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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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2
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Provazza J, Segatta F, Coker DF. Modeling Nonperturbative Field-Driven Vibronic Dynamics: Selective State Preparation and Nonlinear Spectroscopy. J Chem Theory Comput 2020; 17:29-39. [DOI: 10.1021/acs.jctc.0c01035] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Justin Provazza
- Department of Chemistry, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, United States
| | - Francesco Segatta
- Department of Chemistry, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, United States
- Dipartimento di Chimica Industriale “Toso Montanari”, University of Bologna, Viale del Risorgimento, 4, 40136 Bologna, Italy
| | - David F. Coker
- Department of Chemistry, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, United States
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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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Dall'Osto G, Coccia E, Guido CA, Corni S. Investigating ultrafast two-pulse experiments on single DNQDI fluorophores: a stochastic quantum approach. Phys Chem Chem Phys 2020; 22:16734-16746. [PMID: 32658228 DOI: 10.1039/d0cp02557g] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Ultrafast two-pulse experiments on single molecules are invaluable tools to investigate the microscopic dynamics of a fluorophore. The first pulse generates electronic or vibronic coherence and the second pulse probes the time-evolution of the coherence. A protocol that is able to simulate ultrafast experiments on single molecules is applied in this study. It is based on a coupled quantum-mechanical description of the fluorophore and real-time dynamics of the system vibronic wave packet interacting with an electric field, described by means of the stochastic Schrödinger equation within the Markovian limit. This approach is applied to the DNQDI fluorophore, previously investigated experimentally [D. Brinks et al., Nature, 2010, 465, 905-908]. We find this to be in good agreement with the experimental outcomes and provide microscopic and atomistic interpretation.
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Affiliation(s)
- Giulia Dall'Osto
- Department of Chemical Sciences, University of Padova, via Marzolo 1, Padova, Italy.
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Cho D, Rouxel JR, Kowalewski M, Saurabh P, Lee JY, Mukamel S. Phase Cycling RT-TDDFT Simulation Protocol for Nonlinear XUV and X-ray Molecular Spectroscopy. J Phys Chem Lett 2018; 9:1072-1078. [PMID: 29431442 DOI: 10.1021/acs.jpclett.8b00061] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Real-time time-dependent density functional theory (RT-TDDFT) provides a practical algorithm for propagating a many-electron system driven by external laser fields. The fields are included nonperturbatively in the propagation, and the molecular reduced single-electron density operator and various spectroscopic and diffraction signals can be computed directly, avoiding the expensive calculation of many-body states. Nonlinear optical signals contain contributions of multiple pathways. A phase cycling protocol is implemented in order to separate these pathways. Simulations of XUV four-wave mixing signals in the CO molecule are compared with ab initio sum-over-states calculations.
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Affiliation(s)
- Daeheum Cho
- Department of Chemistry, University of California , Irvine, California 92697, United States
- Department of Chemistry, Sungkyunkwan University , Suwon 16419, Korea
- Department of Physics and Astronomy, University of California , Irvine, California 92697, United States
| | - Jérémy R Rouxel
- Department of Chemistry, University of California , Irvine, California 92697, United States
- Department of Physics and Astronomy, University of California , Irvine, California 92697, United States
| | - Markus Kowalewski
- Department of Chemistry, University of California , Irvine, California 92697, United States
- Department of Physics and Astronomy, University of California , Irvine, California 92697, United States
| | - Prasoon Saurabh
- Department of Chemistry, University of California , Irvine, California 92697, United States
- Department of Physics and Astronomy, University of California , Irvine, California 92697, United States
| | - Jin Yong Lee
- Department of Chemistry, Sungkyunkwan University , Suwon 16419, Korea
| | - Shaul Mukamel
- Department of Chemistry, University of California , Irvine, California 92697, United States
- Department of Physics and Astronomy, University of California , Irvine, California 92697, United States
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6
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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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Rao BJ, Gelin MF, Domcke W. Resonant femtosecond stimulated Raman spectroscopy with an intense actinic
pump pulse: Application to conical intersections. J Chem Phys 2017; 146:084105. [DOI: 10.1063/1.4976317] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- B. Jayachander Rao
- 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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8
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Palacino-González E, Gelin MF, Domcke W. Theoretical aspects of femtosecond double-pump single-molecule spectroscopy. I. Weak-field regime. Phys Chem Chem Phys 2017; 19:32296-32306. [DOI: 10.1039/c7cp04809b] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
We present a theoretical description of double-pump femtosecond single-molecule signals with fluorescence detection.
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Affiliation(s)
| | - Maxim F. Gelin
- Department of Chemistry
- Technische Universität München
- Garching
- Germany
| | - Wolfgang Domcke
- Department of Chemistry
- Technische Universität München
- Garching
- Germany
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Gelin MF, Bondarev IV, Meliksetyan AV. Optically promoted bipartite atomic entanglement in hybrid metallic carbon nanotube systems. J Chem Phys 2014; 140:064301. [PMID: 24527909 DOI: 10.1063/1.4863971] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study theoretically a pair of spatially separated extrinsic atomic type species (extrinsic atoms, ions, molecules, or semiconductor quantum dots) near a metallic carbon nanotube, that are coupled both directly via the inter-atomic dipole-dipole interactions and indirectly by means of the virtual exchange by resonance plasmon excitations on the nanotube surface. We analyze how the optical preparation of the system by using strong laser pulses affects the formation and evolution of the bipartite atomic entanglement. Despite a large number of possible excitation regimes and evolution pathways, we find a few generic scenarios for the bipartite entanglement evolution and formulate practical recommendations on how to optimize and control the robust bipartite atomic entanglement in hybrid carbon nanotube systems.
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Affiliation(s)
- M F Gelin
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
| | - I V Bondarev
- Department of Physics, North Carolina Central University, Durham, North Carolina 27707, USA
| | - A V Meliksetyan
- Department of Physics, North Carolina Central University, Durham, North Carolina 27707, USA
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Gelin MF, Rao BJ, Nest M, Domcke W. Domain of validity of the perturbative approach to femtosecond optical spectroscopy. J Chem Phys 2013; 139:224107. [DOI: 10.1063/1.4836636] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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Gelin MF, Tanimura Y, Domcke W. Simulation of femtosecond “double-slit” experiments for a chromophore in a dissipative environment. J Chem Phys 2013; 139:214302. [DOI: 10.1063/1.4832876] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
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12
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Gelin MF, Egorova D, Domcke W. Strong-pump strong-probe spectroscopy: effects of higher excited electronic states. Phys Chem Chem Phys 2013; 15:8119-31. [PMID: 23588665 DOI: 10.1039/c3cp44454f] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The present paper is devoted to the simulation of (integral and dispersed) pump-probe signals in the nonperturbative regime for a series of material systems with multiple electronic states and excited-state absorption. We show that strong-pump strong-probe spectroscopy permits the probing of vibrational wavepackets in high-lying and/or short-lived excited electronic states with a time resolution which is not limited by the pulse durations. The field strength can be regarded as an additional experimentally controllable parameter, which can be tuned to maximize the spectroscopic information for a given material system.
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Affiliation(s)
- Maxim F Gelin
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany.
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Tanimura Y. Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two-dimensional correlation spectroscopy. J Chem Phys 2012; 137:22A550. [DOI: 10.1063/1.4766931] [Citation(s) in RCA: 100] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Gelin MF, Sharp LZ, Egorova D, Domcke W. Bath-induced correlations and relaxation of vibronic dimers. J Chem Phys 2012; 136:034507. [DOI: 10.1063/1.3676063] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Gelin MF, Egorova D, Domcke W. Exact quantum master equation for a molecular aggregate coupled to a harmonic bath. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041139. [PMID: 22181119 DOI: 10.1103/physreve.84.041139] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2011] [Revised: 09/04/2011] [Indexed: 05/31/2023]
Abstract
We consider a molecular aggregate consisting of N identical monomers. Each monomer comprises two electronic levels and a single harmonic mode. The monomers interact with each other via dipole-dipole forces. The monomer vibrational modes are bilinearly coupled to a bath of harmonic oscillators. This is a prototypical model for the description of coherent exciton transport, from quantum dots to photosynthetic antennae. We derive an exact quantum master equation for such systems. Computationally, the master equation may be useful for the testing of various approximations employed in theories of quantum transport. Physically, it offers a plausible explanation of the origins of long-lived coherent optical responses of molecular aggregates in dissipative environments.
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Affiliation(s)
- Maxim F Gelin
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
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16
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Photoisomerization around a Fulvene Double Bond: Coherent Population Transfer to the Electronic Ground State? Chemphyschem 2011; 12:1860-71. [DOI: 10.1002/cphc.201001082] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2010] [Revised: 04/20/2011] [Indexed: 11/07/2022]
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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, Egorova D, Domcke W. Strong and Long Makes Short: Strong-Pump Strong-Probe Spectroscopy. J Phys Chem Lett 2011; 2:114-119. [PMID: 26295529 DOI: 10.1021/jz1015247] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We propose a new time-domain spectroscopic technique that is based on strong pump and probe pulses. The strong-pump strong-probe (SPSP) technique provides temporal resolution that is not limited by the durations of the pump and probe pulses. By numerically exact simulations of SPSP signals for a multilevel vibronic model, we show that the SPSP signals exhibit electronic and vibrational beatings on time scales which are significantly shorter than the pulse durations. This suggests the possible application of SPSP spectroscopy for the real-time investigation of molecular processes that cannot be temporally resolved by pump-probe spectroscopy with weak pump and probe pulses.
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Affiliation(s)
- Maxim F Gelin
- †Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
| | - Dassia Egorova
- ‡Institute of Physical Chemistry, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - Wolfgang Domcke
- †Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
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Tanaka M, Tanimura Y. Multistate electron transfer dynamics in the condensed phase: Exact calculations from the reduced hierarchy equations of motion approach. J Chem Phys 2010; 132:214502. [DOI: 10.1063/1.3428674] [Citation(s) in RCA: 79] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
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Paul AK, Adhikari S, Baer M. Space-time contours to treat intense field-dressed molecular states. J Chem Phys 2010; 132:034303. [PMID: 20095735 DOI: 10.1063/1.3282333] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this article we consider a molecular system exposed to an intense short-pulsed external field. It is a continuation of a previous publication [A. K. Paul, S. Adhikari, D. Mukhopadhyay et al., J. Phys. Chem. A 113, 7331 (2009)] in which a theory is presented that treats quantum effects due to nonclassical photon states (known also as Fock states). Since these states became recently a subject of intense experimental efforts we thought that they can be treated properly within the existing quantum formulation of dynamical processes. This was achieved by incorporating them in the Born-Oppenheimer (BO) treatment with time-dependent coefficients. The extension of the BO treatment to include the Fock states results in a formidable enhancement in numerical efforts expressed, in particular, in a significant increase in CPU time. In the present article we discuss an approach that yields an efficient and reliable approximation with only negligible losses in accuracy. The approximation is tested in detail for the dissociation process of H(2) (+) as caused by a laser field.
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Affiliation(s)
- Amit K Paul
- Department of Physical Chemistry, Indian Association for Cultivation of Science, Jadavpur, Kolkata 700 032, India
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