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Takahashi H, Tanimura Y. Discretized hierarchical equations of motion in mixed Liouville-Wigner space for two-dimensional vibrational spectroscopies of liquid water. J Chem Phys 2023; 158:044115. [PMID: 36725520 DOI: 10.1063/5.0135725] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
A model of a bulk water system describing the vibrational motion of intramolecular and intermolecular modes is constructed, enabling analysis of its linear and nonlinear vibrational spectra as well as the energy transfer processes between the vibrational modes. The model is described as a system of four interacting anharmonic oscillators nonlinearly coupled to their respective heat baths. To perform a rigorous numerical investigation of the non-Markovian and nonperturbative quantum dissipative dynamics of the model, we derive discretized hierarchical equations of motion in mixed Liouville-Wigner space, with Lagrange-Hermite mesh discretization being employed in the Liouville space of the intramolecular modes and Lagrange-Hermite mesh discretization and Hermite discretization in the Wigner space of the intermolecular modes. One-dimensional infrared and Raman spectra and two-dimensional terahertz-infrared-visible and infrared-infrared-Raman spectra are computed as demonstrations of the quantum dissipative description provided by our model.
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Affiliation(s)
- Hideaki Takahashi
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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Jo JY, Tanimura Y. Full molecular dynamics simulations of molecular liquids for single-beam spectrally controlled two-dimensional Raman spectroscopy. J Chem Phys 2021; 154:124115. [PMID: 33810650 DOI: 10.1063/5.0044661] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Single-beam spectrally controlled (SBSC) two-dimensional (2D) Raman spectroscopy is a unique 2D vibrational measurement technique utilizing trains of short pulses that are generated from a single broadband pulse by pulse shaping. This approach overcomes the difficulty of 2D Raman spectroscopy in dealing with small-signal extraction and avoids complicated low-order cascading effects, thus providing a new possibility for measuring the intramolecular and intermolecular modes of molecular liquids using fifth-order 2D Raman spectroscopy. Recently, for quantitatively investigating the mode-mode coupling mechanism, Hurwitz et al. [Opt. Express 28, 3803 (2020)] have developed a new pulse design for this measurement to separate the contributions of the fifth- and third-order polarizations, which are often overlapped in the original single-beam measurements. Here, we describe a method for simulating these original measurements and the new 2D Raman measurements on the basis of a second-order response function approach. We carry out full molecular dynamics simulations for carbon tetrachloride and liquid water using an equilibrium-nonequilibrium hybrid algorithm, with the aim of explaining the key features of the SBSC 2D Raman spectroscopic method from a theoretical point of view. The predicted signal profiles and intensities provide valuable information that can be applied to 2D spectroscopy experiments, allowing them to be carried out more efficiently.
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Affiliation(s)
- Ju-Yeon Jo
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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Full molecular dynamics simulations of liquid water and carbon tetrachloride for two-dimensional Raman spectroscopy in the frequency domain. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.07.002] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Ito H, Tanimura Y. Simulating two-dimensional infrared-Raman and Raman spectroscopies for intermolecular and intramolecular modes of liquid water. J Chem Phys 2016; 144:074201. [DOI: 10.1063/1.4941842] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
Affiliation(s)
- Hironobu Ito
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyoku, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyoku, Kyoto 606-8502, Japan
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Ito H, Jo JY, Tanimura Y. Notes on simulating two-dimensional Raman and terahertz-Raman signals with a full molecular dynamics simulation approach. STRUCTURAL DYNAMICS (MELVILLE, N.Y.) 2015; 2:054102. [PMID: 26798823 PMCID: PMC4711663 DOI: 10.1063/1.4932597] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/29/2015] [Accepted: 09/25/2015] [Indexed: 06/05/2023]
Abstract
Recent developments in two-dimensional (2D) THz-Raman and 2D Raman spectroscopies have created the possibility for quantitatively investigating the role of many dynamic and structural aspects of the molecular system. We explain the significant points for properly simulating 2D vibrational spectroscopic studies of intermolecular modes using the full molecular dynamics approach, in particular, regarding the system size, the treatment of the thermostat, and inclusion of an Ewald summation for the induced polarizability. Moreover, using the simulation results for water employing various polarization functions, we elucidate the roles of permanent and induced optical properties in determining the 2D profiles of the signal.
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Affiliation(s)
- Hironobu Ito
- Department of Chemistry, Graduate School of Science, Kyoto University , Sakyoku, Kyoto 606-8502, Japan
| | - Ju-Yeon Jo
- Department of Chemistry, Graduate School of Science, Kyoto University , Sakyoku, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University , Sakyoku, Kyoto 606-8502, Japan
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Ito H, Hasegawa T, Tanimura Y. Calculating two-dimensional THz-Raman-THz and Raman-THz-THz signals for various molecular liquids: The samplers. J Chem Phys 2014; 141:124503. [PMID: 25273447 DOI: 10.1063/1.4895908] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hironobu Ito
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyoku, Kyoto 606-8502, Japan
| | - Taisuke Hasegawa
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyoku, Kyoto 606-8502, Japan
- Department of Physics, University of Hamburg, Centre for Free Electron Laser Science, DESY, Notkestrasse 85, D-22607 Hamburg, Germany
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyoku, Kyoto 606-8502, Japan
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Nishida J, Shigeto S, Yabumoto S, Hamaguchi HO. Anharmonic coupling of the CH-stretch and CH-bend vibrations of chloroform as studied by near-infrared electroabsorption spectroscopy. J Chem Phys 2012; 137:234501. [DOI: 10.1063/1.4770264] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Hattori T. Classical theory of two-dimensional time-domain terahertz spectroscopy. J Chem Phys 2010; 133:204503. [DOI: 10.1063/1.3507256] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
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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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Li YL, Huang L, Dwayne Miller RJ, Hasegawa T, Tanimura Y. Two-dimensional fifth-order Raman spectroscopy of liquid formamide: Experiment and Theory. J Chem Phys 2008; 128:234507. [DOI: 10.1063/1.2927311] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Saito S, Ohmine I. Fifth-order two-dimensional Raman spectroscopy of liquid water, crystalline ice Ih and amorphous ices: Sensitivity to anharmonic dynamics and local hydrogen bond network structure. J Chem Phys 2006; 125:084506. [PMID: 16965028 DOI: 10.1063/1.2232254] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
The theoretical study of off-resonant fifth-order two-dimensional (2D)-Raman spectroscopy is made to analyze the intermolecular dynamics of liquid and solid water. The 2D-Raman spectroscopy is susceptible to the nonlinear anharmonic dynamics and local hydrogen bond structure in water. It is found that the distinct 2D-Raman response appears as the negative signal near the t(2) axis. The origin of this negative signal for t(2)<15 fs is from the nonlinear polarizability in the librational motions, whereas that for 30 fs<t(2)<150 fs is attributed to the anharmonic translational motions. It is found that the mechanical anharmonicity and nonlinear polarizability couplings among modes clearly can be observed as the sum- and difference-frequency peaks in the 2D-Raman spectrum (i.e., Fourier transforms of the response). The 2D-Raman spectroscopies of ice Ih and amorphous ices, i.e., low density, high density, and very high density amorphous ices, are also investigated. It is found that the 2D-Raman spectroscopy is very sensitive to the anisotropy of the structure of ice Ih. The strong hydrogen bond stretching band is seen in the 2D-Raman spectroscopy of the polarization directions parallel to the c axis, whereas the contributions of the librational motion can be also seen in the spectrum with the polarization directions parallel to the a axis. The 2D-Raman spectroscopy is also found to be also very sensitive to the differences in local hydrogen bond network structures in various amorphous phases.
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Affiliation(s)
- Shinji Saito
- Department of Computational Molecular Science, Institute for Molecular Science, Myodaiji, Okazaki, Aichi 444-8585, Japan.
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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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Hasegawa T, Tanimura Y. Calculating fifth-order Raman signals for various molecular liquids by equilibrium and nonequilibrium hybrid molecular dynamics simulation algorithms. J Chem Phys 2006; 125:074512. [PMID: 16942356 DOI: 10.1063/1.2217947] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
The fifth-order two-dimensional (2D) Raman signals have been calculated from the equilibrium and nonequilibrium (finite field) molecular dynamics simulations. The equilibrium method evaluates response functions with equilibrium trajectories, while the nonequilibrium method calculates a molecular polarizability from nonequilibrium trajectories for different pulse configurations and sequences. In this paper, we introduce an efficient algorithm which hybridizes the existing two methods to avoid the time-consuming calculations of the stability matrices which are inherent in the equilibrium method. Using nonequilibrium trajectories for a single laser excitation, we are able to dramatically simplify the sampling process. With this approach, the 2D Raman signals for liquid xenon, carbon disulfide, water, acetonitrile, and formamide are calculated and discussed. Intensities of 2D Raman signals are also estimated and the peak strength of formamide is found to be only five times smaller than that of carbon disulfide.
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Affiliation(s)
- Taisuke Hasegawa
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyo, Kyoto 606-8502, Japan.
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15
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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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16
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Hyeon-Deuk K, Hyeon-Deuk K, Tanimura Y. Multidimensional infrared spectroscopy for molecular vibrational modes with dipolar interactions, anharmonicity, and nonlinearity of dipole moments and polarizability. J Chem Phys 2005; 123:224310. [PMID: 16375479 DOI: 10.1063/1.2134702] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
We present an analytical expression for the linear and nonlinear infrared spectra of interacting molecular vibrational motions. Each of the molecular modes is explicitly represented by a classical damped oscillator on an anharmonic multidimensional potential-energy surface. The two essential interactions, the dipole-dipole (DD) and the dipole-induced-dipole (DID) interactions, are taken into account, and each dipole moment and polarizability are expanded to nonlinear order with respect to the nuclear vibrational coordinate. Our analytical treatment leads to expressions for the contributions of anharmonicity, DD and DID interactions, and the nonlinearity of dipole moments and polarizability elements to the one-, two-, and three-dimensional spectra as separated terms, which allows us to discuss the relative importance of these respective contributions. We can calculate multidimensional signals for various configurations of molecules interacting through DD and DID interactions for different material parameters over the whole range of frequencies. We demonstrate that contributions from the DD and DID interactions and anharmonicity are separately detectable through the third-order three-dimensional IR spectroscopy, whereas they cannot be distinguished from each other in either the linear or the second-order IR spectroscopies. The possibility of obtaining the intra- or intermolecular structural information from multidimensional spectra is also discussed.
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Affiliation(s)
- Kim Hyeon-Deuk
- Department of Chemistry, Kyoto University, Kyoto 606-8502, Japan.
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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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Fujiyoshi S, Ishibashi TA, Onishi H. Fifth-Order Raman Spectroscopy of Excited-State Molecules. J Phys Chem A 2004. [DOI: 10.1021/jp0461899] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Affiliation(s)
- Satoru Fujiyoshi
- Surface Chemistry Laboratory, Kanagawa Academy of Science and Technology (KAST), KSP, Sakado, Takatsu, Kawasaki, 213-0012, Japan, Core Research for Evolutional Science and Technology, Japan Science and Technology Agency, Honmachi, Kawaguchi, 332-0012, Japan, Department of Chemistry, Faculty of Science, Kobe University, Nada, Kobe, 657-8501, Japan, and Department of Chemistry, Graduate School of Science, Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan
| | - Taka-aki Ishibashi
- Surface Chemistry Laboratory, Kanagawa Academy of Science and Technology (KAST), KSP, Sakado, Takatsu, Kawasaki, 213-0012, Japan, Core Research for Evolutional Science and Technology, Japan Science and Technology Agency, Honmachi, Kawaguchi, 332-0012, Japan, Department of Chemistry, Faculty of Science, Kobe University, Nada, Kobe, 657-8501, Japan, and Department of Chemistry, Graduate School of Science, Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan
| | - Hiroshi Onishi
- Surface Chemistry Laboratory, Kanagawa Academy of Science and Technology (KAST), KSP, Sakado, Takatsu, Kawasaki, 213-0012, Japan, Core Research for Evolutional Science and Technology, Japan Science and Technology Agency, Honmachi, Kawaguchi, 332-0012, Japan, Department of Chemistry, Faculty of Science, Kobe University, Nada, Kobe, 657-8501, Japan, and Department of Chemistry, Graduate School of Science, Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, 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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Saito S, Ohmine I. Off-resonant two-dimensional fifth-order Raman spectroscopy of liquid CS2: Detection of anharmonic dynamics. J Chem Phys 2003. [DOI: 10.1063/1.1609984] [Citation(s) in RCA: 55] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ma A, Stratt RM. Selecting the information content of two-dimensional Raman spectra in liquids. J Chem Phys 2003. [DOI: 10.1063/1.1611873] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
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Mukamel S. Superoperator representation of nonlinear response: unifying quantum field and mode coupling theories. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:021111. [PMID: 14524957 DOI: 10.1103/physreve.68.021111] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2003] [Indexed: 05/24/2023]
Abstract
Computing response functions by following the time evolution of superoperators in Liouville space (whose vectors are ordinary Hilbert space operators) offers an attractive alternative to the diagrammatic perturbative expansion of many-body equilibrium and nonequilibrium Green's functions. The bookkeeping of time ordering is naturally maintained in real (physical) time, allowing the formulation of Wick's theorem for superoperators, giving a factorization of higher order response functions in terms of two fundamental Green's functions. Backward propagations and analytic continuations using artificial times (Keldysh loops and Matsubara contours) are avoided. A generating functional for nonlinear response functions unifies quantum field theory and the classical mode coupling formalism of nonlinear hydrodynamics and may be used for semiclassical expansions. Classical response functions are obtained without the explicit computation of stability matrices.
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Affiliation(s)
- Shaul Mukamel
- Departments of Chemistry and Physics and Astronomy, University of Rochester, Rochester, New York 14627-0216, USA.
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Kühn O, Tanimura Y. Two-dimensional vibrational spectroscopy of a double minimum system in a dissipative environment. J Chem Phys 2003. [DOI: 10.1063/1.1582841] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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Suzuki Y, Tanimura Y. Two-dimensional spectroscopy for a two-dimensional rotator coupled to a Gaussian–Markovian noise bath. J Chem Phys 2003. [DOI: 10.1063/1.1578630] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
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Okumura K, Tanimura Y. Energy-Level Diagrams and Their Contribution to Fifth-Order Raman and Second-Order Infrared Responses: Distinction between Relaxation Models by Two-Dimensional Spectroscopy. J Phys Chem A 2003. [DOI: 10.1021/jp027360o] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Ko Okumura
- Department of Physics, Graduate School of Humanities and Sciences, Ochanomizu, University, 2-1-1, Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan, and Physique de la Matière Condensée, Collège de France, 11 place Marcelin-Berthelot, 75231 Paris Cedex 05, France
| | - Yoshitaka Tanimura
- Theoretical Studies, Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan
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Kano H, Hamaguchi HO. Cascading third-order Raman process studied by six-wave mixing broadband multiplex coherent anti-Stokes Raman scattering spectroscopy. J Chem Phys 2003. [DOI: 10.1063/1.1542881] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Moran AM, Dreyer J, Mukamel S. Ab initiosimulation of the two-dimensional vibrational spectrum of dicarbonylacetylacetonato rhodium(I). J Chem Phys 2003. [DOI: 10.1063/1.1528605] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
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Abstract
Linear optical spectroscopies have long been used to study the behavior of liquids. Laser technology has progressed to the point that it has become possible to perform nonlinear optical experiments that probe higher-order correlation functions in liquids, opening a new window into our understanding of the microscopic details of solution-phase processes. Here we review advances that have been made in recent years in employing higher-order electronic and vibrational spectroscopies to study liquid-state dynamics and structure.
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Affiliation(s)
- John T Fourkas
- Eugene F. Merkert Chemistry Center, Boston College, Chestnut Hill, Massachusetts 02467, USA.
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29
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Ma A, Stratt RM. The molecular origins of the two-dimensional Raman spectrum of an atomic liquid. I. Molecular dynamics simulation. J Chem Phys 2002. [DOI: 10.1063/1.1453401] [Citation(s) in RCA: 32] [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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30
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Ma A, Stratt RM. The molecular origins of the two-dimensional Raman spectrum of an atomic liquid. II. Instantaneous-normal-mode theory. J Chem Phys 2002. [DOI: 10.1063/1.1453402] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Suzuki Y, Tanimura Y. Nonequilibrium initial conditions of a Brownian oscillator system observed by two-dimensional spectroscopy. J Chem Phys 2001. [DOI: 10.1063/1.1379768] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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32
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33
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Tominaga K, Maekawa H. Investigation of Two-Dimensional Vibrational Spectrum by a Diagrammatic Approach. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2001. [DOI: 10.1246/bcsj.74.279] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
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34
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Mukamel S. Multidimensional femtosecond correlation spectroscopies of electronic and vibrational excitations. Annu Rev Phys Chem 2000; 51:691-729. [PMID: 11031297 DOI: 10.1146/annurev.physchem.51.1.691] [Citation(s) in RCA: 545] [Impact Index Per Article: 22.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Femtosecond visible and infrared analogues of multiple-pulse nuclear magnetic resonance techniques provide novel snapshot probes into the structure and electronic and vibrational dynamics of complex molecular assemblies such as photosynthetic antennae, proteins, and hydrogen-bonded liquids. A classical-oscillator description of these spectroscopies in terms of interacting quasiparticles (rather than transitions among global eigenstates) is developed and sets the stage for designing new pulse sequences and inverting the multidimensional signals to yield molecular structures. Considerable computational advantages and a clear physical insight into the origin of the response and the relevant coherence sizes are provided by a real-space analysis of the underlying coherence-transfer pathways in Liouville space.
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Affiliation(s)
- S Mukamel
- Department of Chemistry, University of Rochester, PO Box 270216, Rochester, New York 14627-0216, USA.
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35
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Ma A, Stratt RM. Fifth-order raman spectrum of an atomic liquid: simulation and instantaneous-normal-mode calculation. PHYSICAL REVIEW LETTERS 2000; 85:1004-1007. [PMID: 10991460 DOI: 10.1103/physrevlett.85.1004] [Citation(s) in RCA: 66] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2000] [Indexed: 05/23/2023]
Abstract
Experimental artifacts and technical difficulties in carrying out theoretical calculations have consistently frustrated attempts to obtain the two-dimensional (5th-order) Raman spectrum of a liquid. We report here a new theoretical development: the first microscopic numerical simulation of the 5th-order Raman signal in a liquid. Comparison with an instantaneous-normal-mode treatment, a fully microscopic model which interprets liquid dynamics as arising from coherent harmonic modes, shows that the 5th-order spectrum reveals profound effects stemming from dynamical anharmonicity.
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Affiliation(s)
- A Ma
- Department of Chemistry, Brown University, Providence, Rhode Island 02912, USA
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36
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Park K, Cho M. Two-dimensional vibrational spectroscopy. VI. Higher-order contributions to the two-dimensional vibrational response functions. J Chem Phys 2000. [DOI: 10.1063/1.481684] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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37
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Okumura K, Tokmakoff A, Tanimura Y. Structural information from two-dimensional fifth-order Raman spectroscopy. J Chem Phys 1999. [DOI: 10.1063/1.479383] [Citation(s) in RCA: 70] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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38
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Kirkwood JC, Albrecht AC, Ulness DJ. Fifth-order nonlinear Raman processes in molecular liquids using quasi-cw noisy light. I. Theory. J Chem Phys 1999. [DOI: 10.1063/1.479287] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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39
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Larsen RE, Stratt RM. Instantaneous pair theory for high-frequency vibrational energy relaxation in fluids. J Chem Phys 1999. [DOI: 10.1063/1.478185] [Citation(s) in RCA: 58] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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40
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Mukamel S, Piryatinski A, Chernyak V. Two-Dimensional Raman Echoes: Femtosecond View of Molecular Structure and Vibrational Coherence. Acc Chem Res 1998. [DOI: 10.1021/ar960206y] [Citation(s) in RCA: 133] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Shaul Mukamel
- Department of Chemistry, University of Rochester, P.O. RC Box 270216, Rochester, New York 14627-0216
| | - Andrei Piryatinski
- Department of Chemistry, University of Rochester, P.O. RC Box 270216, Rochester, New York 14627-0216
| | - Vladimir Chernyak
- Department of Chemistry, University of Rochester, P.O. RC Box 270216, Rochester, New York 14627-0216
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41
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The intermolecular interaction mechanisms in liquid CS2 at 295 and 165 K probed with two-dimensional Raman spectroscopy. Chem Phys 1998. [DOI: 10.1016/s0301-0104(98)00026-3] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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42
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Fifth-order two-dimensional vibrational spectroscopy of a Morse potential system in condensed phases. Chem Phys 1998. [DOI: 10.1016/s0301-0104(98)00010-x] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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43
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Steffen T, Duppen K. Mode coupling mechanisms in the impulsive 2D Raman response of liquid CS2. Chem Phys Lett 1998. [DOI: 10.1016/s0009-2614(98)00469-2] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Steffen T, Meinders NACM, Duppen K. Microscopic Origin of the Optical Kerr Effect Response of CS2−Pentane Binary Mixtures. J Phys Chem A 1998. [DOI: 10.1021/jp973422c] [Citation(s) in RCA: 61] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Thomas Steffen
- Ultrafast Laser and Spectroscopy Laboratory, Materials Science Centre, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
| | - Nicole A. C. M. Meinders
- Ultrafast Laser and Spectroscopy Laboratory, Materials Science Centre, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
| | - Koos Duppen
- Ultrafast Laser and Spectroscopy Laboratory, Materials Science Centre, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
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Saito S, Ohmine I. Off-resonant fifth-order nonlinear response of water and CS2: Analysis based on normal modes. J Chem Phys 1998. [DOI: 10.1063/1.475375] [Citation(s) in RCA: 147] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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