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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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Chen L, Sun K, Shalashilin DV, Gelin MF, Zhao Y. Efficient simulation of time- and frequency-resolved four-wave-mixing signals with a multiconfigurational Ehrenfest approach. J Chem Phys 2021; 154:054105. [PMID: 33557567 DOI: 10.1063/5.0038824] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
We have extended the multiconfigurational Ehrenfest approach to the simulation of four-wave-mixing signals of systems involving multiple electronic and vibrational degrees of freedom. As an illustration, we calculate signals of three widely used spectroscopic techniques, time- and frequency-resolved fluorescence spectroscopy, transient absorption spectroscopy, and two-dimensional (2D) electronic spectroscopy, for a two-electronic-state, twenty-four vibrational-mode conical intersection model. It has been shown that all these three spectroscopic signals characterize fast population transfer from the higher excited electronic state to the lower excited electronic state. While the time- and frequency-resolved spectrum maps the wave packet propagation exclusively on the electronically excited states, the transient absorption and 2D electronic spectra reflect the wave packet dynamics on both electronically excited states and the electronic ground state. Combining trajectory-guided Gaussian basis functions and the nonlinear response function formalism, the present approach provides a promising general technique for the applications of various Gaussian basis methods to the calculations of four-wave-mixing spectra of polyatomic molecules.
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Affiliation(s)
- Lipeng Chen
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, Dresden, Germany
| | - Kewei Sun
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | | | - Maxim F Gelin
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Yang Zhao
- Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore
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Begušić T, Vaníček J. On-the-fly ab initio semiclassical evaluation of third-order response functions for two-dimensional electronic spectroscopy. J Chem Phys 2020; 153:184110. [DOI: 10.1063/5.0031216] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Affiliation(s)
- Tomislav Begušić
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Jiří Vaníček
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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Kiessling AJ, Cina JA. Exploring a spectral filtering approach to electronic structure calculations. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1827178] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Alexis J. Kiessling
- Department of Chemistry and Biochemistry, University of Oregon, Eugene, Oregon, USA
- Oregon Center for Optical, Molecular, and Quantum Science, University of Oregon, Eugene, Oregon, USA
| | - Jeffrey A. Cina
- Department of Chemistry and Biochemistry, University of Oregon, Eugene, Oregon, USA
- Oregon Center for Optical, Molecular, and Quantum Science, University of Oregon, Eugene, Oregon, USA
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Picconi D, Burghardt I. Time-resolved spectra of I2 in a krypton crystal by G-MCTDH simulations: nonadiabatic dynamics, dissipation and environment driven decoherence. Faraday Discuss 2020; 221:30-58. [DOI: 10.1039/c9fd00065h] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Time- and frequency-resolved pump-probe spectra of I2 in a krypton crystal are calculated and analyzed using high-dimensional multi-state quantum dynamics by the Gaussian-based multi-configuration time-dependent Hartree (G-MCTDH) method.
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Affiliation(s)
- David Picconi
- Institute of Physical and Theoretical Chemistry
- Goethe University Frankfurt
- D-60438 Frankfurt am Main
- Germany
| | - Irene Burghardt
- Institute of Physical and Theoretical Chemistry
- Goethe University Frankfurt
- D-60438 Frankfurt am Main
- Germany
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Conte R, Parma L, Aieta C, Rognoni A, Ceotto M. Improved semiclassical dynamics through adiabatic switching trajectory sampling. J Chem Phys 2019; 151:214107. [PMID: 31822104 DOI: 10.1063/1.5133144] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We introduce an improved semiclassical dynamics approach to quantum vibrational spectroscopy. In this method, a harmonic-based phase space sampling is preliminarily driven toward non-harmonic quantization by slowly switching on the actual potential. The new coordinates and momenta serve as initial conditions for the semiclassical dynamics calculation, leading to a substantial decrease in the number of chaotic trajectories to deal with. Applications are presented for model and molecular systems of increasing dimensionality characterized by moderate or high chaoticity. They include a bidimensional Henon-Heiles potential, water, formaldehyde, and methane. The method improves accuracy and precision of semiclassical results and it can be easily interfaced with all pre-existing semiclassical theories.
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Affiliation(s)
- Riccardo Conte
- Dipartimento di Chimica, Università degli Studi di Milano, Via Golgi 19, 20133 Milano, Italy
| | - Lorenzo Parma
- Dipartimento di Chimica, Università degli Studi di Milano, Via Golgi 19, 20133 Milano, Italy
| | - Chiara Aieta
- Dipartimento di Chimica, Università degli Studi di Milano, Via Golgi 19, 20133 Milano, Italy
| | - Alessandro Rognoni
- Dipartimento di Chimica, Università degli Studi di Milano, Via Golgi 19, 20133 Milano, Italy
| | - Michele Ceotto
- Dipartimento di Chimica, Università degli Studi di Milano, Via Golgi 19, 20133 Milano, Italy
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Lotshaw PC, Kellman ME. Simulating quantum thermodynamics of a finite system and bath with variable temperature. Phys Rev E 2019; 100:042105. [PMID: 31770971 DOI: 10.1103/physreve.100.042105] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2019] [Indexed: 11/07/2022]
Abstract
We construct a finite bath with variable temperature for quantum thermodynamic simulations in which heat flows between a system S and the bath environment E in time evolution of an initial SE pure state. The bath consists of harmonic oscillators that are not necessarily identical. Baths of various numbers of oscillators are considered; a bath with five oscillators is used in the simulations. The bath has a temperaturelike level distribution. This leads to definition of a system-environment microcanonical temperature T_{SE}(t) which varies with time. The quantum state evolves toward an equilibrium state which is thermal-like, but there is significant deviation from the ordinary energy-temperature relation that holds for an infinite quantum bath, e.g., an infinite system of identical oscillators. There are also deviations from the Einstein quantum heat capacity. The temperature of the finite bath is systematically greater for a given energy than the infinite bath temperature, and asymptotically approaches the latter as the number of oscillators increases. It is suggested that realizations of these finite-size effects may be attained in computational and experimental dynamics of small molecules.
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Affiliation(s)
- Phillip C Lotshaw
- Institute of Theoretical Science and Department of Chemistry and Biochemistry, University of Oregon, Eugene, Oregon 97403, USA
| | - Michael E Kellman
- Institute of Theoretical Science and Department of Chemistry and Biochemistry, University of Oregon, Eugene, Oregon 97403, USA
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Picconi D, Cina JA, Burghardt I. Quantum dynamics and spectroscopy of dihalogens in solid matrices. I. Efficient simulation of the photodynamics of the embedded I 2Kr 18 cluster using the G-MCTDH method. J Chem Phys 2019; 150:064111. [PMID: 30770011 DOI: 10.1063/1.5082650] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
The molecular dynamics following the electronic BΠu30+⟵XΣg+1 photoexcitation of the iodine molecule embedded in solid krypton are studied quantum mechanically using the Gaussian variant of the multiconfigurational time-dependent Hartree method (G-MCTDH). The accuracy of the Gaussian wave packet approximation is validated against numerically exact MCTDH simulations for a fully anharmonic seven-dimensional model of the I2Kr18 cluster in a crystal Kr cage. The linear absorption spectrum, time-evolving vibrational probability densities, and I2 energy expectation value are accurately reproduced by the numerically efficient G-MCTDH approach. The reduced density matrix of the chromophore is analyzed in the coordinate, Wigner and energy representations, so as to obtain a multifaceted dynamical view of the guest-host interactions. Vibrational coherences extending over the bond distance range 2.7 Å < RI-I < 4.0 Å are found to survive for several vibrational periods, despite extensive dissipation. The present results prepare the ground for the simulation of time-resolved coherent Raman spectroscopy of the I2-krypton system addressed in Paper II.
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Affiliation(s)
- David Picconi
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Straße 7, D-60438 Frankfurt am Main, Germany
| | - Jeffrey A Cina
- Department of Chemistry and Biochemistry, and Oregon Center for Optical, Molecular, and Quantum Science, University of Oregon, Eugene, Oregon 97403, USA
| | - Irene Burghardt
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Straße 7, D-60438 Frankfurt am Main, Germany
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Eisenbrandt P, Ruckenbauer M, Römer S, Burghardt I. Gaussian-based multiconfiguration time-dependent Hartree: A two-layer approach. II. Application to vibrational energy transport in a molecular chain. J Chem Phys 2018; 149:174101. [DOI: 10.1063/1.5053414] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- P. Eisenbrandt
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt, Germany
| | - M. Ruckenbauer
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt, Germany
| | - S. Römer
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt, Germany
| | - I. Burghardt
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt, Germany
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Buchholz M, Grossmann F, Ceotto M. Simplified approach to the mixed time-averaging semiclassical initial value representation for the calculation of dense vibrational spectra. J Chem Phys 2018; 148:114107. [DOI: 10.1063/1.5020144] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Max Buchholz
- Dipartimento di Chimica, Università degli Studi di Milano, Via C. Golgi 19, 20133 Milano, Italy
| | - Frank Grossmann
- Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
| | - Michele Ceotto
- Dipartimento di Chimica, Università degli Studi di Milano, Via C. Golgi 19, 20133 Milano, Italy
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