1
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Limbu DK, Shakib FA. Real-Time Dynamics and Detailed Balance in Ring Polymer Surface Hopping: The Impact of Frustrated Hops. J Phys Chem Lett 2023; 14:8658-8666. [PMID: 37732811 DOI: 10.1021/acs.jpclett.3c02085] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/22/2023]
Abstract
Ring polymer surface hopping (RPSH) has been recently introduced as a well-tailored method for incorporating nuclear quantum effects, such as zero-point energy and tunneling, into nonadiabatic molecular dynamics simulations. The practical widespread usage of RPSH demands a comprehensive benchmarking of different reaction regimes and conditions with equal emphasis on demonstrating both the cons and the pros of the method. Here, we investigate the fundamental questions related to the conservation of energy and detailed balance in the context of RPSH. Using Tully's avoided crossing model as well as a 2-state quantum system coupled to a classical bath undergoing Langevin dynamics, we probe the critical problem of the proper treatment of the classically forbidden transitions stemming from the surface hopping algorithm. We show that proper treatment of these frustrated hops is key to the accurate description of real-time dynamics as well as reproducing the correct quantum Boltzmann populations.
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Affiliation(s)
- Dil K Limbu
- Department of Chemistry and Environmental Science, New Jersey Institute of Technology, Newark, New Jersey 07102, United States
| | - Farnaz A Shakib
- Department of Chemistry and Environmental Science, New Jersey Institute of Technology, Newark, New Jersey 07102, United States
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2
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DECIDE: A Deterministic Mixed Quantum-Classical Dynamics Approach. APPLIED SCIENCES-BASEL 2022. [DOI: 10.3390/app12147022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Mixed quantum-classical dynamics provides an efficient way of simulating the dynamics of quantum subsystems coupled to many-body environments. Many processes, including proton-transfer reactions, electron-transfer reactions, and vibrational energy transport, for example, take place in such open systems. The most accurate algorithms for performing mixed quantum-classical simulations require very large ensembles of trajectories to obtain converged expectation values, which is computationally prohibitive for quantum subsystems containing even a few degrees of freedom. The recently developed “Deterministic evolution of coordinates with initial decoupled equations” (DECIDE) method has demonstrated high accuracy and low computational cost for a host of model systems; however, these applications relied on representing the equations of motion in subsystem and adiabatic energy bases. While these representations are convenient for certain systems, the position representation is convenient for many other systems, including systems undergoing proton- and electron-transfer reactions. Thus, in this review, we provide a step-by-step derivation of the DECIDE approach and demonstrate how to cast the DECIDE equations in a quantum harmonic oscillator position basis for a simple one-dimensional (1D) hydrogen bond model. After integrating the DECIDE equations of motion on this basis, we show that the total energy of the system is conserved for this model and calculate various quantities of interest. Limitations of casting the equations in an incomplete basis are also discussed.
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3
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Mandal A, Li X, Huo P. Theory of vibrational polariton chemistry in the collective coupling regime. J Chem Phys 2022; 156:014101. [PMID: 34998324 DOI: 10.1063/5.0074106] [Citation(s) in RCA: 25] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
We theoretically demonstrate that the chemical reaction rate constant can be significantly suppressed by coupling molecular vibrations with an optical cavity, exhibiting both the collective coupling effect and the cavity frequency modification of the rate constant. When a reaction coordinate is strongly coupled to the solvent molecules, the reaction rate constant is reduced due to the dynamical caging effect. We demonstrate that collectively coupling the solvent to the cavity can further enhance this dynamical caging effect, leading to additional suppression of the chemical kinetics. This effect is further amplified when cavity loss is considered.
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Affiliation(s)
- Arkajit Mandal
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Xinyang Li
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
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4
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Brown SE, Shakib FA. Recent progress in approximate quantum dynamics methods for the study of proton-coupled electron transfer reactions. Phys Chem Chem Phys 2021; 23:2535-2556. [PMID: 33367437 DOI: 10.1039/d0cp05166g] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
Proton-coupled electron transfer (PCET) reactions are ubiquitous natural processes at the heart of energy conversion reactions in photosynthesis and respiration, DNA repair, and diverse enzymatic reactions. Theoretical formulation and computational method developments have eyed modeling of thermal and photoinduced PCET for the last three decades. The accumulation of these studies, collected in dozens of reviews, accounts, and perspectives, has firmly established the influence of quantum effects, including non-adiabatic electronic transitions, vibrational relaxation, zero-point energy, and proton tunneling, on the rate and mechanism of PCET reactions. Here, we focus on some recently-developed methods, spanning the last eight years, that can quantitatively capture these effects in the PCET context and provide efficient means for their qualitative description in complex systems. The theoretical background of each method and their accuracy with respect to exact results are discussed and the results of relevant PCET simulations based on each method are presented.
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Affiliation(s)
- Sandra E Brown
- Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, CA 90095, USA
| | - Farnaz A Shakib
- Department of Chemistry and Environmental Science, New Jersey Institute of Technology, Newark, NJ 07102, USA.
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5
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Wang F, Makri N. Quantum-classical path integral with a harmonic treatment of the back-reaction. J Chem Phys 2019; 150:184102. [DOI: 10.1063/1.5091725] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Fei Wang
- Department of Chemistry, University of Illinois, 505 S. Mathews Avenue, Urbana, Illinois 61801, USA
| | - Nancy Makri
- Department of Chemistry, University of Illinois, 505 S. Mathews Avenue, Urbana, Illinois 61801, USA
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6
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Ikeda T, Tanimura Y. Phase-space wavepacket dynamics of internal conversion via conical intersection: Multi-state quantum Fokker-Planck equation approach. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2018.07.013] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
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7
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Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths. Symmetry (Basel) 2018. [DOI: 10.3390/sym10100518] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations, or through quasi-Lie brackets augmented by dissipative terms. Quasi-Lie brackets possess the unique feature that, while conserving the energy (which the Noether theorem links to time-translation symmetry), they violate the time-translation symmetry of their algebra. This fact can be heuristically understood in terms of the dynamics of the open quantum subsystem. We then describe an example in which a quantum subsystem is embedded in a bath of classical spins, which are described by non-canonical coordinates. In this case, it has been shown that an off-diagonal open-bath geometric phase enters into the propagation of the quantum-classical dynamics. Next, we discuss how non-Hamiltonian dynamics may be employed to generate the constant-temperature evolution of phase space degrees of freedom coupled to the quantum subsystem. Constant-temperature dynamics may be generated by either a classical Langevin stochastic process or a Nosé–Hoover deterministic thermostat. These two approaches are not equivalent but have different advantages and drawbacks. In all cases, the calculation of the operator-valued quasi-probability function allows one to compute time-dependent statistical averages of observables. This may be accomplished in practice using a hybrid Molecular Dynamics/Monte Carlo algorithms, which we outline herein.
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8
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Liu J, Hanna G. Efficient and Deterministic Propagation of Mixed Quantum-Classical Liouville Dynamics. J Phys Chem Lett 2018; 9:3928-3933. [PMID: 29947224 DOI: 10.1021/acs.jpclett.8b01619] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We propose a highly efficient mixed quantum-classical molecular dynamics scheme based on a solution of the quantum-classical Liouville equation (QCLE). By casting the equations of motion for the quantum subsystem and classical bath degrees of freedom onto an approximate set of coupled first-order differential equations for c-numbers, this scheme propagates the composite system in time deterministically in terms of independent classical-like trajectories. To demonstrate its performance, we apply the method to the spin-boson model, a photoinduced electron transfer model, and a Fenna-Matthews-Olsen complex model, and find excellent agreement out to long times with the numerically exact results, using several orders of magnitude fewer trajectories than surface-hopping solutions of the QCLE. Owing to its accuracy and efficiency, this method promises to be very useful for studying the dynamics of mixed quantum-classical systems.
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Affiliation(s)
- Junjie Liu
- Department of Chemistry , University of Alberta , Edmonton , Alberta T6G 2G2 , Canada
| | - Gabriel Hanna
- Department of Chemistry , University of Alberta , Edmonton , Alberta T6G 2G2 , Canada
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9
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Zauleck JPP, Peschel MT, Rott F, Thallmair S, de Vivie-Riedle R. Ultrafast Reactive Quantum Dynamics Coupled to Classical Solvent Dynamics Using an Ehrenfest Approach. J Phys Chem A 2018; 122:2849-2857. [PMID: 29498853 DOI: 10.1021/acs.jpca.7b10372] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
The inclusion of solvent effects in the theoretical analysis of molecular processes becomes increasingly important. Currently, it is not feasible to directly include the solvent on the quantum level. We use an Ehrenfest approach to study the coupled time evolution of quantum dynamically treated solutes and classical solvents system. The classical dynamics of the solvent is coupled to the wavepacket dynamics of the solute and rotational and translational degrees of freedom of the solute are included classically. This allows quantum dynamics simulations for ultrafast processes that are decided by environment interactions without explicit separation of time scales. We show the application to the dissociation of ICN in liquid Ar as a proof of principal system and to the more applied example of uracil in water.
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Affiliation(s)
- Julius P P Zauleck
- Department of Chemistry , Ludwig-Maximilians-Universität München , D-81377 München , Germany
| | - Martin T Peschel
- Department of Chemistry , Ludwig-Maximilians-Universität München , D-81377 München , Germany
| | - Florian Rott
- Department of Chemistry , Ludwig-Maximilians-Universität München , D-81377 München , Germany
| | - Sebastian Thallmair
- Department of Chemistry , Ludwig-Maximilians-Universität München , D-81377 München , Germany
| | - Regina de Vivie-Riedle
- Department of Chemistry , Ludwig-Maximilians-Universität München , D-81377 München , Germany
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10
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Kananenka AA, Sun X, Schubert A, Dunietz BD, Geva E. A comparative study of different methods for calculating electronic transition rates. J Chem Phys 2018; 148:102304. [DOI: 10.1063/1.4989509] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alexei A. Kananenka
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Xiang Sun
- 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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Xu Y, Song K, Shi Q. Mixed quantum-classical simulation of the hydride transfer reaction catalyzed by dihydrofolate reductase based on a mapped system-harmonic bath model. J Chem Phys 2018; 148:102322. [DOI: 10.1063/1.4990515] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yang Xu
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Kai Song
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
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12
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Dell’Angelo D, Hanna G. On the performance of multi-state transition filtering in mixed quantum-classical Liouville surface-hopping simulations: beyond two- and three-state quantum subsystems. Theor Chem Acc 2018. [DOI: 10.1007/s00214-017-2194-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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13
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Importance of eigenvector sign consistency in computations of expectation values via mixed quantum-classical surface-hopping dynamics. Theor Chem Acc 2017. [DOI: 10.1007/s00214-017-2105-z] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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14
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Kananenka AA, Hsieh CY, Cao J, Geva E. Accurate Long-Time Mixed Quantum-Classical Liouville Dynamics via the Transfer Tensor Method. J Phys Chem Lett 2016; 7:4809-4814. [PMID: 27934045 DOI: 10.1021/acs.jpclett.6b02389] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In this Letter, we combine the recently introduced transfer tensor method with the mixed quantum-classical Liouville method. The resulting protocol provides an accurate, general, flexible and robust new route for simulating the reduced dynamics of the quantum subsystem for arbitrarily long times, starting with computationally feasible short-time mixed quantum-classical Liouville dynamical maps. The accuracy and feasibility of the methodology are demonstrated on a spin-boson benchmark model.
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Affiliation(s)
- Alexei A Kananenka
- Department of Chemistry, University of Michigan , Ann Arbor, Michigan 48109, United States
| | - Chang-Yu Hsieh
- Department of Chemistry, Massachusetts Institute of Technology , Cambridge, Massachusetts 02319, United States
| | - Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology , Cambridge, Massachusetts 02319, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan , Ann Arbor, Michigan 48109, United States
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15
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16
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Lu J, Zhou Z. Improved sampling and validation of frozen Gaussian approximation with surface hopping algorithm for nonadiabatic dynamics. J Chem Phys 2016; 145:124109. [DOI: 10.1063/1.4963107] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jianfeng Lu
- Department of Mathematics, Duke University, Box 90320, Durham, North Carolina 27708, USA
- Department of Physics and Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Zhennan Zhou
- Department of Mathematics, Duke University, Box 90320, Durham, North Carolina 27708, USA
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17
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Freedman H, Hanna G. Mixed quantum–classical Liouville simulation of vibrational energy transfer in a model α-helix at 300 K. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.08.015] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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18
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Affiliation(s)
- M. C. Sherman
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - S. A. Corcelli
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, USA
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19
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Shakib F, Hanna G. Mixed Quantum-Classical Liouville Approach for Calculating Proton-Coupled Electron-Transfer Rate Constants. J Chem Theory Comput 2016; 12:3020-9. [DOI: 10.1021/acs.jctc.6b00362] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Affiliation(s)
- Farnaz Shakib
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
| | - Gabriel Hanna
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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20
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Xie W, Xu M, Bai S, Shi Q. Mixed Quantum-Classical Study of Nonadiabatic Curve Crossing in Condensed Phases. J Phys Chem A 2016; 120:3225-32. [DOI: 10.1021/acs.jpca.5b11695] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Weiwei Xie
- Beijing
National Laboratory
for Molecular Sciences, State Key Laboratory for Structural Chemistry
of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
| | - Meng Xu
- Beijing
National Laboratory
for Molecular Sciences, State Key Laboratory for Structural Chemistry
of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
| | - Shuming Bai
- Beijing
National Laboratory
for Molecular Sciences, State Key Laboratory for Structural Chemistry
of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
| | - 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, Zhongguancun, Beijing 100190, China
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21
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Martinez F, Hanna G. Mixed Quantum-Classical Simulations of Transient Absorption Pump–Probe Signals for a Photo-Induced Electron Transfer Reaction Coupled to an Inner-Sphere Vibrational Mode. J Phys Chem A 2016; 120:3196-205. [DOI: 10.1021/acs.jpca.5b11727] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Franz Martinez
- Department
of Chemistry, University of Alberta, Edmonton, Alberta T6G 2R3, Canada
| | - Gabriel Hanna
- Department
of Chemistry, University of Alberta, Edmonton, Alberta T6G 2R3, Canada
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22
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Shakib FA, Hanna G. New insights into the nonadiabatic state population dynamics of model proton-coupled electron transfer reactions from the mixed quantum-classical Liouville approach. J Chem Phys 2016; 144:024110. [DOI: 10.1063/1.4939586] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Affiliation(s)
- Farnaz A. Shakib
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
| | - Gabriel Hanna
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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23
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Dell’Angelo D, Hanna G. Self-Consistent Filtering Scheme for Efficient Calculations of Observables via the Mixed Quantum-Classical Liouville Approach. J Chem Theory Comput 2016; 12:477-85. [DOI: 10.1021/acs.jctc.5b00991] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- David Dell’Angelo
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
| | - Gabriel Hanna
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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24
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Kapral R. Quantum dynamics in open quantum-classical systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:073201. [PMID: 25634784 DOI: 10.1088/0953-8984/27/7/073201] [Citation(s) in RCA: 49] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence on the properties of the quantum system. In many instances the environment is well-approximated by classical mechanics, so that one is led to consider the dynamics of open quantum-classical systems. Since a full quantum dynamical description of large many-body systems is not currently feasible, mixed quantum-classical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantum-classical Liouville dynamics, one of several quantum-classical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum-classical Liouville dynamics, as well as methods for simulating the dynamics.
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Affiliation(s)
- Raymond Kapral
- Department of Chemistry, Chemical Physics Theory Group, University of Toronto, Toronto, ON, M5S 3H6 Canada
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25
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Sherman MC, Corcelli SA. Thermal equilibrium properties of surface hopping with an implicit Langevin bath. J Chem Phys 2015; 142:024110. [DOI: 10.1063/1.4905253] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- M. C. Sherman
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - S. A. Corcelli
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, USA
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26
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Shakib FA, Hanna G. An analysis of model proton-coupled electron transfer reactions via the mixed quantum-classical Liouville approach. J Chem Phys 2014; 141:044122. [DOI: 10.1063/1.4890915] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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27
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Subotnik JE, Ouyang W, Landry BR. Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence. J Chem Phys 2014; 139:214107. [PMID: 24320364 DOI: 10.1063/1.4829856] [Citation(s) in RCA: 133] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this article, we demonstrate that Tully's fewest-switches surface hopping (FSSH) algorithm approximately obeys the mixed quantum-classical Liouville equation (QCLE), provided that several conditions are satisfied--some major conditions, and some minor. The major conditions are: (1) nuclei must be moving quickly with large momenta; (2) there cannot be explicit recoherences or interference effects between nuclear wave packets; (3) force-based decoherence must be added to the FSSH algorithm, and the trajectories can no longer rigorously be independent (though approximations for independent trajectories are possible). We furthermore expect that FSSH (with decoherence) will be most robust when nonadiabatic transitions in an adiabatic basis are dictated primarily by derivative couplings that are presumably localized to crossing regions, rather than by small but pervasive off-diagonal force matrix elements. In the end, our results emphasize the strengths of and possibilities for the FSSH algorithm when decoherence is included, while also demonstrating the limitations of the FSSH algorithm and its inherent inability to follow the QCLE exactly.
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Affiliation(s)
- Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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28
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Martinez F, Hanna G. Assessment of approximate solutions of the quantum–classical Liouville equation for dynamics simulations of quantum subsystems embedded in classical environments. MOLECULAR SIMULATION 2014. [DOI: 10.1080/08927022.2014.923573] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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29
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Ouyang W, Subotnik JE. Estimating the entropy and quantifying the impurity of a swarm of surface-hopping trajectories: A new perspective on decoherence. J Chem Phys 2014; 140:204102. [DOI: 10.1063/1.4876491] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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30
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Xie W, Xu Y, Zhu L, Shi Q. Mixed quantum classical calculation of proton transfer reaction rates: From deep tunneling to over the barrier regimes. J Chem Phys 2014; 140:174105. [DOI: 10.1063/1.4873135] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Schwerdtfeger CA, Soudackov AV, Hammes-Schiffer S. Nonadiabatic dynamics of electron transfer in solution: Explicit and implicit solvent treatments that include multiple relaxation time scales. J Chem Phys 2014; 140:034113. [DOI: 10.1063/1.4855295] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
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32
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33
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Kwac K, Geva E. A Mixed Quantum-Classical Molecular Dynamics Study of anti-Tetrol and syn-Tetrol Dissolved in Liquid Chloroform II: Infrared Emission Spectra, Vibrational Excited-State Lifetimes, and Nonequilibrium Hydrogen-Bond Dynamics. J Phys Chem B 2013; 117:14457-67. [DOI: 10.1021/jp408580n] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Kijeong Kwac
- 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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34
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Tomkins J, Hanna G. Signatures of nanoconfinement on the linear and nonlinear vibrational spectroscopy of a model hydrogen-bonded complex dissolved in a polar solvent. J Phys Chem B 2013; 117:13619-30. [PMID: 24079369 DOI: 10.1021/jp407469f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The one-dimensional IR (1D-IR) absorption and IR pump-probe spectra of a hydrogen stretch in a model hydrogen-bonded complex dissolved in a polar solvent confined in spherical hydrophobic cavities of different sizes were simulated using ground-state mixed quantum-classical dynamics. Due to a thorough analysis of key properties of the complex and solvent from equilibrium trajectory data, we were able to gain insight into the microscopic details underlying the spectra. Both the 1D-IR and IR pump-probe spectra manifested the effects of confinement on the relative stabilities of the covalent and ionic forms of the complex through pronounced changes in their peak intensities and numbers. However, in contrast to the 1D-IR spectra, the time-resolved pump-probe spectra were found to be uniquely sensitive to the changes in the molecular dynamics as the cavity size is varied. In particular, it was found that the variations in the time evolutions of the peak intensities in the pump-probe spectra reflect the differences in the solvation dynamics associated with the various forms of the complex in different locations within the cavities. The ability to detect these differences underscores the advantage of using pump-probe spectroscopy for studying nanoconfined systems.
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Affiliation(s)
- Joseph Tomkins
- Department of Chemistry, University of Alberta , Edmonton, Alberta, Canada T6G 2G2
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35
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Sow CS, Tomkins J, Hanna G. Computational study of the one- and two-dimensional infrared spectra of a proton-transfer mode in a hydrogen-bonded complex dissolved in a polar nanocluster. Chemphyschem 2013; 14:3309-18. [PMID: 23946271 DOI: 10.1002/cphc.201300610] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2013] [Indexed: 11/07/2022]
Abstract
The signatures of nanosolvation on the one- and two-dimensional (1D and 2D) IR spectra of a proton-transfer mode in a hydrogen-bonded complex dissolved in polar solvent molecule nanoclusters of varying size are elucidated by using mixed quantum-classical molecular dynamics simulations. For this particular system, increasing the number of solvent molecules successively from N=7 to N=9 initiates the transition of the system from a cluster state to a bulk-like state. Both the 1D and 2D IR spectra reflect this transition through pronounced changes in their peak intensities and numbers, but the time-resolved 2D IR spectra also manifest spectral features that uniquely identify the onset of the cluster-to-bulk transition. In particular, it is observed that in the 1D IR spectra, the relative intensities of the peaks change such that the number of peaks decreases from three to two as the size of the cluster increases from N=7 to N=9. In the 2D IR spectra, off-diagonal peaks are observed in the N=7 and N=8 cases at zero waiting time, but not in the N=9 case. It is known that there are no off-diagonal peaks in the 2D IR spectrum of the bulk version of this system at zero waiting time, so the disappearance of these peaks is a unique signature of the onset of bulk-like behavior. Through an examination of the trajectories of various properties of the complex and solvent, it is possible to relate the emergence of these off-diagonal peaks to an interplay between the vibrations of the complex and the solvent polarization dynamics.
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Affiliation(s)
- Chia Shen Sow
- Department of Chemistry, University of Alberta, Edmonton, AB T6G 2G2 (Canada)
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36
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Uken DA, Sergi A, Petruccione F. Filtering schemes in the quantum-classical Liouville approach to nonadiabatic dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:033301. [PMID: 24125379 DOI: 10.1103/physreve.88.033301] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2013] [Indexed: 06/02/2023]
Abstract
We study a number of filtering schemes for the reduction of the statistical error in nonadiabatic calculations by means of the quantum-classical Liouville equation. In particular, we focus on a scheme based on setting a threshold value on the sampling weights, so that when the threshold is overcome the value of the weight is reset, and on another approach which prunes the ensemble of the allowed nonadiabatic transitions according to a generalized sampling probability. Both methods have advantages and drawbacks, however, their combination drastically improves the performance of an algorithm known as the sequential short-time step propagation [MacKernan et al., J. Phys: Condens. Matter 14, 9069 (2002)], which is derived from a simple first order expansion of the quantum-classical propagator. Such an algorithm together with the combined filtering procedures produce results that compare very well with those obtained by means of numerically accurate path integral quantum calculations for the spin-boson model, even for intermediate and strong coupling regimes.
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Affiliation(s)
- Daniel A Uken
- School of Chemistry and Physics, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209 Pietermaritzburg, South Africa
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37
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Kelly A, Markland TE. Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics. J Chem Phys 2013; 139:014104. [DOI: 10.1063/1.4812355] [Citation(s) in RCA: 79] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
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38
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Abedi A, Agostini F, Suzuki Y, Gross EKU. Dynamical steps that bridge piecewise adiabatic shapes in the exact time-dependent potential energy surface. PHYSICAL REVIEW LETTERS 2013; 110:263001. [PMID: 23848868 DOI: 10.1103/physrevlett.110.263001] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2013] [Indexed: 06/02/2023]
Abstract
We study the exact time-dependent potential energy surface (TDPES) in the presence of strong nonadiabatic coupling between the electronic and nuclear motion. The concept of the TDPES emerges from the exact factorization of the full electron-nuclear wave function [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)]. Employing a one-dimensional model system, we show that the TDPES exhibits a dynamical step that bridges between piecewise adiabatic shapes. We analytically investigate the position of the steps and the nature of the switching between the adiabatic pieces of the TDPES.
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Affiliation(s)
- Ali Abedi
- Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
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39
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Kwac K, Geva E. A Mixed Quantum-Classical Molecular Dynamics Study of the Hydroxyl Stretch in Methanol/Carbon Tetrachloride Mixtures III: Nonequilibrium Hydrogen-Bond Dynamics and Infrared Pump–Probe Spectra. J Phys Chem B 2013; 117:7737-49. [DOI: 10.1021/jp403726t] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Kijeong Kwac
- 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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40
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Martinez F, Rekik N, Hanna G. Simulation of nonlinear optical signals via approximate solutions of the quantum–classical Liouville equation: Application to the pump–probe spectroscopy of a condensed phase electron transfer reaction. Chem Phys Lett 2013. [DOI: 10.1016/j.cplett.2013.04.018] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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41
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Rekik N, Hsieh CY, Freedman H, Hanna G. A mixed quantum-classical Liouville study of the population dynamics in a model photo-induced condensed phase electron transfer reaction. J Chem Phys 2013; 138:144106. [DOI: 10.1063/1.4799272] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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42
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Hsieh CY, Kapral R. Analysis of the forward-backward trajectory solution for the mixed quantum-classical Liouville equation. J Chem Phys 2013; 138:134110. [DOI: 10.1063/1.4798221] [Citation(s) in RCA: 61] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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43
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Habershon S, Manolopoulos DE, Markland TE, Miller TF. Ring-Polymer Molecular Dynamics: Quantum Effects in Chemical Dynamics from Classical Trajectories in an Extended Phase Space. Annu Rev Phys Chem 2013; 64:387-413. [DOI: 10.1146/annurev-physchem-040412-110122] [Citation(s) in RCA: 448] [Impact Index Per Article: 40.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Scott Habershon
- Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom;
| | - David E. Manolopoulos
- Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom;
| | - Thomas E. Markland
- Department of Chemistry, Stanford University, Stanford, California 94305;
| | - Thomas F. Miller
- Department of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125;
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44
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Kelly A, van Zon R, Schofield J, Kapral R. Mapping quantum-classical Liouville equation: Projectors and trajectories. J Chem Phys 2012; 136:084101. [DOI: 10.1063/1.3685420] [Citation(s) in RCA: 82] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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45
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Kwac K, Geva E. Mixed quantum-classical molecular dynamics study of the hydroxyl stretch in methanol/carbon-tetrachloride mixtures II: excited state hydrogen bonding structure and dynamics, infrared emission spectrum, and excited state lifetime. J Phys Chem B 2012; 116:2856-66. [PMID: 22283660 DOI: 10.1021/jp211792j] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We present a mixed quantum-classical molecular dynamics study of the hydrogen-bonding structure and dynamics of a vibrationally excited hydroxyl stretch in methanol/carbon-tetrachloride mixtures. The adiabatic Hamiltonian of the quantum-mechanical hydroxyl is diagonalized on-the-fly to obtain the ground and first-excited adiabatic energy levels and wave functions which depend parametrically on the instantaneous configuration of the classical degrees of freedom. The dynamics of the classical degrees of freedom are determined by Hellmann-Feynman forces obtained by taking the expectation value of the force with respect to the ground or excited vibrational wave functions. Polarizable force fields are used which were previously shown to reproduce the experimental infrared absorption spectrum rather well, for different isotopomers and over a wide composition range [Kwac, K.; Geva, E. J. Phys. Chem. B 2011, 115, 9184]. We show that the agreement of the absorption spectra with experiment can be further improved by accounting for the dependence of the dipole moment derivatives on the configuration of the classical degrees of freedom. We find that the propensity of a methanol molecule to form hydrogen bonds increases upon photoexcitation of its hydroxyl stretch, thereby leading to a sizable red-shift of the corresponding emission spectrum relative to the absorption spectrum. Treating the relaxation from the first excited to the ground state as a nonadiabatic process, and calculating its rate within the framework of Fermi's golden rule and the harmonic-Schofield quantum correction factor, we were able to predict a lifetime which is of the same order of magnitude as the experimental value. The experimental dependence of the lifetime on the transition frequency is also reproduced. Nonlinear mapping relations between the hydroxyl transition frequency and bond length in the excited state and the electric field along the hydroxyl bond axis are established. These mapping relations make it possible to reduce the computational cost of the mixed quantum-classical treatment to that of a fully classical treatment.
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Affiliation(s)
- Kijeong Kwac
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, USA.
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46
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Ka BJ, Thompson WH. Sampling the Proton Transfer Reaction Coordinate in Mixed Quantum-Classical Molecular Dynamics Simulations. J Phys Chem A 2012; 116:832-8. [DOI: 10.1021/jp206772e] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Being J. Ka
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
| | - Ward H. Thompson
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
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47
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ARTECA GUSTAVOA, RANK JEANPIERRE, TAPIA O. TOPOLOGICAL STUDY OF REACTIVE POTENTIAL-ENERGY SURFACES FROM MODEL DIABATIC STATES COUPLED TO SURROUNDING MEDIA. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1142/s0219633607003350] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Reaction paths are studied with the help of diabatic potential-energy surfaces coupled in a generic external field. We show that all putative geometrical and topological features of two-dimensional (2D) potential-energy surfaces for an isomerization can be generated with a model consisting of strictly diabatic harmonic 2D wells coupled in a static (yet uniform) external field. For a large class of three-state models, we provide a phase diagram of possible topologies in the relevant parameter space for three-state models. By following the shift in diabatic electronic amplitudes (denoted by {|ck|2}) in coherent quantum states produced in the field, we assess whether the models within each phase can produce reaction paths visiting regions of configurational space that are structurally similar to the diabatic transition state.
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Affiliation(s)
- GUSTAVO A. ARTECA
- Département de Chimie et Biochimie & Biomolecular Sciences Programme, Laurentian University, Ramsey Lake Road, Sudbury, Ontario, Canada P3E 2C6, Canada
- Department of Physical Chemistry, Uppsala University, Box 579, S-751 23 Uppsala, Sweden
| | - JEAN PIERRE RANK
- Département de Chimie et Biochimie & Biomolecular Sciences Programme, Laurentian University, Ramsey Lake Road, Sudbury, Ontario, Canada P3E 2C6, Canada
| | - O. TAPIA
- Department of Physical Chemistry, Uppsala University, Box 579, S-751 23 Uppsala, Sweden
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48
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Gelman D, Schwartz SD. Finite temperature application of the corrected propagator method to reactive dynamics in a condensed-phase environment. J Chem Phys 2011; 134:034109. [PMID: 21261332 PMCID: PMC3041154 DOI: 10.1063/1.3545978] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2010] [Accepted: 01/04/2011] [Indexed: 12/14/2022] Open
Abstract
The recently proposed mixed quantum-classical method is extended to applications at finite temperatures. The method is designed to treat complex systems consisting of a low-dimensional quantum part (the primary system) coupled to a dissipative bath described classically. The method is based on a formalism showing how to systematically correct the approximate zeroth-order evolution rule. The corrections are defined in terms of the total quantum Hamiltonian and are taken to the classical limit by introducing the frozen Gaussian approximation for the bath degrees of freedom. The evolution of the primary system is governed by the corrected propagator yielding the exact quantum dynamics. The method has been tested on a standard model system describing proton transfer in a condensed-phase environment: a symmetric double-well potential bilinearly coupled to a bath of harmonic oscillators. Flux correlation functions and thermal rate constants have been calculated at two different temperatures for a range of coupling strengths. The results have been compared to the fully quantum simulations of Topaler and Makri [J. Chem. Phys. 101, 7500 (1994)] with the real path integral method.
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Affiliation(s)
- David Gelman
- Department of Biophysics, Albert Einstein College of Medicine, 1300 Morris Park Ave., Bronx, New York 10461, USA
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49
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Nassimi A, Bonella S, Kapral R. Analysis of the quantum-classical Liouville equation in the mapping basis. J Chem Phys 2010; 133:134115. [DOI: 10.1063/1.3480018] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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50
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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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