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Gelin MF, Chen L, Domcke W. Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals. Chem Rev 2022; 122:17339-17396. [PMID: 36278801 DOI: 10.1021/acs.chemrev.2c00329] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.
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Affiliation(s)
- Maxim F Gelin
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Lipeng Chen
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technical University of Munich, D-85747 Garching,Germany
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Bai Y, Ni W, Sun K, Chen L, Ma L, Zhao Y, Gurzadyan GG, Gelin MF. Plenty of Room on the Top: Pathways and Spectroscopic Signatures of Singlet Fission from Upper Singlet States. J Phys Chem Lett 2022; 13:11086-11094. [PMID: 36417755 DOI: 10.1021/acs.jpclett.2c03053] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
We investigate dynamic signatures of the singlet fission (SF) process triggered by the excitation of a molecular system to an upper singlet state SN (N > 1) and develop a computational methodology for the simulation of nonlinear spectroscopic signals revealing the SN → TT1 SF in real time. We demonstrate that SF can proceed directly from the upper state SN, bypassing the lowest excited state, S1. We determine the main SN → TT1 reaction pathways and show by computer simulation and spectroscopic measurements that the SN-initiated SF can be faster and more efficient than the traditionally studied S1 → TT1 SF. We claim that the SN → TT1 SF offers novel promising opportunities for engineering SF systems and enhancing SF yields.
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Affiliation(s)
- Yiting Bai
- School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Wenjun Ni
- School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Kewei Sun
- School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China
| | | | - Lin Ma
- School of Physics and Optoelectronic Engineering, Guangdong University of Technology, Guangdong 510006, China
| | - Yang Zhao
- School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore
| | - Gagik G Gurzadyan
- State Key Laboratory of Fine Chemicals, Institute of Artificial Photosynthesis, Dalian University of Technology, Dalian 116024, China
| | - Maxim F Gelin
- School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China
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3
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Chen Q, Kwok YH, Zhou W, Chen G, Mukamel S. Time-dependent simulation of photocurrent-detected two-dimensional spectroscopy of open systems. J Chem Phys 2021; 155:194113. [PMID: 34800940 DOI: 10.1063/5.0067362] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new time-domain simulation protocol of two-dimensional electronic spectra with photocurrent detection is presented. Time-dependent density functional theory for open systems at finite temperature is applied to evaluate the photocurrent response to four laser pulses, and a non-perturbative phase-matching approach is implemented to extract the fourth-order photocurrent signal with a desired phase-matching condition. Simulations for an open three-level model indicates that transition dipoles interact resonantly with the incident pulses and that different sample-electrode couplings may be identified by appearance of different peaks/valleys in photocurrent spectra from different electrodes. Moreover, qualitative reproduction of experimental spectra of a PbS quantum dot photocell [Karki et al., Nat. Commun. 5(1), 5869 (2014)] reveals the stimulated electron dynamics.
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Affiliation(s)
- Qizhou Chen
- Department of Chemistry, The University of Hong Kong, Pok Fu Lam Road, Hong Kong, China
| | - Yan Ho Kwok
- Department of Chemistry, The University of Hong Kong, Pok Fu Lam Road, Hong Kong, China
| | - Weijun Zhou
- Department of Chemistry, The University of Hong Kong, Pok Fu Lam Road, Hong Kong, China
| | - Guanhua Chen
- Department of Chemistry, The University of Hong Kong, Pok Fu Lam Road, Hong Kong, China
| | - Shaul Mukamel
- Department of Chemistry, Department of Physics and Astronomy, University of California, Irvine, California 92617, USA
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Chen L, Borrelli R, Shalashilin DV, Zhao Y, Gelin MF. Simulation of Time- and Frequency-Resolved Four-Wave-Mixing Signals at Finite Temperatures: A Thermo-Field Dynamics Approach. J Chem Theory Comput 2021; 17:4359-4373. [PMID: 34107216 DOI: 10.1021/acs.jctc.1c00259] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We propose a new approach to simulate four-wave-mixing signals of molecular systems at finite temperatures by combining the multiconfigurational Ehrenfest method with the thermo-field dynamics theory. In our approach, the four-time correlation functions at finite temperatures are mapped onto those at zero temperature in an enlarged Hilbert space with twice the vibrational degrees of freedom. As an illustration, we have simulated three multidimensional spectroscopic signals, time- and frequency-resolved fluorescence spectra, transient-absorption pump-probe spectra, and electronic two-dimensional (2D) spectra at finite temperatures, for a conical intersection-mediated singlet fission model of a rubrene crystal. It is shown that a detailed dynamical picture of the singlet fission process can be extracted from the three spectroscopic signals. An increasing temperature leads to lower intensities of the signals and broadened vibrational peaks, which can be attributed to faster singlet-triplet population transfer and stronger bath-induced electronic dephasing at higher temperatures.
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Affiliation(s)
- Lipeng Chen
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str 38, 01187 Dresden, Germany
| | - Raffaele Borrelli
- Department of Agricultural, Forestry and Food Science, Universitá di Torino, I-10095 Grugliasco, TO, Italy
| | | | - Yang Zhao
- Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore
| | - Maxim F Gelin
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
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5
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Rose PA, Krich JJ. Efficient numerical method for predicting nonlinear optical spectroscopies of open systems. J Chem Phys 2021; 154:034108. [PMID: 33499622 DOI: 10.1063/5.0024104] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Abstract
Nonlinear optical spectroscopies are powerful tools for probing quantum dynamics in molecular and nanoscale systems. While intuition about ultrafast spectroscopies is often built by considering impulsive optical pulses, actual experiments have finite-duration pulses, which can be important for interpreting and predicting experimental results. We present a new freely available open source method for spectroscopic modeling, called Ultrafast Ultrafast (UF2) spectroscopy, which enables computationally efficient and convenient prediction of nonlinear spectra, such as treatment of arbitrary finite duration pulse shapes. UF2 is a Fourier-based method that requires diagonalization of the Liouvillian propagator of the system density matrix. We also present a Runge-Kutta-Euler (RKE) direct propagation method. We include open system dynamics in the secular Redfield, full Redfield, and Lindblad formalisms with Markovian baths. For non-Markovian systems, the degrees of freedom corresponding to memory effects are brought into the system and treated nonperturbatively. We analyze the computational complexity of the algorithms and demonstrate numerically that, including the cost of diagonalizing the propagator, UF2 is 20-200 times faster than the direct propagation method for secular Redfield models with arbitrary Hilbert space dimension; it is similarly faster for full Redfield models at least up to system dimensions where the propagator requires more than 20 GB to store; and for Lindblad models, it is faster up to Hilbert space dimension near 100 with speedups for small systems by factors of over 500. UF2 and RKE are part of a larger open source Ultrafast Software Suite, which includes tools for automatic generation and calculation of Feynman diagrams.
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Affiliation(s)
- Peter A Rose
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Jacob J Krich
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
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Kwok Y, Chen G, Mukamel S. STM Imaging of Electron Migration in Real Space and Time: A Simulation Study. NANO LETTERS 2019; 19:7006-7012. [PMID: 31509425 DOI: 10.1021/acs.nanolett.9b02389] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Using a simulation protocol that mimics ultrafast scanning tunneling microscopy (STM) experiments, we demonstrate how pump-probe ultrafast STM may be used to image electron migration in molecules. Two pulses are applied to a model system, and the time-integrated current through the tip is calculated versus the delay time and tip position to generate STM images. With suitable pump and probe parameters, the images can track charge migration with atomistic spatial and femtosecond temporal resolutions.
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Affiliation(s)
- YanHo Kwok
- Department of Chemistry , The University of Hong Kong , Pofkulam Road , Hong Kong
- QuantumFabless Limited , Sha Tin , Hong Kong
| | - GuanHua Chen
- Department of Chemistry , The University of Hong Kong , Pofkulam Road , Hong Kong
| | - Shaul Mukamel
- Department of Chemistry and Physics and Astronomy , University of California , Irvine , California 92617 , United States
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Rose PA, Krich JJ. Numerical method for nonlinear optical spectroscopies: Ultrafast ultrafast spectroscopy. J Chem Phys 2019; 150:214105. [DOI: 10.1063/1.5094062] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Peter A. Rose
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Jacob J. Krich
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
- School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
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Gelin MF, Borrelli R, Domcke W. Efficient orientational averaging of nonlinear optical signals in
multi-chromophore systems. J Chem Phys 2017; 147:044114. [DOI: 10.1063/1.4996205] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Affiliation(s)
- Maxim F. Gelin
- Department of Chemistry, Technische Universität
München, D-85747 Garching, Germany
| | | | - Wolfgang Domcke
- Department of Chemistry, Technische Universität
München, D-85747 Garching, Germany
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Abstract
Femtosecond two-dimensional (2D) spectroscopy has become a widely employed method for the investigation of the dynamics of complex chemical and biological systems. In 2D spectroscopy, the sample is excited with three phase-locked femtosecond pulses, and the signal is heterodyned with the local oscillator field. The 2D spectrum is obtained by double Fourier transform with respect to the time delay between the first two pulses and the time delay between the third pulse and the local oscillator field. We show that 2D optical signals can alternatively be measured and computationally simulated as four-wave-mixing signals generated by two femtosecond pulses and two one-sided continuous-wave (CW) pulses. The first femtosecond pulse and one-sided CW pulse create the doorway state, while the second femtosecond pulse and one-sided CW pulse create the window state. This picture relates 2D spectroscopy to other mixed time-frequency-domain techniques, which is useful for the interpretation of the corresponding signals. Moreover, it allows a computationally efficient evaluation of 2D spectra.
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Affiliation(s)
- Maxim F Gelin
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
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Gelin MF, Domcke W, Rao BJ. Femtosecond stimulated Raman spectroscopy as a tool to detect molecular vibrations in ground and excited electronic states. J Chem Phys 2016; 144:184307. [PMID: 27179484 DOI: 10.1063/1.4948707] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We give a detailed theoretical analysis of the simplest variant of femtosecond stimulated Raman spectroscopy, where a picosecond Raman pump pulse and a femtosecond Raman probe pulse are applied resonantly to a chromophore in thermal equilibrium in the ground electronic state. We demonstrate that this technique is capable of the detection of dephasing-free Raman-like lines revealing vibrational modes not only in the electronic ground state but also in the excited electronic state of the chromophore. The analytical results obtained with simplifying assumptions for the shape of the laser pulses are substantiated by numerical simulations with realistic laser pulses, employing the equation-of-motion phase-matching approach.
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Affiliation(s)
- Maxim F Gelin
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
| | - B Jayachander Rao
- Departamento de Química and Centro de Química, Universidade de Coimbra, 3004-535 Coimbra, Portugal
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Rao BJ, Gelin MF, Domcke W. Resonant Femtosecond Stimulated Raman Spectra: Theory and Simulations. J Phys Chem A 2016; 120:3286-95. [DOI: 10.1021/acs.jpca.5b12316] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- B. Jayachander Rao
- Departamento de Química,
and Centro de Química, Universidade de Coimbra, 3004-535 Coimbra, Portugal
| | - Maxim F. Gelin
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
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Martinez F, Hanna G. Mixed Quantum-Classical Simulations of Transient Absorption Pump–Probe Signals for a Photo-Induced Electron Transfer Reaction Coupled to an Inner-Sphere Vibrational Mode. J Phys Chem A 2016; 120:3196-205. [DOI: 10.1021/acs.jpca.5b11727] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Franz Martinez
- Department
of Chemistry, University of Alberta, Edmonton, Alberta T6G 2R3, Canada
| | - Gabriel Hanna
- Department
of Chemistry, University of Alberta, Edmonton, Alberta T6G 2R3, Canada
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Krčmář J, Gelin MF, Domcke W. Simulation of femtosecond two-dimensional electronic spectra of conical intersections. J Chem Phys 2015; 143:074308. [PMID: 26298135 DOI: 10.1063/1.4928685] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have simulated femtosecond two-dimensional (2D) electronic spectra for an excited-state conical intersection using the wave-function version of the equation-of-motion phase-matching approach. We show that 2D spectra at fixed values of the waiting time provide information on the structure of the vibronic eigenstates of the conical intersection, while the evolution of the spectra with the waiting time reveals predominantly ground-state wave-packet dynamics. The results show that 2D spectra of conical intersection systems differ significantly from those obtained for chromophores with well separated excited-state potential-energy surfaces. The spectral signatures which can be attributed to conical intersections are discussed.
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Affiliation(s)
- Jindřich Krčmář
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
| | - Maxim F Gelin
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
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Sun KW, Gelin MF, Chernyak VY, Zhao Y. Davydov Ansatz as an efficient tool for the simulation of nonlinear optical response of molecular aggregates. J Chem Phys 2015; 142:212448. [DOI: 10.1063/1.4921575] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Ke-Wei Sun
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
| | - Maxim F. Gelin
- Department of Chemistry, Technische Universität München, Garching D-85747, Germany
| | - Vladimir Y. Chernyak
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
- Department of Chemistry, Wayne State University, Detroit, Michigan 48202, USA
| | - Yang Zhao
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
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15
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Martinez F, Hanna G. Assessment of approximate solutions of the quantum–classical Liouville equation for dynamics simulations of quantum subsystems embedded in classical environments. MOLECULAR SIMULATION 2014. [DOI: 10.1080/08927022.2014.923573] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Krčmář J, Gelin MF, Domcke W. Calculation of third-order signals via driven Schrödinger equations: General results and application to electronic 2D photon echo spectroscopy. Chem Phys 2013. [DOI: 10.1016/j.chemphys.2013.01.002] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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17
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Martinez F, Rekik N, Hanna G. Simulation of nonlinear optical signals via approximate solutions of the quantum–classical Liouville equation: Application to the pump–probe spectroscopy of a condensed phase electron transfer reaction. Chem Phys Lett 2013. [DOI: 10.1016/j.cplett.2013.04.018] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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18
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Monitoring bipartite entanglement in hybrid carbon nanotube systems via optical 2D photon-echo spectroscopy. Chem Phys 2013. [DOI: 10.1016/j.chemphys.2012.09.027] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Gelin MF, Egorova D, Domcke W. Optical N-wave-mixing spectroscopy with strong and temporally well-separated pulses: the doorway-window representation. J Phys Chem B 2011; 115:5648-58. [PMID: 21425818 DOI: 10.1021/jp112055h] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
We have extended the doorway-window representation of optical pump-probe spectroscopy with weak pulses toward N-wave-mixing spectroscopy with temporally well-separated pulses of arbitrary strength. The expressions for the signals in the strong-pulse doorway-window representation are derived in the framework of the nonperturbative theory of N-wave-mixing spectroscopy. The strong-pulse doorway-window representation is complementary to the equation-of-motion phase-matching approach. The latter fully accounts for pulse-overlap effects in signals induced by weak pulses but is computationally more expensive. The performance of the doorway-window approximation for temporally well-separated strong pulses is illustrated for an electronic two-level system with an underdamped Condon-active vibrational mode.
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Affiliation(s)
- Maxim F Gelin
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
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Gelin MF, Riehn C, Kunitski M, Brutschy B. Strong field effects in rotational femtosecond degenerate four-wave mixing. J Chem Phys 2010; 132:134301. [DOI: 10.1063/1.3367726] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
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