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Liu Z, Lyu N, Hu Z, Zeng H, Batista VS, Sun X. Benchmarking various nonadiabatic semiclassical mapping dynamics methods with tensor-train thermo-field dynamics. J Chem Phys 2024; 161:024102. [PMID: 38980091 DOI: 10.1063/5.0208708] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2024] [Accepted: 06/20/2024] [Indexed: 07/10/2024] Open
Abstract
Accurate quantum dynamics simulations of nonadiabatic processes are important for studies of electron transfer, energy transfer, and photochemical reactions in complex systems. In this comparative study, we benchmark various approximate nonadiabatic dynamics methods with mapping variables against numerically exact calculations based on the tensor-train (TT) representation of high-dimensional arrays, including TT-KSL for zero-temperature dynamics and TT-thermofield dynamics for finite-temperature dynamics. The approximate nonadiabatic dynamics methods investigated include mixed quantum-classical Ehrenfest mean-field and fewest-switches surface hopping, linearized semiclassical mapping dynamics, symmetrized quasiclassical dynamics, the spin-mapping method, and extended classical mapping models. Different model systems were evaluated, including the spin-boson model for nonadiabatic dynamics in the condensed phase, the linear vibronic coupling model for electronic transition through conical intersections, the photoisomerization model of retinal, and Tully's one-dimensional scattering models. Our calculations show that the optimal choice of approximate dynamical method is system-specific, and the accuracy is sensitively dependent on the zero-point-energy parameter and the initial sampling strategy for the mapping variables.
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Affiliation(s)
- Zengkui Liu
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- Department of Chemistry, New York University, New York, New York 10003, USA
| | - Ningyi Lyu
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Zhubin Hu
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Hao Zeng
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Victor S Batista
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Xiang Sun
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- Department of Chemistry, New York University, New York, New York 10003, USA
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
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2
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Sayer T, Montoya-Castillo A. Generalized quantum master equations can improve the accuracy of semiclassical predictions of multitime correlation functions. J Chem Phys 2024; 161:011101. [PMID: 38949578 DOI: 10.1063/5.0219205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2024] [Accepted: 06/12/2024] [Indexed: 07/02/2024] Open
Abstract
Multitime quantum correlation functions are central objects in physical science, offering a direct link between the experimental observables and the dynamics of an underlying model. While experiments such as 2D spectroscopy and quantum control can now measure such quantities, the accurate simulation of such responses remains computationally expensive and sometimes impossible, depending on the system's complexity. A natural tool to employ is the generalized quantum master equation (GQME), which can offer computational savings by extending reference dynamics at a comparatively trivial cost. However, dynamical methods that can tackle chemical systems with atomistic resolution, such as those in the semiclassical hierarchy, often suffer from poor accuracy, limiting the credence one might lend to their results. By combining work on the accuracy-boosting formulation of semiclassical memory kernels with recent work on the multitime GQME, here we show for the first time that one can exploit a multitime semiclassical GQME to dramatically improve both the accuracy of coarse mean-field Ehrenfest dynamics and obtain orders of magnitude efficiency gains.
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Affiliation(s)
- Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
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3
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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: 20] [Impact Index Per Article: 10.0] [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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4
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Malpathak S, Church MS, Ananth N. A Semiclassical Framework for Mixed Quantum Classical Dynamics. J Phys Chem A 2022; 126:6359-6375. [PMID: 36070472 DOI: 10.1021/acs.jpca.2c03467] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Semiclassical (SC) approximations for quantum dynamic simulations in complex chemical systems range from rigorously accurate methods that are computationally expensive to methods that exhibit near-classical scaling with system size but are limited in their ability to describe quantum effects. In practical studies of high-dimensional reactions, neither extreme is the best choice: frequently a high-level quantum mechanical description is only required for a handful of modes, while the majority of environment modes that do not play a key role in the reactive event of interest are well served with a lower level of theory. In this feature, we introduce modified Filinov filtration as a powerful tool to construct mixed quantum-classical SC theories where different subsystems can be quantized to different extents without introducing ad hoc intersubsystem interaction terms. We demonstrate that these Filinov-based SC methods can systematically tune between quantum and classical limit SC behavior, offering a practical way forward to accurate and computationally efficient simulations of high-dimensional quantum processes.
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Affiliation(s)
- Shreyas Malpathak
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University Ithaca, New York 14853, United States
| | - Matthew S Church
- Department of Chemistry, Brown University, Providence, Rhode Island 02906, United States
| | - Nandini Ananth
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University Ithaca, New York 14853, United States
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5
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Mannouch JR, Richardson JO. A partially linearized spin-mapping approach for simulating nonlinear optical spectra. J Chem Phys 2022; 156:024108. [PMID: 35032975 DOI: 10.1063/5.0077744] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a partially linearized method based on spin-mapping for computing both linear and nonlinear optical spectra. As observables are obtained from ensembles of classical trajectories, the approach can be applied to the large condensed-phase systems that undergo photosynthetic light-harvesting processes. In particular, the recently derived spin partially linearized density matrix method has been shown to exhibit superior accuracy in computing population dynamics compared to other related classical-trajectory methods. Such a method should also be ideally suited to describing the quantum coherences generated by interaction with light. We demonstrate that this is, indeed, the case by calculating the nonlinear optical response functions relevant for the pump-probe and 2D photon-echo spectra for a Frenkel biexciton model and the Fenna-Matthews-Olsen light-harvesting complex. One especially desirable feature of our approach is that the full spectrum can be decomposed into its constituent components associated with the various Liouville-space pathways, offering a greater insight beyond what can be directly obtained from experiments.
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6
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Hu Z, Brian D, Sun X. Multi-state harmonic models with globally shared bath for nonadiabatic dynamics in the condensed phase. J Chem Phys 2021; 155:124105. [PMID: 34598571 DOI: 10.1063/5.0064763] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
Model Hamiltonians constructed from quantum chemistry calculations and molecular dynamics simulations are widely used for simulating nonadiabatic dynamics in the condensed phase. The most popular two-state spin-boson model could be built by mapping the all-atom anharmonic Hamiltonian onto a two-level system bilinearly coupled to a harmonic bath using the energy gap time correlation function. However, for more than two states, there lacks a general strategy to construct multi-state harmonic (MSH) models since the energy gaps between different pairs of electronic states are not entirely independent and need to be considered consistently. In this paper, we extend the previously proposed approach for building three-state harmonic models for photoinduced charge transfer to the arbitrary number of electronic states with a globally shared bath and the system-bath couplings are scaled differently according to the reorganization energies between each pair of states. We demonstrate the MSH model construction for an organic photovoltaic carotenoid-porphyrin-C60 molecular triad dissolved in explicit tetrahydrofuran solvent. Nonadiabatic dynamics was simulated using mixed quantum-classical techniques, including the linearized semiclassical and symmetrical quasiclassical dynamics with the mapping Hamiltonians, mean-field Ehrenfest, and mixed quantum-classical Liouville dynamics in two-state, three-state, and four-state harmonic models of the triad system. The MSH models are shown to provide a general and flexible framework for simulating nonadiabatic dynamics in complex systems.
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Affiliation(s)
- Zhubin Hu
- Division of Arts and Sciences, NYU Shanghai, 1555 Century Avenue, Shanghai 200122, China
| | - Dominikus Brian
- Division of Arts and Sciences, NYU Shanghai, 1555 Century Avenue, Shanghai 200122, China
| | - Xiang Sun
- Division of Arts and Sciences, NYU Shanghai, 1555 Century Avenue, Shanghai 200122, China
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7
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Provazza J, Tempelaar R, Coker DF. Analytic and numerical vibronic spectra from quasi-classical trajectory ensembles. J Chem Phys 2021; 155:014108. [PMID: 34241392 DOI: 10.1063/5.0053735] [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
The truncated Wigner approximation to quantum dynamics in phase space is explored in the context of computing vibronic line shapes for monomer linear optical spectra. We consider multiple model potential forms including a shifted harmonic oscillator with both equal and unequal frequencies on the ground and excited state potentials as well as a shifted Morse potential model. For the equal-frequency shifted harmonic oscillator model, we derive an analytic expression for the exact vibronic line shape that emphasizes the importance of using a quantum mechanical distribution of phase space initial conditions. For the unequal-frequency shifted harmonic oscillator model, we are no longer able to obtain an exact expression for the vibronic line shape in terms of independent deterministic classical trajectories. We show how one can rigorously account for corrections to the truncated Wigner approximation through nonlinear responses of the line shape function to momentum fluctuations along a classical trajectory and demonstrate the qualitative improvement in the resulting spectrum when the leading-order quantum correction is included. Finally, we numerically simulate absorption spectra of a highly anharmonic shifted Morse potential model. We find that, while finite quantization and the dissociation limit are captured with reasonable accuracy, there is a qualitative breakdown of the quasi-classical trajectory ensemble's ability to describe the vibronic line shape when the relative shift in Morse potentials becomes large. The work presented here provides clarity on the origin of unphysical negative features known to contaminate absorption spectra computed with quasi-classical trajectory ensembles.
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Affiliation(s)
- Justin Provazza
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
| | - Roel Tempelaar
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
| | - David F Coker
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA
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8
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Gao X, Geva E. Improving the Accuracy of Quasiclassical Mapping Hamiltonian Methods by Treating the Window Function Width as an Adjustable Parameter. J Phys Chem A 2020; 124:11006-11016. [DOI: 10.1021/acs.jpca.0c09750] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xing Gao
- School of Materials, Sun Yat-sen University, Shenzhen, Guangdong 518100, China
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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9
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Gao X, Saller MAC, Liu Y, Kelly A, Richardson JO, Geva E. Benchmarking Quasiclassical Mapping Hamiltonian Methods for Simulating Electronically Nonadiabatic Molecular Dynamics. J Chem Theory Comput 2020; 16:2883-2895. [DOI: 10.1021/acs.jctc.9b01267] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xing Gao
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | | | - Yudan Liu
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Aaron Kelly
- Department of Chemistry, Dalhousie University, 15000 Halifax, Nova Scotia, Canada
| | | | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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10
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Mulvihill E, Gao X, Liu Y, Schubert A, Dunietz BD, Geva E. Combining the mapping Hamiltonian linearized semiclassical approach with the generalized quantum master equation to simulate electronically nonadiabatic molecular dynamics. J Chem Phys 2019; 151:074103. [DOI: 10.1063/1.5110891] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ellen Mulvihill
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Xing Gao
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Yudan Liu
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Alexander Schubert
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, USA
| | - Barry D. Dunietz
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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11
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Polley K, Loring RF. Two-dimensional vibronic spectra from classical trajectories. J Chem Phys 2019; 150:164114. [DOI: 10.1063/1.5093911] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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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12
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Karsten S, Ivanov SD, Bokarev SI, Kühn O. Quasi-classical approaches to vibronic spectra revisited. J Chem Phys 2018; 148:102337. [DOI: 10.1063/1.5011764] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Sven Karsten
- Institute of Physics, Rostock University, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
| | - Sergei D. Ivanov
- Institute of Physics, Rostock University, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
| | - Sergey I. Bokarev
- Institute of Physics, Rostock University, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
| | - Oliver Kühn
- Institute of Physics, Rostock University, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
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13
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Ramesh P, Loring RF. Thermal Population Fluctuations in Two-Dimensional Infrared Spectroscopy Captured with Semiclassical Mechanics. J Phys Chem B 2018; 122:3647-3654. [DOI: 10.1021/acs.jpcb.7b12122] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Prashanth Ramesh
- 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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14
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Antipov SV, Bhattacharyya S, El Hage K, Xu ZH, Meuwly M, Rothlisberger U, Vaníček J. Ultrafast dynamics induced by the interaction of molecules with electromagnetic fields: Several quantum, semiclassical, and classical approaches. STRUCTURAL DYNAMICS (MELVILLE, N.Y.) 2017; 4:061509. [PMID: 29376107 PMCID: PMC5758379 DOI: 10.1063/1.4996559] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/17/2017] [Accepted: 10/11/2017] [Indexed: 06/07/2023]
Abstract
Several strategies for simulating the ultrafast dynamics of molecules induced by interactions with electromagnetic fields are presented. After a brief overview of the theory of molecule-field interaction, we present several representative examples of quantum, semiclassical, and classical approaches to describe the ultrafast molecular dynamics, including the multiconfiguration time-dependent Hartree method, Bohmian dynamics, local control theory, semiclassical thawed Gaussian approximation, phase averaging, dephasing representation, molecular mechanics with proton transfer, and multipolar force fields. In addition to the general overview, some focus is given to the description of nuclear quantum effects and to the direct dynamics, in which the ab initio energies and forces acting on the nuclei are evaluated on the fly. Several practical applications, performed within the framework of the Swiss National Center of Competence in Research "Molecular Ultrafast Science and Technology," are presented: These include Bohmian dynamics description of the collision of H with H2, local control theory applied to the photoinduced ultrafast intramolecular proton transfer, semiclassical evaluation of vibrationally resolved electronic absorption, emission, photoelectron, and time-resolved stimulated emission spectra, infrared spectroscopy of H-bonding systems, and multipolar force fields applications in the condensed phase.
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Affiliation(s)
- Sergey V Antipov
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Swarnendu Bhattacharyya
- Laboratory of Computational Chemistry and Biochemistry, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Krystel El Hage
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Zhen-Hao Xu
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Markus Meuwly
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Ursula Rothlisberger
- Laboratory of Computational Chemistry and Biochemistry, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Jiří Vaníček
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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15
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Karsten S, Bokarev SI, Aziz SG, Ivanov SD, Kühn O. A time-correlation function approach to nuclear dynamical effects in X-ray spectroscopy. J Chem Phys 2017; 146:224203. [DOI: 10.1063/1.4984930] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sven Karsten
- Institute of Physics, Rostock University, Universitätsplatz 3, 18055 Rostock, Germany
| | - Sergey I. Bokarev
- Institute of Physics, Rostock University, Universitätsplatz 3, 18055 Rostock, Germany
| | - Saadullah G. Aziz
- Chemistry Department, Faculty of Science, King Abdulaziz University, 21589 Jeddah, Saudi Arabia
| | - Sergei D. Ivanov
- Institute of Physics, Rostock University, Universitätsplatz 3, 18055 Rostock, Germany
| | - Oliver Kühn
- Institute of Physics, Rostock University, Universitätsplatz 3, 18055 Rostock, Germany
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16
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Petrone A, Williams-Young DB, Lingerfelt DB, Li X. Ab Initio Excited-State Transient Raman Analysis. J Phys Chem A 2017; 121:3958-3965. [DOI: 10.1021/acs.jpca.7b02905] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Alessio Petrone
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | | | - David B. Lingerfelt
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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17
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Loring RF. Mean-trajectory approximation for electronic and vibrational-electronic nonlinear spectroscopy. J Chem Phys 2017; 146:144106. [DOI: 10.1063/1.4979621] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Roger F. Loring
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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18
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Petrone A, Lingerfelt DB, Williams-Young DB, Li X. Ab Initio Transient Vibrational Spectral Analysis. J Phys Chem Lett 2016; 7:4501-4508. [PMID: 27788583 DOI: 10.1021/acs.jpclett.6b02292] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Pump probe spectroscopy techniques have enabled the direct observation of a variety of transient molecular species in both ground and excited electronic states. Time-resolved vibrational spectroscopy is becoming an indispensable tool for investigating photoinduced nuclear dynamics of chemical systems of all kinds. On the other hand, a complete picture of the chemical dynamics encoded in these spectra cannot be achieved without a full temporal description of the structural relaxation, including the explicit time-dependence of vibrational coordinates that are substantially displaced from equilibrium by electronic excitation. Here we present a transient vibrational analysis protocol combining ab initio direct molecular dynamics and time-integrated normal modes introduced in this work, relying on the recent development of analytic time-dependent density functional theory (TDDFT) second derivatives for excited states. Prototypical molecules will be used as test cases, showing the evolution of the vibrational signatures that follow electronic excitation. This protocol provides a direct route to assigning the vibrations implicated in the (photo)dynamics of several (photoactive) systems.
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Affiliation(s)
- Alessio Petrone
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - David B Lingerfelt
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - David B Williams-Young
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
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19
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Sun X, Geva E. Non-Condon nonequilibrium Fermi’s golden rule rates from the linearized semiclassical method. J Chem Phys 2016. [DOI: 10.1063/1.4960337] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Xiang Sun
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
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20
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Sun X, Geva E. Non-Condon equilibrium Fermi’s golden rule electronic transition rate constants via the linearized semiclassical method. J Chem Phys 2016; 144:244105. [DOI: 10.1063/1.4954509] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Xiang Sun
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
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21
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Vaníček J, Cohen D. Path integral approach to the quantum fidelity amplitude. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2016; 374:rsta.2015.0164. [PMID: 27140973 PMCID: PMC4855403 DOI: 10.1098/rsta.2015.0164] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 10/13/2015] [Indexed: 06/05/2023]
Abstract
The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and in its applications, such as time-resolved electronic spectroscopy. We derive an exact path integral formula for the fidelity amplitude and use it to obtain a series of increasingly accurate semiclassical approximations by truncating an exact expansion of the path integral exponent. While the zeroth-order expansion results in a remarkably simple, yet non-trivial approximation for the fidelity amplitude, the first-order expansion yields an alternative derivation of the so-called 'dephasing representation,' circumventing the use of a semiclassical propagator as in the original derivation. We also obtain an approximate expression for fidelity based on the second-order expansion, which resolves several shortcomings of the dephasing representation. The rigorous derivation from the path integral permits the identification of sufficient conditions under which various approximations obtained become exact.
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Affiliation(s)
- Jiří Vaníček
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
| | - Doron Cohen
- Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
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22
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Sun X, Geva E. Nonequilibrium Fermi’s Golden Rule Charge Transfer Rates via the Linearized Semiclassical Method. J Chem Theory Comput 2016; 12:2926-41. [DOI: 10.1021/acs.jctc.6b00236] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xiang Sun
- Department
of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, United States
| | - Eitan Geva
- Department
of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, United States
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23
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Megow J, Kulesza A, May V. A mixed quantum-classical description of pheophorbide a linear absorption spectra: Quantum-corrections of the Qy- and Qx-absorption vibrational satellites. Chem Phys Lett 2016. [DOI: 10.1016/j.cplett.2015.11.016] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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24
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Sun X, Geva E. Equilibrium Fermi’s Golden Rule Charge Transfer Rate Constants in the Condensed Phase: The Linearized Semiclassical Method vs Classical Marcus Theory. J Phys Chem A 2015; 120:2976-90. [DOI: 10.1021/acs.jpca.5b08280] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xiang Sun
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, United States
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25
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Moberg DR, Alemi M, Loring RF. Thermal weights for semiclassical vibrational response functions. J Chem Phys 2015; 143:084101. [PMID: 26328812 DOI: 10.1063/1.4929377] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Semiclassical approximations to response functions can allow the calculation of linear and nonlinear spectroscopic observables from classical dynamics. Evaluating a canonical response function requires the related tasks of determining thermal weights for initial states and computing the dynamics of these states. A class of approximations for vibrational response functions employs classical trajectories at quantized values of action variables and represents the effects of the radiation-matter interaction by discontinuous transitions. Here, we evaluate choices for a thermal weight function which are consistent with this dynamical approximation. Weight functions associated with different semiclassical approximations are compared, and two forms are constructed which yield the correct linear response function for a harmonic potential at any temperature and are also correct for anharmonic potentials in the classical mechanical limit of high temperature. Approximations to the vibrational linear response function with quantized classical trajectories and proposed thermal weight functions are assessed for ensembles of one-dimensional anharmonic oscillators. This approach is shown to perform well for an anharmonic potential that is not locally harmonic over a temperature range encompassing the quantum limit of a two-level system and the limit of classical dynamics.
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Affiliation(s)
- Daniel R Moberg
- Baker Laboratory, Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Mallory Alemi
- Baker Laboratory, Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Roger F Loring
- Baker Laboratory, Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
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26
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Petit AS, Subotnik JE. Appraisal of Surface Hopping as a Tool for Modeling Condensed Phase Linear Absorption Spectra. J Chem Theory Comput 2015; 11:4328-41. [DOI: 10.1021/acs.jctc.5b00510] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Andrew S. Petit
- Department of Chemistry, University of Pennsylvania, 231 South
34th Street, Philadelphia, Pennsylvania 19104, United States
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, 231 South
34th Street, Philadelphia, Pennsylvania 19104, United States
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27
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Alemi M, Loring RF. Two-Dimensional Vibrational Spectroscopy of a Dissipative System with the Optimized Mean-Trajectory Approximation. J Phys Chem B 2015; 119:8950-9. [PMID: 25275943 PMCID: PMC4383732 DOI: 10.1021/jp5076884] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2014] [Revised: 09/10/2014] [Indexed: 11/30/2022]
Abstract
The optimized mean-trajectory (OMT) approximation is a semiclassical method for computing vibrational response functions from action-quantized classical trajectories connected by discrete transitions representing radiation-matter interactions. Here we apply this method to an anharmonic chromophore coupled to a harmonic bath. A forward-backward trajectory implementation of the OMT method is described that addresses the numerical challenges of applying the OMT to large systems with disparate frequency scales. The OMT is shown to well reproduce line shapes and waiting time dynamics in the pure dephasing limit of weak coupling to an off-resonant bath. The OMT is also shown to describe a case where energy transfer is the predominant source of line broadening.
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Affiliation(s)
- Mallory Alemi
- 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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28
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Alemi M, Loring RF. Vibrational coherence and energy transfer in two-dimensional spectra with the optimized mean-trajectory approximation. J Chem Phys 2015; 142:212417. [PMID: 26049437 DOI: 10.1063/1.4916644] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
The optimized mean-trajectory (OMT) approximation is a semiclassical method for computing vibrational response functions from action-quantized classical trajectories connected by discrete transitions that represent radiation-matter interactions. Here, we extend the OMT to include additional vibrational coherence and energy transfer processes. This generalized approximation is applied to a pair of anharmonic chromophores coupled to a bath. The resulting 2D spectra are shown to reflect coherence transfer between normal modes.
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Affiliation(s)
- Mallory Alemi
- Baker Laboratory, Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Roger F Loring
- Baker Laboratory, Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
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29
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Zimmermann T, Vaníček J. Efficient on-the-fly ab initio semiclassical method for computing time-resolved nonadiabatic electronic spectra with surface hopping or Ehrenfest dynamics. J Chem Phys 2015; 141:134102. [PMID: 25296779 DOI: 10.1063/1.4896735] [Citation(s) in RCA: 34] [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 derive a somewhat crude, yet very efficient semiclassical approximation for computing nonadiabatic spectra. The resulting method, which is a generalization of the multiple-surface dephasing representation, includes quantum effects through interference of mixed quantum-classical trajectories and through quantum treatment of the collective electronic degree of freedom. The method requires very little computational effort beyond the fewest-switches surface hopping or Ehrenfest locally mean-field dynamics and is very easy to implement. The proposed approximation is tested by computing the absorption and time-resolved stimulated emission spectra of pyrazine using the four-dimensional three-surface model which allows for comparison with the numerically exact quantum spectra. As expected, the multiple-surface dephasing representation is not suitable for high-resolution linear spectra, yet it seems to capture all the important features of pump-probe spectra. Finally, the method is combined with on-the-fly ab initio evaluation of the electronic structure (i.e., energies, forces, electric-dipole, and nonadiabatic couplings) in order to compute fully dimensional nonadiabatic spectra of pyrazine without approximations inherent to analytical, including vibronic-coupling models. The Appendix provides derivations of perturbative expressions for linear and pump-probe spectra of arbitrary mixed states and for arbitrary laser pulse shapes.
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Affiliation(s)
- Tomáš Zimmermann
- 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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30
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Petit AS, Subotnik JE. Calculating time-resolved differential absorbance spectra for ultrafast pump-probe experiments with surface hopping trajectories. J Chem Phys 2014; 141:154108. [DOI: 10.1063/1.4897258] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Affiliation(s)
- Andrew S. Petit
- Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, Pennsylvania 19104, USA
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31
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Petit AS, Subotnik JE. How to calculate linear absorption spectra with lifetime broadening using fewest switches surface hopping trajectories: A simple generalization of ground-state Kubo theory. J Chem Phys 2014; 141:014107. [DOI: 10.1063/1.4884945] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andrew S. Petit
- Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, Pennsylvania 19104, USA
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32
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Bai S, Xie W, Zhu L, Shi Q. Calculation of absorption spectra involving multiple excited states: Approximate methods based on the mixed quantum classical Liouville equation. J Chem Phys 2014; 140:084105. [DOI: 10.1063/1.4866367] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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33
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Šulc M, Hernández H, Martínez TJ, Vaníček J. Relation of exact Gaussian basis methods to the dephasing representation: theory and application to time-resolved electronic spectra. J Chem Phys 2014; 139:034112. [PMID: 23883015 DOI: 10.1063/1.4813124] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We recently showed that the dephasing representation (DR) provides an efficient tool for computing ultrafast electronic spectra and that further acceleration is possible with cellularization [M. Šulc and J. Vaníček, Mol. Phys. 110, 945 (2012)]. Here, we focus on increasing the accuracy of this approximation by first implementing an exact Gaussian basis method, which benefits from the accuracy of quantum dynamics and efficiency of classical dynamics. Starting from this exact method, the DR is derived together with ten other methods for computing time-resolved spectra with intermediate accuracy and efficiency. These methods include the Gaussian DR, an exact generalization of the DR, in which trajectories are replaced by communicating frozen Gaussian basis functions evolving classically with an average Hamiltonian. The newly obtained methods are tested numerically on time correlation functions and time-resolved stimulated emission spectra in the harmonic potential, pyrazine S0∕S1 model, and quartic oscillator. Numerical results confirm that both the Gaussian basis method and the Gaussian DR increase the accuracy of the DR. Surprisingly, in chaotic systems the Gaussian DR can outperform the presumably more accurate Gaussian basis method, in which the two bases are evolved separately.
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Affiliation(s)
- Miroslav Šulc
- 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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34
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Gerace M, Loring RF. Two-dimensional spectroscopy of coupled vibrations with the optimized mean-trajectory approximation. J Phys Chem B 2013; 117:15452-61. [PMID: 23924378 PMCID: PMC3865215 DOI: 10.1021/jp405225g] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The optimized mean-trajectory (OMT) approximation is a semiclassical representation of the nonlinear vibrational response function used to compute multidimensional infrared spectra. In this method, response functions are calculated from a sequence of classical trajectories linked by discontinuities representing the effects of radiation-matter interactions, thus providing an approximation to quantum dynamics using classical inputs. This approach was previously formulated and assessed numerically for a single anharmonic degree of freedom. Our previous work is generalized here in two respects. First, the derivation of the OMT is extended to any number of coupled anharmonic vibrations by determining semiclassical approximations for pairs of double-sided Feynman diagrams. Second, an efficient numerical procedure is developed for calculating two-dimensional infrared spectra of coupled anharmonic vibrations in the OMT approximation. The OMT approximation is shown to reproduce the fundamental features of the quantum response function including both coherence and population dynamics.
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Affiliation(s)
- Mallory Gerace
- 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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35
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Kocia L, Heller EJ. Generalized dephasing relation for fidelity and application as an efficient propagator. J Chem Phys 2013; 139:124110. [DOI: 10.1063/1.4820880] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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36
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Zambrano E, Šulc M, Vaníček J. Improving the accuracy and efficiency of time-resolved electronic spectra calculations: Cellular dephasing representation with a prefactor. J Chem Phys 2013; 139:054109. [DOI: 10.1063/1.4817005] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [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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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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38
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Gerace M, Loring RF. An optimized semiclassical approximation for vibrational response functions. J Chem Phys 2013; 138:124104. [PMID: 23556706 DOI: 10.1063/1.4795941] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The observables of multidimensional infrared spectroscopy may be calculated from nonlinear vibrational response functions. Fully quantum dynamical calculations of vibrational response functions are generally impractical, while completely classical calculations are qualitatively incorrect at long times. These challenges motivate the development of semiclassical approximations to quantum mechanics, which use classical mechanical information to reconstruct quantum effects. The mean-trajectory (MT) approximation is a semiclassical approach to quantum vibrational response functions employing classical trajectories linked by deterministic transitions representing the effects of the radiation-matter interaction. Previous application of the MT approximation to the third-order response function R(3)(t3, t2, t1) demonstrated that the method quantitatively describes the coherence dynamics of the t3 and t1 evolution times, but is qualitatively incorrect for the waiting-time t2 period. Here we develop an optimized version of the MT approximation by elucidating the connection between this semiclassical approach and the double-sided Feynman diagrams (2FD) that represent the quantum response. Establishing the direct connection between 2FD and semiclassical paths motivates a systematic derivation of an optimized MT approximation (OMT). The OMT uses classical mechanical inputs to accurately reproduce quantum dynamics associated with all three propagation times of the third-order vibrational response function.
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Affiliation(s)
- Mallory Gerace
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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39
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Zimmermann T, Vaníček J. Evaluation of the importance of spin-orbit couplings in the nonadiabatic quantum dynamics with quantum fidelity and with its efficient "on-the-fly" ab initio semiclassical approximation. J Chem Phys 2013; 137:22A516. [PMID: 23249053 DOI: 10.1063/1.4738878] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose to measure the importance of spin-orbit couplings (SOCs) in the nonadiabatic molecular quantum dynamics rigorously with quantum fidelity. To make the criterion practical, quantum fidelity is estimated efficiently with the multiple-surface dephasing representation (MSDR). The MSDR is a semiclassical method that includes nuclear quantum effects through interference of mixed quantum-classical trajectories without the need for the Hessian of potential energy surfaces. Two variants of the MSDR are studied, in which the nuclei are propagated either with the fewest-switches surface hopping or with the locally mean field dynamics. The fidelity criterion and MSDR are first tested on one-dimensional model systems amenable to numerically exact quantum dynamics. Then, the MSDR is combined with "on-the-fly" computed electronic structure to measure the importance of SOCs and nonadiabatic couplings in the photoisomerization dynamics of CH(2)NH(2)(+) considering 20 electronic states and in the collision of F + H(2) considering six electronic states.
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Affiliation(s)
- Tomáš Zimmermann
- 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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40
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Zimmermann T, Vaníček J. Measuring nonadiabaticity of molecular quantum dynamics with quantum fidelity and with its efficient semiclassical approximation. J Chem Phys 2012; 136:094106. [PMID: 22401428 DOI: 10.1063/1.3690458] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose to measure nonadiabaticity of molecular quantum dynamics rigorously with the quantum fidelity between the Born-Oppenheimer and fully nonadiabatic dynamics. It is shown that this measure of nonadiabaticity applies in situations where other criteria, such as the energy gap criterion or the extent of population transfer, fail. We further propose to estimate this quantum fidelity efficiently with a generalization of the dephasing representation to multiple surfaces. Two variants of the multiple-surface dephasing representation (MSDR) are introduced, in which the nuclei are propagated either with the fewest-switches surface hopping or with the locally mean field dynamics (LMFD). The LMFD can be interpreted as the Ehrenfest dynamics of an ensemble of nuclear trajectories, and has been used previously in the nonadiabatic semiclassical initial value representation. In addition to propagating an ensemble of classical trajectories, the MSDR requires evaluating nonadiabatic couplings and solving the Schrödinger (or more generally, the quantum Liouville-von Neumann) equation for a single discrete degree of freedom. The MSDR can be also used in the diabatic basis to measure the importance of the diabatic couplings. The method is tested on three model problems introduced by Tully and on a two-surface model of dissociation of NaI.
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Affiliation(s)
- Tomáš Zimmermann
- 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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41
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Šulc M, Vaníček J. Accelerating the calculation of time-resolved electronic spectra with the cellular dephasing representation. Mol Phys 2012. [DOI: 10.1080/00268976.2012.668971] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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42
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Mollica C, Zimmermann T, Vaníček J. Efficient sampling avoids the exponential wall in classical simulations of fidelity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:066205. [PMID: 22304176 DOI: 10.1103/physreve.84.066205] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2011] [Indexed: 05/31/2023]
Abstract
We analyze the efficiency of available algorithms for the simulation of classical fidelity and show that their computational costs increase exponentially with the number of degrees of freedom. Then we present an algorithm for which the number of trajectories needed for convergence is independent of the system's dimensionality and show that, within a continuous family of algorithms, this algorithm is the only one with this property. Simultaneously we propose a general analytical approach to estimate efficiency of trajectory-based methods and suggest how to use it to accelerate calculations of other classical correlation functions. Converged numerical results are provided for systems with phase space volume 2^{1700} times larger than the volume of the initial state.
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Affiliation(s)
- Cesare Mollica
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
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43
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Mollica C, Vaníček J. Beating the efficiency of both quantum and classical simulations with a semiclassical method. PHYSICAL REVIEW LETTERS 2011; 107:214101. [PMID: 22181883 DOI: 10.1103/physrevlett.107.214101] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2011] [Indexed: 05/16/2023]
Abstract
While rigorous quantum dynamical simulations of many-body systems are extremely difficult (or impossible) due to exponential scaling with dimensionality, the corresponding classical simulations ignore quantum effects. Semiclassical methods are generally more efficient but less accurate than quantum methods and more accurate but less efficient than classical methods. We find a remarkable exception to this rule by showing that a semiclassical method can be both more accurate and faster than a classical simulation. Specifically, we prove that for the semiclassical dephasing representation the number of trajectories needed to simulate quantum fidelity is independent of dimensionality and also that this semiclassical method is even faster than the most efficient corresponding classical algorithm. Analytical results are confirmed with simulations of fidelity in up to 100 dimensions with 2(1700)-dimensional Hilbert space.
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Affiliation(s)
- Cesare Mollica
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne, Switzerland
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44
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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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45
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Hanna G, Geva E. Signature of Nonadiabatic Transitions on the Pump−Probe Infrared Spectra of a Hydrogen-Bonded Complex Dissolved in a Polar Solvent: A Computational Study. J Phys Chem B 2010; 115:5191-200. [DOI: 10.1021/jp1061495] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Gabriel Hanna
- Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109
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46
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Tao G, Miller WH. Gaussian approximation for the structure function in semiclassical forward-backward initial value representations of time correlation functions. J Chem Phys 2009; 131:224107. [PMID: 20001024 DOI: 10.1063/1.3271241] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Initial value representations (IVRs) of semiclassical (SC) theory provide a general approach for adding quantum mechanical effects to classical molecular dynamics simulations of large molecular systems. Of the various versions of SC-IVR methodology for evaluating time correlation functions, the Fourier transform forward-backward (FB) approach is the simplest one that is able to describe true quantum coherence effects, so it is of considerable importance to find efficient and systematic ways for implementing it. It is shown in this paper that a Gaussian approximation for the "structure function"-the dependence of the correlation function on the (typically) momentum jump parameter-provides an efficient and accurate way for doing so. The approach is illustrated by an application to the time-dependent radial distribution function of I(2) (after photoexcitation) in a cluster of (up to 16) argon atoms.
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Affiliation(s)
- Guohua Tao
- Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720-1460, USA
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47
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McRobbie PL, Hanna G, Shi Q, Geva E. Signatures of nonequilibrium solvation dynamics on multidimensional spectra. Acc Chem Res 2009; 42:1299-309. [PMID: 19552404 DOI: 10.1021/ar800280s] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Abstract
Multidimensional electronic and vibrational spectroscopies have established themselves over the last decade as uniquely detailed probes of intramolecular structure and dynamics. However, these spectroscopies can also provide powerful tools for probing solute-solvent interactions and the solvation dynamics that they give rise to. To this end, it should be noted that multidimensional spectra can be expressed in terms of optical response functions that differ with respect to the chromophore's quantum state during the various time intervals separating light-matter interactions. The dynamics of the photoinactive degrees of freedom during those time intervals (that is, between pulses) is dictated by potential energy surfaces that depend on the corresponding state of the chromophore. One therefore expects the system to hop between potential surfaces in a manner dictated by the optical response functions. Thus, the corresponding spectra should reflect the system's dynamics during the resulting sequence of nonequilibrium solvation processes. However, the interpretation of multidimensional spectra is often based on the assumption that they reflect the equilibrium dynamics of the photoinactive degrees of freedom on the potential surface that corresponds to the chromophore's ground state. In this Account, we present a systematic analysis of the signature of nonequilibrium solvation dynamics on multidimensional spectra and the ability of various computational methods to capture it. The analysis is performed in the context of the following three model systems: (A) a two-state chromophore with shifted harmonic potential surfaces that differ in frequency, (B) a two-state atomic chromophore in an atomic liquid, and (C) the hydrogen stretch of a moderately strong hydrogen-bonded complex in a dipolar liquid. The following computational methods are employed and compared: (1) exact quantum dynamics (model A only), (2) the semiclassical forward-backward initial value representation (FB-IVR) method (models A and B only), (3) the linearized semiclassical (LSC) method (all three models), and (4) the standard ground-state equilibrium dynamics approach (all three models). The results demonstrate how multidimensional spectra can be used to probe nonequilibrium solvation dynamics in real time and with an unprecedented level of detail. We also show that, unlike the standard method, the LSC and FB-IVR methods can accurately capture the signature of solvation dynamics on the spectra. Our results also suggest that LSC and FB-IVR yield similar results in the presence of rapid dephasing, which is typical in complex condensed-phase systems. This observation gives credence to the use of the LSC method for modeling spectra in complex systems for which an exact or even FB-IVR-based calculation is prohibitively expensive.
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Affiliation(s)
- Porscha L. McRobbie
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Gabriel Hanna
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences (CAS), Zhongguancun, Beijing 100190, P. R. China
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
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48
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McRobbie PL, Geva E. A Benchmark Study of Different Methods for Calculating One- And Two-Dimensional Optical Spectra. J Phys Chem A 2009; 113:10425-34. [DOI: 10.1021/jp905305t] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Porscha L. McRobbie
- Department of Chemistry and the FOCUS Center, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Eitan Geva
- Department of Chemistry and the FOCUS Center, University of Michigan, Ann Arbor, Michigan 48109-1055
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49
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Time and frequency resolved spontaneous emission from supramolecular pheophorbide-a complexes: A mixed quantum classical computation. Chem Phys 2009. [DOI: 10.1016/j.chemphys.2009.05.022] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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50
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Hanna G, Geva E. Multidimensional Spectra via the Mixed Quantum-Classical Liouville Method: Signatures of Nonequilibrium Dynamics. J Phys Chem B 2009; 113:9278-88. [DOI: 10.1021/jp902797z] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Gabriel Hanna
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
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