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Polley K, Loring RF. 2D electronic-vibrational spectroscopy with classical trajectories. J Chem Phys 2022; 156:204110. [DOI: 10.1063/5.0090868] [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
Two-dimensional electronic-vibrational (2DEV) spectra have the capacity to probe electron–nuclear interactions in molecules by measuring correlations between initial electronic excitations and vibrational transitions at a later time. The trajectory-based semiclassical optimized mean trajectory approach is applied to compute 2DEV spectra for a system with excitonically coupled electronic excited states vibronically coupled to a chromophore vibration. The chromophore mode is in turn coupled to a bath, inducing redistribution of vibrational populations. The lineshapes and delay-time dynamics of the resulting spectra compare well with benchmark calculations, both at the level of the observable and with respect to contributions from distinct spectroscopic processes.
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Affiliation(s)
- Kritanjan Polley
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
| | - Roger F. Loring
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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2
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Polley K, Loring RF. Two-dimensional vibronic spectroscopy with semiclassical thermofield dynamics. J Chem Phys 2022; 156:124108. [DOI: 10.1063/5.0083868] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
Thermofield dynamics is an exactly correct formulation of quantum mechanics at finite temperature in which a wavefunction is governed by an effective temperature-dependent quantum Hamiltonian. The optimized mean trajectory (OMT) approximation allows the calculation of spectroscopic response functions from trajectories produced by the classical limit of a mapping Hamiltonian that includes physical nuclear degrees of freedom and other effective degrees of freedom representing discrete vibronic states. Here, we develop a thermofield OMT (TF-OMT) approach in which the OMT procedure is applied to a temperature-dependent classical Hamiltonian determined from the thermofield-transformed quantum mapping Hamiltonian. Initial conditions for bath nuclear degrees of freedom are sampled from a zero-temperature distribution. Calculations of two-dimensional electronic spectra and two-dimensional vibrational–electronic spectra are performed for models that include excitonically coupled electronic states. The TF-OMT calculations agree very closely with the corresponding OMT results, which, in turn, represent well benchmark calculations with the hierarchical equations of motion method.
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Affiliation(s)
- Kritanjan Polley
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
| | - Roger F. Loring
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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3
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Liu Y, Yan Y, Xing T, Shi Q. Understanding the Large Kinetic Isotope Effect of Hydrogen Tunneling in Condensed Phases by Using Double-Well Model Systems. J Phys Chem B 2021; 125:5959-5970. [PMID: 34033714 DOI: 10.1021/acs.jpcb.1c02851] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In recent years, many experiments have shown large kinetic isotope effects (KIEs) for hydrogen transfer reactions in condensed phases as evidence of strong quantum tunneling effects. Since accurate calculation of the tunneling dynamics in such systems still present significant challenges, previous studies have employed different types of approximations to estimate the tunneling effects and KIEs. In this work, by employing model systems consisting of a double-well coupled to a harmonic bath, we calculate the tunneling effects and KIEs using the numerically exact hierarchical equations of motion (HEOM) method. It is found that hydrogen and deuterium transfer reactions in the same system may show rather different behaviors, where hydrogen transfer is dominated by tunneling between the two lowest vibrational states and deuterium transfer is controlled by excited vibrational states close to the barrier top. The simulation results are also used to test the validity of various approximate methods. It is shown that the Wolynes theory of dissipative tunneling gives a good estimation of rate constants in the over-the-barrier regime, while the nonadiabatic reaction rate theory based on the Landau-Zener formula is more suitable for deep tunneling reactions.
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Affiliation(s)
- Yanying Liu
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China.,University of Chinese Academy of Sciences, Beijing 100049, China.,Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
| | - Yaming Yan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China.,University of Chinese Academy of Sciences, Beijing 100049, China.,Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
| | - Tao Xing
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China.,University of Chinese Academy of Sciences, Beijing 100049, China.,Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China.,University of Chinese Academy of Sciences, Beijing 100049, China.,Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
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4
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Tanimura Y. Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM). J Chem Phys 2021; 153:020901. [PMID: 32668942 DOI: 10.1063/5.0011599] [Citation(s) in RCA: 140] [Impact Index Per Article: 46.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
An open quantum system refers to a system that is further coupled to a bath system consisting of surrounding radiation fields, atoms, molecules, or proteins. The bath system is typically modeled by an infinite number of harmonic oscillators. This system-bath model can describe the time-irreversible dynamics through which the system evolves toward a thermal equilibrium state at finite temperature. In nuclear magnetic resonance and atomic spectroscopy, dynamics can be studied easily by using simple quantum master equations under the assumption that the system-bath interaction is weak (perturbative approximation) and the bath fluctuations are very fast (Markovian approximation). However, such approximations cannot be applied in chemical physics and biochemical physics problems, where environmental materials are complex and strongly coupled with environments. The hierarchical equations of motion (HEOM) can describe the numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system-bath interactions, which has been verified on the basis of exact analytical solutions (non-Markovian tests) with any desired numerical accuracy. The HEOM theory has been used to treat systems of practical interest, in particular, to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories. This article presents an overview of the HEOM theory, focusing on its theoretical background and applications, to help further the development of the study of open quantum dynamics.
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Affiliation(s)
- Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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5
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Polley K, Loring RF. One and Two Dimensional Vibronic Spectra for an Exciton Dimer from Classical Trajectories. J Phys Chem B 2020; 124:9913-9920. [DOI: 10.1021/acs.jpcb.0c07078] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Kritanjan Polley
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, United States
| | - Roger F. Loring
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, United States
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6
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Zhang J, Borrelli R, Tanimura Y. Proton tunneling in a two-dimensional potential energy surface with a non-linear system–bath interaction: Thermal suppression of reaction rate. J Chem Phys 2020; 152:214114. [DOI: 10.1063/5.0010580] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Affiliation(s)
- Jiaji Zhang
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Raffaele Borrelli
- DISAFA, University of Torino, Largo Paolo Braccini 2, I-10095 Grugliasco, Italy
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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7
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Jansen TLC. Simple Quantum Dynamics with Thermalization. J Phys Chem A 2018; 122:172-183. [PMID: 29199829 PMCID: PMC5770886 DOI: 10.1021/acs.jpca.7b10380] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2017] [Revised: 12/04/2017] [Indexed: 02/05/2023]
Abstract
In this paper, we introduce two simple quantum dynamics methods. One is based on the popular surface-hopping method, and the other is based on rescaling of the propagation on the bath ground-state potential surface. The first method is special, as it avoids specific feedback from the simulated quantum system to the bath and can be applied for precalculated classical trajectories. It is based on the equipartition theorem to determine if hops between different potential energy surfaces are allowed. By comparing with the formally exact Hierarchical Equations Of Motion approach for four model systems we find that the method generally approximates the quantum dynamics toward thermal equilibrium very well. The second method is based on rescaling of the nonadiabatic coupling and also neglect the effect of the state of the quantum system on the bath. By the nature of the approximations, they cannot reproduce the effect of bath relaxation following excitation. However, the methods are both computationally more tractable than the conventional fewest switches surface hopping, and we foresee that the methods will be powerful for simulations of quantum dynamics in systems with complex bath dynamics, where the system-bath coupling is not too strong compared to the thermal energy.
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Affiliation(s)
- Thomas L. C. Jansen
- Zernike Institute for Advanced
Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
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8
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Wilkins DM, Dattani NS. Why Quantum Coherence Is Not Important in the Fenna–Matthews–Olsen Complex. J Chem Theory Comput 2015; 11:3411-9. [DOI: 10.1021/ct501066k] [Citation(s) in RCA: 74] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- David M. Wilkins
- Physical and Theoretical
Chemistry Laboratory, Oxford University, South Parks Road, Oxford, OX1 3QZ, United Kingdom
| | - Nikesh S. Dattani
- Quantum
Chemistry Laboratory,
Department of Chemistry, Kyoto University, 606-8502, Kyoto, Japan
- School of Materials Science
and Engineering, Nanyang Technological University, Block N4.1, Nanyang Avenue, Singapore 639798
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9
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Xie W, Xu Y, Zhu L, Shi Q. Mixed quantum classical calculation of proton transfer reaction rates: From deep tunneling to over the barrier regimes. J Chem Phys 2014; 140:174105. [DOI: 10.1063/1.4873135] [Citation(s) in RCA: 11] [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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10
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Tanimura Y. Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two-dimensional correlation spectroscopy. J Chem Phys 2012; 137:22A550. [DOI: 10.1063/1.4766931] [Citation(s) in RCA: 100] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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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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12
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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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13
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Sakurai A, Tanimura Y. Does ℏ Play a Role in Multidimensional Spectroscopy? Reduced Hierarchy Equations of Motion Approach to Molecular Vibrations. J Phys Chem A 2011; 115:4009-22. [DOI: 10.1021/jp1095618] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Atsunori Sakurai
- Department of Chemistry, Graduate School of Science, Kyoto Universiy, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto Universiy, Kyoto 606-8502, Japan
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14
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Venkataraman C, Soudackov AV, Hammes-Schiffer S. Photoinduced homogeneous proton-coupled electron transfer: Model study of isotope effects on reaction dynamics. J Chem Phys 2009; 131:154502. [DOI: 10.1063/1.3249964] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
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15
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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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16
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Chen L, Zheng R, Shi Q, Yan Y. Optical line shapes of molecular aggregates: Hierarchical equations of motion method. J Chem Phys 2009; 131:094502. [DOI: 10.1063/1.3213013] [Citation(s) in RCA: 111] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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17
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Fujisaki H, Stock G. Dynamic treatment of vibrational energy relaxation in a heterogeneous and fluctuating environment. J Chem Phys 2008; 129:134110. [DOI: 10.1063/1.2985606] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
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18
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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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19
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Sakumichi N, Ando K. Semiquantal analysis of adiabatic hydrogen transfer rate. J Chem Phys 2008; 128:164516. [DOI: 10.1063/1.2903746] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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20
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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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21
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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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22
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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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23
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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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24
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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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25
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Goj A, Loring RF. Effect of noise on the classical and quantum mechanical nonlinear response of resonantly coupled anharmonic oscillators. J Chem Phys 2006; 124:194101. [PMID: 16729797 DOI: 10.1063/1.2198203] [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
Multidimensional infrared spectroscopy probes coupled molecular vibrations in complex, condensed phase systems. Recent theoretical studies have focused on the analytic structure of the nonlinear response functions required to calculate experimental observables in a perturbative treatment of the radiation-matter interaction. Classical mechanical nonlinear response functions have been shown to exhibit unbounded growth for anharmonic, integrable systems, as a consequence of the nonlinearity of classical mechanics, a feature that is absent in a quantum mechanical treatment. We explore the analytic structure of the third-order vibrational response function for an exactly solvable quantum mechanical model that includes some of the important and theoretically challenging aspects of realistic models of condensed phase systems: anharmonicity, resonant coupling, fluctuations, and a well-defined classical mechanical limit.
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Affiliation(s)
- Anne Goj
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, NY 14853, USA
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26
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Cho BM, Carlsson CF, Jimenez R. Photon echo spectroscopy of porphyrins and heme proteins: Effects of quasidegenerate electronic structure on the peak shift decay. J Chem Phys 2006; 124:144905. [PMID: 16626243 DOI: 10.1063/1.2186318] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Three pulse photon echo peak shift spectroscopy and transient grating measurements on Zn-substituted cytochrome c, Zn-tetraphenylporphyrin, and Zn-protoporphyrin IX are reported. The effects of protein conformation, axial ligation, and solvent are investigated. Numerical simulations of the peak shift and transient grating experiments are presented. The simulations employed recently derived optical response functions for square-symmetric molecules with doubly degenerate excited states. Simulations exploring the effects of excited-state energy splitting, symmetric and asymmetric fluctuations, and excited-state lifetime show that the time scales of the peak shift decay in the three-level system largely reflect the same dynamics as in the two-level system. However, the asymptotic peak shift, which is a clear indicator of inhomogeneous broadening in a two-level system, must be interpreted more carefully for three-level systems, as it is also influenced by the magnitude of the excited-state splitting. The calculated signals qualitatively reproduce the data.
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Affiliation(s)
- Byung Moon Cho
- JILA, University of Colorado and National Institute of Standards and Technology, Boulder, Colorado 80309-0440, USA
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27
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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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