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Takatsuka K. Electron Dynamics in Molecular Elementary Processes and Chemical Reactions. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2021. [DOI: 10.1246/bcsj.20200388] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Kazuo Takatsuka
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan
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2
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Mignolet B, Curchod BFE. Excited-State Molecular Dynamics Triggered by Light Pulses—Ab Initio Multiple Spawning vs Trajectory Surface Hopping. J Phys Chem A 2019; 123:3582-3591. [DOI: 10.1021/acs.jpca.9b00940] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Benoit Mignolet
- Theoretical Physical Chemistry, UR MolSYS, B6c, University of Liège, B4000 Liège, Belgium
| | - Basile F. E. Curchod
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
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3
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Tóth A, Badankó P, Halász GJ, Vibók Á, Csehi A. Importance of the lowest-lying Π electronic state in the photodissociation dynamics of LiF. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2018.05.002] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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4
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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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Arasaki Y, Mizuno Y, Scheit S, Takatsuka K. Stark-assisted quantum confinement of wavepackets. A coupling of nonadiabatic interaction and CW-laser. J Chem Phys 2016; 144:044107. [DOI: 10.1063/1.4940341] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Yasuki Arasaki
- Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, 153-8902 Tokyo, Japan
| | - Yuta Mizuno
- Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, 153-8902 Tokyo, Japan
| | - Simona Scheit
- Theoretische Chemie, Universität Heidelberg, Im Neuneheimer Feld 229, 69120 Heidelberg, Germany
| | - Kazuo Takatsuka
- Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, 153-8902 Tokyo, Japan
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6
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Curchod BFE, Penfold TJ, Rothlisberger U, Tavernelli I. Local Control Theory in Trajectory Surface Hopping Dynamics Applied to the Excited-State Proton Transfer of 4-Hydroxyacridine. Chemphyschem 2015; 16:2127-33. [PMID: 26036986 DOI: 10.1002/cphc.201500190] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2015] [Indexed: 11/08/2022]
Abstract
The application of local control theory combined with nonadiabatic ab initio molecular dynamics to study the photoinduced intramolecular proton transfer reaction in 4-hydroxyacridine was investigated. All calculations were performed within the framework of linear-response time-dependent density functional theory. The computed pulses revealed important information about the underlying excited-state nuclear dynamics highlighting the involvement of collective vibrational modes that would normally be neglected in a study performed on model systems constrained to a subset of the full configuration space. This study emphasizes the strengths of local control theory for the design of pulses that can trigger chemical reactions associated with the population of a given molecular excited state. In addition, analysis of the generated pulses can help to shed new light on the photophysics and photochemistry of complex molecular systems.
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Affiliation(s)
- Basile F E Curchod
- Laboratory of Computational Chemistry and Biochemistry, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne (Switzerland).,Current address: Department of Chemistry, Stanford University, Stanford, California 94305 (USA)
| | | | - Ursula Rothlisberger
- Laboratory of Computational Chemistry and Biochemistry, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne (Switzerland)
| | - Ivano Tavernelli
- Laboratory of Computational Chemistry and Biochemistry, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne (Switzerland). .,Current address: IBM Research GmbH, Zurich Research Laboratory, 8803 Rüschlikon (Switzerland).
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Bajo JJ, Granucci G, Persico M. Interplay of radiative and nonradiative transitions in surface hopping with radiation-molecule interactions. J Chem Phys 2015; 140:044113. [PMID: 25669511 DOI: 10.1063/1.4862738] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We implemented a method for the treatment of field induced transitions in trajectory surface hopping simulations, in the framework of the local diabatization scheme, especially suited for on-the-fly dynamics. The method is applied to a simple one-dimensional model with an avoided crossing and compared with quantum wavepacket dynamics. The results show the importance of introducing a proper decoherence correction to surface hopping, in order to obtain meaningful results. Also the energy conservation policy of standard surface hopping must be revised: in fact, the quantum wavepacket energetics is well reproduced if energy absorption/emission is allowed for in the hops determined by radiation-molecule coupling. To our knowledge, this is the first time the issues of decoherence and energy conservation have been analyzed in depth to devise a mixed quantum-classical method for dynamics with molecule-field interactions.
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Affiliation(s)
- Juan José Bajo
- Departamento de Química-Física I, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Giovanni Granucci
- Università di Pisa, Dipartimento di Chimica e Chimica Industriale, via Risorgimento 35, 56126 Pisa, Italy
| | - Maurizio Persico
- Università di Pisa, Dipartimento di Chimica e Chimica Industriale, via Risorgimento 35, 56126 Pisa, Italy
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An overview of nonadiabatic dynamics simulations methods, with focus on the direct approach versus the fitting of potential energy surfaces. Theor Chem Acc 2014. [DOI: 10.1007/s00214-014-1526-1] [Citation(s) in RCA: 102] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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9
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González L, Marquetand P, Richter M, González-Vázquez J, Sola I. Ultrafast Laser-Induced Processes Described by Ab Initio Molecular Dynamics. ACTA ACUST UNITED AC 2014. [DOI: 10.1007/978-3-319-02051-8_7] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/20/2023]
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10
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Curchod BFE, Rothlisberger U, Tavernelli I. Trajectory-Based Nonadiabatic Dynamics with Time-Dependent Density Functional Theory. Chemphyschem 2013; 14:1314-40. [DOI: 10.1002/cphc.201200941] [Citation(s) in RCA: 153] [Impact Index Per Article: 13.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2012] [Indexed: 11/11/2022]
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11
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Kling MF, von den Hoff P, Znakovskaya I, de Vivie-Riedle R. (Sub-)femtosecond control of molecular reactions via tailoring the electric field of light. Phys Chem Chem Phys 2013; 15:9448-67. [DOI: 10.1039/c3cp50591j] [Citation(s) in RCA: 76] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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12
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NEST M. DETERMINATION OF THE ELECTRONIC GROUND STATE OF MOLECULAR SYSTEMS WITH THE MULTI-CONFIGURATION TIME-DEPENDENT HARTREE–FOCK METHOD. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1142/s0219633607003180] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, we present progress in the application of the explicitly time-dependent multi-configuration time-dependent Hartree–Fock (MCTDHF) method. The spin–orbitals and equations of motion are expressed in the basis of Gaussian Type Orbitals. MCTDHF is then applied to the calculation of the electronic ground state of various small molecules by imaginary time propagation. We were able to take between four and 12 active electrons into account. We discuss the suitability of a core guess as initial wave function, the possibility to obtain excited states, as well as the consequences of a neglect of core excitations.
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Affiliation(s)
- M. NEST
- Universität Potsdam, Institut für Chemie, Karl-Liebknecht-Str. 25, 14476 Potsdam, Germany
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Richter M, Marquetand P, González-Vázquez J, Sola I, González L. SHARC: ab Initio Molecular Dynamics with Surface Hopping in the Adiabatic Representation Including Arbitrary Couplings. J Chem Theory Comput 2011; 7:1253-8. [DOI: 10.1021/ct1007394] [Citation(s) in RCA: 334] [Impact Index Per Article: 25.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Martin Richter
- Institut für Physikalische Chemie, Friedrich-Schiller-Universität Jena, Helmholtzweg 4, 07743 Jena, Germany
| | - Philipp Marquetand
- Institut für Physikalische Chemie, Friedrich-Schiller-Universität Jena, Helmholtzweg 4, 07743 Jena, Germany
| | - Jesús González-Vázquez
- Institut für Physikalische Chemie, Friedrich-Schiller-Universität Jena, Helmholtzweg 4, 07743 Jena, Germany
| | - Ignacio Sola
- Departamento de Química Física I, Universidad Complutense, 28040 Madrid, Spain
| | - Leticia González
- Institut für Physikalische Chemie, Friedrich-Schiller-Universität Jena, Helmholtzweg 4, 07743 Jena, Germany
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Marquetand P, Richter M, González-Vázquez J, Sola I, González L. Nonadiabatic ab initio molecular dynamics including spin–orbit coupling and laser fields. Faraday Discuss 2011; 153:261-73; discussion 293-319. [DOI: 10.1039/c1fd00055a] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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15
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Takatsuka K, Yonehara T. Nonadiabatic Chemical Dynamics in Intermediate and Intense Laser Fields. ADVANCES IN CHEMICAL PHYSICS 2010. [DOI: 10.1002/9780470564318.ch2] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
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16
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Yonehara T, Takatsuka K. Characterization of electron-deficient chemical bonding of diborane with attosecond electron wavepacket dynamics and laser response. Chem Phys 2009. [DOI: 10.1016/j.chemphys.2009.09.001] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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17
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Attosecond control of the dissociative ionization via electron localization: A comparison between and CO. Chem Phys 2009. [DOI: 10.1016/j.chemphys.2009.09.021] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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18
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Christov IP. Molecular dynamics with time dependent quantum Monte Carlo. J Chem Phys 2008; 129:214107. [DOI: 10.1063/1.3031214] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
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19
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Yonehara T, Takatsuka K. Nonadiabatic electron wavepacket dynamics of molecules in an intense optical field: An ab initio electronic state study. J Chem Phys 2008; 128:154104. [DOI: 10.1063/1.2904867] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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20
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Takatsuka K. Generalization of classical mechanics for nuclear motions on nonadiabatically coupled potential energy surfaces in chemical reactions. J Phys Chem A 2007; 111:10196-204. [PMID: 17676718 DOI: 10.1021/jp072233j] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Classical trajectory study of nuclear motion on the Born-Oppenheimer potential energy surfaces is now one of the standard methods of chemical dynamics. In particular, this approach is inevitable in the studies of large molecular systems. However, as soon as more than a single potential energy surface is involved due to nonadiabatic coupling, such a naive application of classical mechanics loses its theoretical foundation. This is a classic and fundamental issue in the foundation of chemistry. To cope with this problem, we propose a generalization of classical mechanics that provides a path even in cases where multiple potential energy surfaces are involved in a single event and the Born-Oppenheimer approximation breaks down. This generalization is made by diagonalization of the matrix representation of nuclear forces in nonadiabatic dynamics, which is derived from a mixed quantum-classical representation of the electron-nucleus entangled Hamiltonian [Takatsuka, K. J. Chem. Phys. 2006, 124, 064111]. A manifestation of quantum fluctuation on a classical subsystem that directly contacts with a quantum subsystem is discussed. We also show that the Hamiltonian thus represented gives a theoretical foundation to examine the validity of the so-called semiclassical Ehrenfest theory (or mean-field theory) for electron quantum wavepacket dynamics, and indeed, it is pointed out that the electronic Hamiltonian to be used in this theory should be slightly modified.
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Affiliation(s)
- Kazuo Takatsuka
- Department of Basic Science, The University of Tokyo, Komaba, 153-8902 Tokyo, Japan
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Bargheer M, Cohen A, Gerber RB, Gühr M, Korolkov MV, Manz J, Niv MY, Schröder M, Schwentner N. Dynamics of Electronic States and Spin−Flip for Photodissociation of Dihalogens in Matrices: Experiment and Semiclassical Surface-Hopping and Quantum Model Simulations for F2 and ClF in Solid Ar. J Phys Chem A 2007; 111:9573-85. [PMID: 17629252 DOI: 10.1021/jp071771t] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Three approaches are combined to study the electronic states' dynamics in the photodissociation of F(2) and ClF in solid argon. These include (a) semiclassical surface-hopping simulations of the nonadiabatic processes involved. These simulations are carried out for the F(2) molecule in a slab of 255 argon atoms with periodic boundary conditions at the ends. The full manifold of 36 electronic states relevant to the process is included. (b) The second approach involves quantum mechanical reduced-dimensionality models for the initial processes induced by a pump laser pulse, which involve wavepacket propagation for the preoriented ClF in the frozen argon lattice and incorporate the important electronic states. The focus is on the study of quantum coherence effects. (c) The final approach is femtosecond laser pump-probe experiments for ClF in Ar. The combined results for the different systems shed light on general properties of the nonadiabatic processes involved, including the singlet to triplet and intertriplet transition dynamics. The main findings are (1) that the system remains in the initially excited-state only for a very brief, subpicosecond, time period. Thereafter, most of the population is transferred by nonadiabatic transitions to other states, with different time constants depending on the systems. (2) Another finding is that the dynamics is selective with regard to the electronic quantum numbers, including the Lambda and Omega quantum numbers, and the spin of the states. (3) The semiclassical simulations show that prior to the first "collision" of the photodissociated F atom with an Ar atom, the argon atoms can be held frozen, without affecting the process. This justifies the rigid-lattice reduced-dimensionality quantum model for a brief initial time interval. (4) Finally, degeneracies between triplets and singlets are fairly localized, but intertriplet degeneracies and near degeneracies can span an extensive range. The importance of quantum effects in photochemistry of matrix-isolated molecules is discussed in light of the results.
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Affiliation(s)
- M Bargheer
- Institut für Experimentalphysik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
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Nest M, Padmanaban R, Saalfrank P. Time-dependent approach to electronically excited states of molecules with the multiconfiguration time-dependent Hartree-Fock method. J Chem Phys 2007; 126:214106. [PMID: 17567189 DOI: 10.1063/1.2743007] [Citation(s) in RCA: 63] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
In this paper the authors show how the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method can be used for the calculation of electronic properties of molecules associated with the population of excited states. In contrast to other methods for correlated electron dynamics, such as configuration interaction, MCTDHF does not rely on a solution of the electronic Schrodinger equation prior to the propagation. The authors apply this approach to the calculation of vertical excitation energies, transition dipole moments, and oscillator strengths for two test molecules, lithium hydride and methane.
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Affiliation(s)
- M Nest
- Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 25, 14476 Potsdam, Germany
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Mechanisms of the Elementary Processes of Electron Wavepacket Dynamics Coupled with Proton Transfer and Hydrogen-Atom Migration in H2O+H3O+. Angew Chem Int Ed Engl 2007. [DOI: 10.1002/ange.200603553] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Ushiyama H, Takatsuka K. Mechanisms of the Elementary Processes of Electron Wavepacket Dynamics Coupled with Proton Transfer and Hydrogen-Atom Migration in H2O+H3O+. Angew Chem Int Ed Engl 2007; 46:587-90. [PMID: 17152107 DOI: 10.1002/anie.200603553] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Hiroshi Ushiyama
- Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, 153-8902 Tokyo, Japan
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25
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Kuchitsu T, Tachikawa M, Shiga M. Attosecond electron dynamics with linear combination of floating gaussian type basis function. Chem Phys Lett 2006. [DOI: 10.1016/j.cplett.2006.10.126] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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26
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Takahashi S, Takatsuka K. On the validity range of the Born-Oppenheimer approximation: A semiclassical study for all-particle quantization of three-body Coulomb systems. J Chem Phys 2006; 124:144101. [PMID: 16626174 DOI: 10.1063/1.2173997] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The validity range of the Born-Oppenheimer (BO) approximation is studied with respect to the variation of the mass (m) of negatively charged particle by substituting an electron (e) with muon (mu) and antiproton (p) in hydrogen molecule cation. With the use of semiclassical quantization applied to these (ppe), (ppmu), and (ppp) under a constrained geometry, we estimate the energy difference of the non-BO vibronic ground state from the BO counterpart. It is found that the error in the BO approximation scales to the power of 3/2 to the mass of negative particles, that is, m(1.5). The origin of this clear-cut relation is analyzed based on the original perturbation theory due to Born and Oppenheimer, with which we show that the fifth order term proportional to m(5/4) is zero and thereby the first correction to the BO approximation should arise from the sixth order term that is proportional to m(6/4). Therefore, the validity range of the Born-Oppenheimer approximation is wider than that often mistakenly claimed to be proportional to m(1/4).
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Affiliation(s)
- Satoshi Takahashi
- Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Komaba, 153-8902 Tokyo, Japan.
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Takatsuka K. Non-Born-Oppenheimer path in anti-Hermitian dynamics for nonadiabatic transitions. J Chem Phys 2006; 124:64111. [PMID: 16483200 DOI: 10.1063/1.2167648] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
A serious difficulty in the semiclassical Ehrenfest theory for nonadiabatic transitions is that a path passing across the avoided crossing is forced to run on a potential averaged over comprising adiabatic potential surfaces that commit the avoided crossing. Therefore once a path passes through the crossing region, it immediately becomes incompatible with the standard view of "classical trajectory" running on an adiabatic surface. This casts a fundamental question to the theoretical structure of chemical dynamics. In this paper, we propose a non-Born-Oppenheimer path that is generated by an anti-Hermitian Hamiltonian, whose complex-valued eigenenergies can cross in their real parts and avoid crossing in the imaginary parts in the vicinity of the nonadiabatic transition region. We discuss the properties of this non-Born-Oppenheimer path and thereby show its compatibility with the Born-Oppenheimer classical trajectories. This theory not only allows the geometrical branching of the paths but gives the nonadiabatic transition amplitudes and quantum phases along the generated paths.
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Affiliation(s)
- Kazuo Takatsuka
- Department of Basic Science, The University of Tokyo, Komaba, Japan.
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