, Technical University of Munich, D-85747 Garching, Germany
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Adolphs J, Renger T. How proteins trigger excitation energy transfer in the FMO complex of green sulfur bacteria. Biophys J 2006; 91:2778-97. [PMID: 16861264 PMCID: PMC1578489 DOI: 10.1529/biophysj.105.079483] [Citation(s) in RCA: 421] [Impact Index Per Article: 23.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
A simple electrostatic method for the calculation of optical transition energies of pigments in protein environments is presented and applied to the Fenna-Matthews-Olson (FMO) complex of Prosthecochloris aestuarii and Chlorobium tepidum. The method, for the first time, allows us to reach agreement between experimental optical spectra and calculations based on transition energies of pigments that are calculated in large part independently, rather than fitted to the spectra. In this way it becomes possible to understand the molecular mechanism allowing the protein to trigger excitation energy transfer reactions. The relative shift in excitation energies of the seven bacteriochlorophyll-a pigments of the FMO complex of P. aestuarii and C. tepidum are obtained from calculations of electrochromic shifts due to charged amino acids, assuming a standard protonation pattern of the protein, and by taking into account the three different ligand types of the pigments. The calculations provide an explanation of some of the earlier results for the transition energies obtained from fits of optical spectra. In addition, those earlier fits are verified here by using a more advanced theory of optical spectra, a genetic algorithm, and excitonic couplings obtained from electrostatic calculations that take into account the influence of the dielectric protein environment. The two independent calculations of site energies strongly favor one of the two possible orientations of the FMO trimer relative to the photosynthetic membrane, which were identified by electron microscopic studies and linear dichroism experiments. Efficient transfer of excitation energy to the reaction center requires bacteriochlorophylls 3 and 4 to be the linker pigments. The temporal and spatial transfer of excitation energy through the FMO complex is calculated to proceed along two branches, with transfer times that differ by an order of magnitude.
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Affiliation(s)
- Julia Adolphs
- Institut für Chemie und Biochemie, Freie Universität Berlin, Berlin, Germany
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