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Jansen TLC, Saito S, Jeon J, Cho M. Theory of coherent two-dimensional vibrational spectroscopy. J Chem Phys 2019; 150:100901. [DOI: 10.1063/1.5083966] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Thomas la Cour Jansen
- University of Groningen, Zernike Institute for Advanced Materials, Nijenborgh 4, 9747 AG Groningen, The Netherlands
| | - Shinji Saito
- Institute for Molecular Science, Myodaiji, Okazaki, Aichi 444-8585, Japan and The Graduate University for Advanced Studies, Myodaiji, Okazaki, Aichi 444-8585, Japan
| | - Jonggu Jeon
- Center for Molecular Spectroscopy and Dynamics, Institute for Basic Science (IBS), Seoul 02841, South Korea
| | - Minhaeng Cho
- Center for Molecular Spectroscopy and Dynamics, Institute for Basic Science (IBS), Seoul 02841, South Korea
- Department of Chemistry, Korea University, Seoul 02841, South Korea
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2
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Schröter M, Pullerits T, Kühn O. Using fluorescence detected two-dimensional spectroscopy to investigate initial exciton delocalization between coupled chromophores. J Chem Phys 2018; 149:114107. [DOI: 10.1063/1.5046645] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Marco Schröter
- Institute of Physics, University of Rostock, Albert Einstein Straße 23-24, 18059 Rostock, Germany
| | - Tõnu Pullerits
- Chemical Physics and NanoLund, Lund University, P.O. Box 124, 22100 Lund, Sweden
| | - Oliver Kühn
- Institute of Physics, University of Rostock, Albert Einstein Straße 23-24, 18059 Rostock, Germany
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3
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Gottwald F, Ivanov SD, Kühn O. Applicability of the Caldeira-Leggett Model to Vibrational Spectroscopy in Solution. J Phys Chem Lett 2015; 6:2722-2727. [PMID: 26266853 DOI: 10.1021/acs.jpclett.5b00718] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Formulating a rigorous system-bath partitioning approach remains an open issue. In this context, the famous Caldeira-Leggett model that enables quantum and classical treatment of Brownian motion on equal footing has enjoyed popularity. Although this model is by any means a useful theoretical tool, its ability to describe anharmonic dynamics of real systems is often taken for granted. In this Letter, we show that the mapping between a molecular system under study and the model cannot be established in a self-consistent way, unless the system part of the potential is taken effectively harmonic. Mathematically, this implies that the mapping is not invertible. This "invertibility problem" is not dependent on the peculiarities of particular molecular systems and is rooted in the anharmonicity of the system part of the Caldeira-Leggett model potential.
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Affiliation(s)
- Fabian Gottwald
- Institute of Physics, University of Rostock, Universitätsplatz 3, 18055 Rostock, Germany
| | - Sergei D Ivanov
- Institute of Physics, University of Rostock, Universitätsplatz 3, 18055 Rostock, Germany
| | - Oliver Kühn
- Institute of Physics, University of Rostock, Universitätsplatz 3, 18055 Rostock, Germany
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4
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Shi Q, Zhu L, Chen L. Quantum rate dynamics for proton transfer reaction in a model system: Effect of the rate promoting vibrational mode. J Chem Phys 2011; 135:044505. [DOI: 10.1063/1.3611050] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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5
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Strümpfer J, Schulten K. The effect of correlated bath fluctuations on exciton transfer. J Chem Phys 2011; 134:095102. [PMID: 21385000 PMCID: PMC3064689 DOI: 10.1063/1.3557042] [Citation(s) in RCA: 86] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2010] [Accepted: 02/01/2011] [Indexed: 01/27/2023] Open
Abstract
Excitation dynamics of various light harvesting systems have been investigated with many theoretical methods including various non-Markovian descriptions of dissipative quantum dynamics. It is typically assumed that each excited state is coupled to an independent thermal environment, i.e., that fluctuations in different environments are uncorrelated. Here the assumption is dropped and the effect of correlated bath fluctuations on excitation transfer is investigated. Using the hierarchy equations of motion for dissipative quantum dynamics it is shown for models of the B850 bacteriochlorophylls of LH2 that correlated bath fluctuations have a significant effect on the LH2→LH2 excitation transfer rate. It is also demonstrated that inclusion of static disorder is crucial for an accurate description of transfer dynamics.
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Affiliation(s)
- Johan Strümpfer
- Center for Biophysics and Computational Biology, University of Illinois at Urbana-Champaign, Urbana, USA
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6
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Sahrapour MM, Makri N. Multitime response functions and nonlinear spectra for model quantum dissipative systems. J Chem Phys 2010; 132:134506. [DOI: 10.1063/1.3336463] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
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7
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Tanimura Y, Ishizaki A. Modeling, calculating, and analyzing multidimensional vibrational spectroscopies. Acc Chem Res 2009; 42:1270-9. [PMID: 19441802 DOI: 10.1021/ar9000444] [Citation(s) in RCA: 77] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Spectral line shapes in a condensed phase contain information from various dynamic processes that modulate the transition energy, such as microscopic dynamics, inter- and intramolecular couplings, and solvent dynamics. Because nonlinear response functions are sensitive to the complex dynamics of chemical processes, multidimensional vibrational spectroscopies can separate these processes. In multidimensional vibrational spectroscopy, the nonlinear response functions of a molecular dipole or polarizability are measured using ultrashort pulses to monitor inter- and intramolecular vibrational motions. Because a complex profile of such signals depends on the many dynamic and structural aspects of a molecular system, researchers would like to have a theoretical understanding of these phenomena. In this Account, we explore and describe the roles of different physical phenomena that arise from the peculiarities of the system-bath coupling in multidimensional spectra. We also present simple analytical expressions for a weakly coupled multimode Brownian system, which we use to analyze the results obtained by the experiments and simulations. To calculate the nonlinear optical response, researchers commonly use a particular form of a system Hamiltonian fit to the experimental results. The optical responses of molecular vibrational motions have been studied in either an oscillator model or a vibration energy state model. In principle, both models should give the same results as long as the energy states are chosen to be the eigenstates of the oscillator model. The energy state model can provide a simple description of nonlinear optical processes because the diagrammatic Liouville space theory that developed in the electronically resonant spectroscopies can easily handle three or four energy states involved in high-frequency vibrations. However, the energy state model breaks down if we include the thermal excitation and relaxation processes in the dynamics to put the system in a thermal equilibrium state. The roles of these excitation and relaxation processes are different and complicated compared with those in the resonant spectroscopy. Observing the effects of such thermal processes is more intuitive with the oscillator model because the bath modes, which cause the fluctuation and dissipation processes, are also described in the coordinate space. This coordinate space system-bath approach complements a realistic full molecular dynamics simulation approach. By comparing the calculated 2D spectra from the coordinate space model and the energy state model, we can examine the role of thermal processes and anharmonic mode-mode couplings in the energy state model. For this purpose, we employed the Brownian oscillator model with the nonlinear system-bath interaction. Using the hierarchy formalism, we could precisely calculate multidimensional spectra for a single and multimode anharmonic system for inter- and intramolecular vibrational modes.
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Affiliation(s)
- Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University Kitashirakawa, Sakyoku, Kyoto 606-8502, Japan
| | - Akihito Ishizaki
- Department of Chemistry, Graduate School of Science, Kyoto University Kitashirakawa, Sakyoku, Kyoto 606-8502, Japan
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8
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Mercer IP, El-Taha YC, Kajumba N, Marangos JP, Tisch JWG, Gabrielsen M, Cogdell RJ, Springate E, Turcu E. Instantaneous mapping of coherently coupled electronic transitions and energy transfers in a photosynthetic complex using angle-resolved coherent optical wave-mixing. PHYSICAL REVIEW LETTERS 2009. [PMID: 19257551 DOI: 10.1103/physreva.82.043406] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
Understanding the role of coherent electronic motion is expected to resolve general questions of importance in macromolecular energy transfer. We demonstrate a novel nonlinear optical method, angle-resolved coherent wave mixing, that separates out coherently coupled electronic transitions and energy transfers in an instantaneous two-dimensional mapping. Angular resolution of the signal is achieved by using millimeter laser beam waists at the sample and by signal relay to the far field; for this we use a high energy, ultrabroadband hollow fiber laser source. We reveal quantum electronic beating with a time-ordered selection of transition energies in a photosynthetic complex.
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Affiliation(s)
- Ian P Mercer
- School of Physics, Centre for Synthesis and Chemical Biology, University College Dublin, Dublin 4, Ireland
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9
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Ishizaki A, Tanimura Y. Nonperturbative non-Markovian quantum master equation: Validity and limitation to calculate nonlinear response functions. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2007.10.037] [Citation(s) in RCA: 92] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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10
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Ishizaki A, Tanimura Y. Dynamics of a Multimode System Coupled to Multiple Heat Baths Probed by Two-Dimensional Infrared Spectroscopy. J Phys Chem A 2007; 111:9269-76. [PMID: 17880172 DOI: 10.1021/jp072880a] [Citation(s) in RCA: 76] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Reduced equation of motion for a multimode system coupled to multiple heat baths is constructed by extending the quantum Fokker-Planck equation with low-temperature correction terms (J. Phys. Soc. Jpn. 2005, 74, 3131). Unlike such common approaches used to describe intramolecular multimode vibration as a Bloch-Redfield theory and a stochastic theory, the present formalism is defined by the molecular coordinates. To explore the correlation among different modes through baths, we consider two cases of system-bath couplings. One is a correlated case in which two modes are coupled to a single bath, and the other is an uncorrelated case in which each mode is coupled to a different bath. We further classify the correlated case into two cases, the plus- and minus-correlated cases, according to distinct correlation manners. For these, one-dimensional and two-dimensional infrared (2D-IR) spectra are calculated numerically by solving the equation of motion. It is demonstrated that 2D-IR spectroscopy has the ability to analyze the correlation of fluctuation-dissipation processes among different modes.
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Affiliation(s)
- Akihito Ishizaki
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
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11
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Ishizaki A, Tanimura Y. Modeling vibrational dephasing and energy relaxation of intramolecular anharmonic modes for multidimensional infrared spectroscopies. J Chem Phys 2006; 125:084501. [PMID: 16965023 DOI: 10.1063/1.2244558] [Citation(s) in RCA: 100] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Starting from a system-bath Hamiltonian in a molecular coordinate representation, we examine an applicability of a stochastic multilevel model for vibrational dephasing and energy relaxation in multidimensional infrared spectroscopy. We consider an intramolecular anharmonic mode nonlinearly coupled to a colored noise bath at finite temperature. The system-bath interaction is assumed linear plus square in the system coordinate, but linear in the bath coordinates. The square-linear system-bath interaction leads to dephasing due to the frequency fluctuation of system vibration, while the linear-linear interaction contributes to energy relaxation and a part of dephasing arises from anharmonicity. To clarify the role and origin of vibrational dephasing and energy relaxation in the stochastic model, the system part is then transformed into an energy eigenstate representation without using the rotating wave approximation. Two-dimensional (2D) infrared spectra are then calculated by solving a low-temperature corrected quantum Fokker-Planck (LTC-QFP) equation for a colored noise bath and by the stochastic theory. In motional narrowing regime, the spectra from the stochastic model are quite different from those from the LTC-QFP. In spectral diffusion regime, however, the 2D line shapes from the stochastic model resemble those from the LTC-QFP besides the blueshifts caused by the dissipation from the colored noise bath. The preconditions for validity of the stochastic theory for molecular vibrational motion are also discussed.
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Affiliation(s)
- Akihito Ishizaki
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
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12
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Nagata Y, Hasegawa T, Tanimura Y. Analyzing atomic liquids and solids by means of two-dimensional Raman spectra in frequency domain. J Chem Phys 2006; 124:194504. [PMID: 16729822 DOI: 10.1063/1.2191850] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
A practical method to evaluate the contributions of the nonlinear polarizability and anharmonicity of potentials from the experimental and simulation data by using double Fourier transformation is presented. In a Lennard-Jones potential system, an approximated expression of the fifth-order response function using the ratio between nonlinear polarizability and anharmonicity exhibits a good agreement with the results of the molecular dynamics simulation. In a soft-core case, the fifth-order Raman signal indicates that the system consists of the delocalized and localized modes, and only the delocalized mode affects the dramatic change of the fifth-order Raman response functions between solid and liquid phases through nonlinear polarizability.
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Affiliation(s)
- Yuki Nagata
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyoku, Kyoto 606-8502, Japan.
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13
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Strodel B, Stock G. Quantum modeling of transient infrared spectra reflecting photoinduced electron-transfer dynamics. J Chem Phys 2006; 124:114105. [PMID: 16555872 DOI: 10.1063/1.2166629] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A theoretical description of transient vibrational spectra following the impulsive optical excitation of a molecular system is presented. The approach combines the nonsecular evaluation of the Redfield equations to describe the dissipative dynamics of the system with an efficient implementation of the doorway-window formalism to calculate optical pump/infrared probe (vis/IR) spectra. Both parts of the calculation scale with N2, thus facilitating the treatment of systems with a dimension up to 10(4). The formulation is applied to a simple model of photoinduced electron transfer, which takes into account two coupled electronic states and a single anharmonic vibrational mode. Despite its simplicity, the model is found to exhibit quite complex electronic and vibrational relaxation dynamics, which in turn give rise to rather complex time- and frequency-resolved vis/IR spectra. Interestingly, the calculated IR spectra of the electron-transfer system predict the appearance of novel vibronically induced sidebands, which may even dominate the spectrum at early times.
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Affiliation(s)
- Birgit Strodel
- Institute of Physical and Theoretical Chemistry, J. W. Goethe University, Marie-Curie-Strasse 11, D-60439 Frankfurt, Germany
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14
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Nagata Y, Tanimura Y. Two-dimensional Raman spectra of atomic solids and liquids. J Chem Phys 2006; 124:024508. [PMID: 16422612 DOI: 10.1063/1.2131053] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We calculate third- and fifth-order Raman spectra of simple atoms interacting through a soft-core potential by means of molecular-dynamics (MD) simulations. The total polarizability of molecules is treated by the dipole-induced dipole model. Two- and three-body correlation functions of the polarizability at various temperatures are evaluated from equilibrium MD simulations based on a stability matrix formulation. To analyze the processes involved in the spectroscopic measurements, we divide the fifth-order response functions into symmetric and antisymmetric integrated response functions; the symmetric one is written as a simple three-body correlation function, while the antisymmetric one depends on a stability matrix. This analysis leads to a better understanding of the time scales and molecular motions that govern the two-dimensional (2D) signal. The 2D Raman spectra show novel differences between the solid and liquid phases, which are associated with the decay rates of coherent motions. On the other hand, these differences are not observed in the linear Raman spectra.
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Affiliation(s)
- Yuki Nagata
- Department of Chemistry, Kyoto University, Oiwakecho, Kitashirakawa, Sakyoku, Kyoto 606-8502, Japan.
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15
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Kjellberg P, Pullerits T. Three-pulse photon echo of an excitonic dimer modeled via Redfield theory. J Chem Phys 2006; 124:024106. [PMID: 16422570 DOI: 10.1063/1.2150447] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
In this article the third-order response of an excitonically coupled dimer is studied. The three-pulse photon echo signals were calculated by extracting polarization components from the total polarization in the corresponding phase-matched directions. The total nonlinear response was obtained by numeric propagation of the density matrix, with the exciton-vibrational coupling modeled via Redfield relaxation theory. The full two-dimensional three-pulse photon echo signals and the peak shift were analyzed in terms of the density-matrix dynamics of coherence dephasing and population relaxation. The location of the two-exciton state was found to be essential for proper modeling of the three-pulse photon echo. In particular, an oscillation in the three-pulse photon echo peak shift is found if the two-exciton state is displaced. The oscillations can be related to the dynamics of the one-exciton coherences.
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Affiliation(s)
- Pär Kjellberg
- Department of Chemical Physics, Lund University, Box 124, 22100 Lund, Sweden
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Ishizaki A, Tanimura Y. Multidimensional vibrational spectroscopy for tunneling processes in a dissipative environment. J Chem Phys 2005; 123:014503. [PMID: 16035851 DOI: 10.1063/1.1906215] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
Simulating tunneling processes as well as their observation are challenging problems for many areas. In this study, we consider a double-well potential system coupled to a heat bath with a linear-linear (LL) and square-linear (SL) system-bath interactions. The LL interaction leads to longitudinal (T1) and transversal (T2) homogeneous relaxations, whereas the SL interaction leads to the inhomogeneous dephasing (T2*) relaxation in the white noise limit with a rotating wave approximation. We discuss the dynamics of the double-well system under infrared (IR) laser excitations from a Gaussian-Markovian quantum Fokker-Planck equation approach, which was developed by generalizing Kubo's stochastic Liouville equation. Analytical expression of the Green function is obtained for a case of two-state-jump modulation by performing the Fourier-Laplace transformation. We then calculate a two-dimensional infrared signal, which is defined by the four-body correlation function of optical dipole, for various noise correlation time, system-bath coupling parameters, and temperatures. It is shown that the bath-induced vibrational excitation and relaxation dynamics between the tunneling splitting levels can be detected as the isolated off-diagonal peaks in the third-order two-dimensional infrared (2D-IR) spectroscopy for a specific phase matching condition. Furthermore, this spectroscopy also allows us to directly evaluate the rate constants for tunneling reactions, which relates to the coherence between the splitting levels; it can be regarded as a novel technique for measuring chemical reaction rates. We depict the change of reaction rates as a function of system-bath coupling strength and a temperature through the 2D-IR signal.
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Affiliation(s)
- Akihito Ishizaki
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
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Gelin M, Egorova D, Domcke W. A new method for the calculation of two-pulse time- and frequency-resolved spectra. Chem Phys 2005. [DOI: 10.1016/j.chemphys.2004.11.033] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Egorova D, Gelin MF, Domcke W. Time- and frequency-resolved fluorescence spectra of nonadiabatic dissipative systems: What photons can tell us. J Chem Phys 2005; 122:134504. [PMID: 15847478 DOI: 10.1063/1.1862618] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Abstract
The monitoring of the excited-state dynamics by time- and frequency-resolved spontaneous emission spectroscopy has been studied in detail for a model exhibiting an excited-state curve crossing. The model represents characteristic aspects of the photoinduced ultrafast dynamics in large molecules in the gas or condensed phases and accounts for strong nonadiabatic and electron-vibrational coupling effects, as well as for vibrational relaxation and optical dephasing. A comprehensive overview of the dependence of spontaneous emission spectra on the characteristics of the excitation and detection processes (such as carrier frequencies, pump/gate pulse durations, as well as optical dephasing) is presented. A systematic comparison of ideal spectra, which provide simultaneously perfect time and frequency resolution and thus contain maximal information on the system dynamics, with actually measurable time- and frequency-gated spectra has been carried out. The calculations of real time- and frequency-gated spectra demonstrate that complementary information on the excited-state dynamics can be extracted when the duration of the gate pulse is varied.
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Affiliation(s)
- Dassia Egorova
- Department of Chemistry, Technical University of Munich, D-85747 Garching, Germany
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Mikami T, Okazaki S. Path integral influence functional theory of dynamics of coherence between vibrational states of solute in condensed phase. J Chem Phys 2004; 121:10052-64. [PMID: 15549880 DOI: 10.1063/1.1805517] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Path integral influence functional theory has been applied to the dynamics of coherence between vibrational states of solute in condensed phase. First, time evolution of the off-diagonal term of the reduced density matrix rho(mn)(t) was algebraically described by the cumulant expansion of the perturbative influence functional. Then, the theory is compared with the Redfield theory, rearranging the present description in a familiar way to that found in the Redfield theory. A numerical example of the theory is presented for the vibrational dynamics of cyanide ion in water assuming a coherent state (1/radical2)(|0> + |1>) at t = 0. We find that Re rho(10)(t) oscillates with high frequency and shows a fast damping. Relaxation time of the oscillation amplitude is estimated to be 5.1 ps for a certain configuration of the solution. Then, secular approximation often used in the Redfield theory is found to work well, at least, in the present system. Population relaxation time for the first excited state and pure dephasing time may also be calculated from the component of Re rho(10)(t) to be 7.9 and 7.5 ps, respectively. Further, the many-particle measurement for Re rho(10)(t) gives the relaxation rate about three times faster than the single-measurement above. This comes from the inhomogeneity of the solute environment. We also found the fast oscillation in the diagonal part of the calculated density matrix, Re rho(11)(t). This oscillation is generated only when the initial density matrix includes the coherence.
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Affiliation(s)
- Taiji Mikami
- Department of Electronic Chemistry, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan
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Kato T, Tanimura Y. Two-dimensional Raman and infrared vibrational spectroscopy for a harmonic oscillator system nonlinearly coupled with a colored noise bath. J Chem Phys 2004; 120:260-71. [PMID: 15267286 DOI: 10.1063/1.1629272] [Citation(s) in RCA: 64] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Abstract
Multidimensional vibrational response functions of a harmonic oscillator are reconsidered by assuming nonlinear system-bath couplings. In addition to a standard linear-linear (LL) system-bath interaction, we consider a square-linear (SL) interaction. The LL interaction causes the vibrational energy relaxation, while the SL interaction is mainly responsible for the vibrational phase relaxation. The dynamics of the relevant system are investigated by the numerical integration of the Gaussian-Markovian Fokker-Planck equation under the condition of strong couplings with a colored noise bath, where the conventional perturbative approach cannot be applied. The response functions for the fifth-order nonresonant Raman and the third-order infrared (or equivalently the second-order infrared and the seventh-order nonresonant Raman) spectra are calculated under the various combinations of the LL and the SL coupling strengths. Calculated two-dimensional response functions demonstrate that those spectroscopic techniques are very sensitive to the mechanism of the system-bath couplings and the correlation time of the bath fluctuation. We discuss the primary optical transition pathways involved to elucidate the corresponding spectroscopic features and to relate them to the microscopic sources of the vibrational nonlinearity induced by the system-bath interactions. Optical pathways for the fifth-order Raman spectroscopies from an "anisotropic" medium were newly found in this study, which were not predicted by the weak system-bath coupling theory or the standard Brownian harmonic oscillator model.
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Affiliation(s)
- Tsuyoshi Kato
- Institute for Molecular Science, Myodaiji, Okazaki, Aichi 444-8585, Japan
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