1
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De PK, Jain A. Exciton energy transfer inside cavity-A benchmark study of polaritonic dynamics using the surface hopping method. J Chem Phys 2024; 161:054117. [PMID: 39105549 DOI: 10.1063/5.0216787] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2024] [Accepted: 07/22/2024] [Indexed: 08/07/2024] Open
Abstract
Strong coupling between the molecular system and photon inside the cavity generates polaritons, which can alter reaction rates by orders of magnitude. In this work, we benchmark the surface hopping method to simulate non-adiabatic dynamics in a cavity. The comparison is made against a numerically exact method (the hierarchical equations of motion) for a model system investigating excitonic energy transfer for a broad range of parameters. Surface hopping captures the effects of the radiation mode well, both at resonance and off-resonance. We have further investigated parameters that can increase or decrease the rate of population transfer, and we find that surface hopping in general can capture both effects well. Finally, we show that the dipole self-energy term within our parameter regime does not significantly affect the system's dynamics.
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Affiliation(s)
- Priyam Kumar De
- Department of Chemistry, Indian Institute of Technology, Mumbai 400076, India
| | - Amber Jain
- Department of Chemistry, Indian Institute of Technology, Mumbai 400076, India
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2
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Shu Y, Truhlar DG. Generalized Semiclassical Ehrenfest Method: A Route to Wave Function-Free Photochemistry and Nonadiabatic Dynamics with Only Potential Energies and Gradients. J Chem Theory Comput 2024; 20:4396-4426. [PMID: 38819014 DOI: 10.1021/acs.jctc.4c00424] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/01/2024]
Abstract
We reconsider recent methods by which direct dynamics calculations of electronically nonadiabatic processes can be carried out while requiring only adiabatic potential energies and their gradients. We show that these methods can be understood in terms of a new generalization of the well-known semiclassical Ehrenfest method. This is convenient because it eliminates the need to evaluate electronic wave functions and their matrix elements along the mixed quantum-classical trajectories. The new approximations and procedures enabling this advance are the curvature-driven approximation to the time-derivative coupling, the generalized semiclassical Ehrenfest method, and a new gradient correction scheme called the time-derivative matrix (TDM) scheme. When spin-orbit coupling is present, one can carry out dynamics calculations in the fully adiabatic basis using potential energies and gradients calculated without spin-orbit coupling plus the spin-orbit coupling matrix elements. Even when spin-orbit coupling is neglected, the method is useful because it allows calculations by electronic structure methods for which nonadiabatic coupling vectors are unavailable. In order to place the new considerations in context, the article starts out with a review of background material on trajectory surface hopping, the semiclassical Ehrenfest scheme, and methods for incorporating decoherence. We consider both internal conversion and intersystem crossing. We also review several examples from our group of successful applications of the curvature-driven approximation.
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Affiliation(s)
- Yinan Shu
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
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3
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Zhou Z, Wu Y, Bian X, Subotnik JE. Nonadiabatic Dynamics in a Continuous Circularly Polarized Laser Field with Floquet Phase-Space Surface Hopping. J Chem Theory Comput 2023; 19:718-732. [PMID: 36655857 DOI: 10.1021/acs.jctc.2c00948] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
Nonadiabatic chemical reactions involving continuous circularly polarized light (cw CPL) have not attracted as much attention as dynamics in unpolarized/linearly polarized light. However, including circularly (in contrast to linearly) polarized light allows one to effectively introduce a complex-valued time-dependent Hamiltonian, which offers a new path for control or exploration through the introduction of Berry forces. Here, we investigate several inexpensive semiclassical approaches for modeling such nonadiabatic dynamics in the presence of a time-dependent complex-valued Hamiltonian, beginning with a straightforward instantaneous adiabatic fewest-switches surface hopping (IA-FSSH) approach (where the electronic states depend on position and time), continuing to a standard Floquet fewest switches surface hopping (F-FSSH) approach (where the electronic states depend on position and frequency), and ending with an exotic Floquet phase-space surface hopping (F-PSSH) approach (where the electronic states depend on position, frequency, and momentum). Using a set of model systems with time-dependent complex-valued Hamiltonians, we show that the Floquet phase-space adiabats are the optimal choice of basis as far as accounting for Berry phase effects and delivering accuracy. Thus, the F-PSSH algorithm sets the stage for future modeling of nonadiabatic dynamics under strong externally pumped circular polarization.
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Affiliation(s)
- Zeyu Zhou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Joseph Eli Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
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4
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Shu Y, Truhlar DG. Decoherence and Its Role in Electronically Nonadiabatic Dynamics. J Chem Theory Comput 2023; 19:380-395. [PMID: 36622843 PMCID: PMC9878713 DOI: 10.1021/acs.jctc.2c00988] [Citation(s) in RCA: 14] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Indexed: 01/10/2023]
Abstract
Decoherence is the tendency of a time-evolved reduced density matrix for a subsystem to assume a form corresponding to a statistical ensemble of states rather than a coherent combination of pure-state wave functions. When a molecular process involves changes in the electronic state and the coordinates of the nuclei, as in ultraviolet or visible light photochemistry or electronically inelastic collisions, the reduced density matrix of the electronic subsystem suffers decoherence, due to its interaction with the nuclear subsystem. We present the background necessary to conceptualize this decoherence; in particular, we discuss the density matrix description of pure states and mixed states, and we discuss pointer states and decoherence time. We then discuss how decoherence is treated in the coherent switching with decay of mixing algorithm and the trajectory surface hopping method for semiclassical calculations of electronically nonadiabatic processes.
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Affiliation(s)
- Yinan Shu
- Department of Chemistry,
Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota55455-0431, United States
| | - Donald G. Truhlar
- Department of Chemistry,
Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota55455-0431, United States
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5
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Ab initio Nonadiabatic Dynamics of Semiconductor Nanomaterials via Surface Hopping Method. CHINESE J CHEM PHYS 2022. [DOI: 10.1063/1674-0068/cjcp2111247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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6
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Wu Y, Subotnik JE. Semiclassical description of nuclear dynamics moving through complex-valued single avoided crossings of two electronic states. J Chem Phys 2021; 154:234101. [PMID: 34241259 DOI: 10.1063/5.0054014] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The standard fewest-switches surface hopping (FSSH) approach fails to model nonadiabatic dynamics when the electronic Hamiltonian is complex-valued and there are multiple nuclear dimensions; FSSH does not include geometric magnetic effects and does not have access to a gauge independent direction for momentum rescaling. In this paper, for the case of a Hamiltonian with two electronic states, we propose an extension of Tully's FSSH algorithm, which includes geometric magnetic forces and, through diabatization, establishes a well-defined rescaling direction. When combined with a decoherence correction, our new algorithm shows satisfying results for a model set of two-dimensional single avoided crossings.
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Affiliation(s)
- Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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7
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Bian X, Wu Y, Teh HH, Zhou Z, Chen HT, Subotnik JE. Modeling nonadiabatic dynamics with degenerate electronic states, intersystem crossing, and spin separation: A key goal for chemical physics. J Chem Phys 2021; 154:110901. [DOI: 10.1063/5.0039371] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Affiliation(s)
- Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Hung-Hsuan Teh
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Zeyu Zhou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Hsing-Ta Chen
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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8
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Miao G, Bian X, Zhou Z, Subotnik J. A "backtracking" correction for the fewest switches surface hopping algorithm. J Chem Phys 2020; 153:111101. [PMID: 32962370 DOI: 10.1063/5.0022436] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a "backtracking" mechanism within Tully's fewest switches surface hopping (FSSH) algorithm, whereby whenever one detects consecutive (double) hops during a short period of time, one simply rewinds the dynamics backward in time. In doing so, one reduces the number of hopping events and comes closer to a truly fewest switches surface hopping approach with independent trajectories. With this algorithmic change, we demonstrate that surface hopping can be reasonably accurate for nuclear dynamics in a multidimensional configuration space with a complex-valued (i.e., not real-valued) electronic Hamiltonian; without this adjustment, surface hopping often fails. The added computational cost is marginal. Future research will be needed to assess whether or not this backtracking correction can improve the accuracy of a typical FSSH calculation with a real-valued electronic Hamiltonian (that ignores spin).
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Affiliation(s)
- Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Zeyu Zhou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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9
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Nematiaram T, Troisi A. Modeling charge transport in high-mobility molecular semiconductors: Balancing electronic structure and quantum dynamics methods with the help of experiments. J Chem Phys 2020; 152:190902. [DOI: 10.1063/5.0008357] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Affiliation(s)
- Tahereh Nematiaram
- Department of Chemistry and Materials Innovation Factory, University of Liverpool, Liverpool L69 7ZD, United Kingdom
| | - Alessandro Troisi
- Department of Chemistry and Materials Innovation Factory, University of Liverpool, Liverpool L69 7ZD, United Kingdom
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10
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Zhou Z, Chen HT, Nitzan A, Subotnik JE. Nonadiabatic Dynamics in a Laser Field: Using Floquet Fewest Switches Surface Hopping To Calculate Electronic Populations for Slow Nuclear Velocities. J Chem Theory Comput 2020; 16:821-834. [PMID: 31951404 DOI: 10.1021/acs.jctc.9b00950] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
We investigate two well-known approaches for extending the fewest switches surface hopping (FSSH) algorithm to periodic time-dependent couplings. The first formalism acts as if the instantaneous adiabatic electronic states were standard adiabatic states, which just happen to evolve in time. The second formalism replaces the role of the usual adiabatic states by the time-independent adiabatic Floquet states. For a set of modified Tully model problems, the Floquet FSSH (F-FSSH) formalism gives a better estimate for both transmission and reflection probabilities than the instantaneous adiabatic FSSH (IA-FSSH) formalism, especially for slow nuclear velocities. More importantly, only F-FSSH predicts the correct final scattering momentum. Finally, in order to use Floquet theory accurately, we find that it is crucial to account for the interference between wavepackets on different Floquet states. Our results should be of interest to all those interested in laser-induced molecular dynamics.
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Affiliation(s)
- Zeyu Zhou
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States
| | - Hsing-Ta Chen
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States
| | - Abraham Nitzan
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States
| | - Joseph Eli Subotnik
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States
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11
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Abstract
Dynamics at molecule-metal interfaces are a subject of intense current interest and come in many different flavors of experiments: gas-phase scattering, chemisorption, electrochemistry, nanojunction transport, and heterogeneous catalysis, to name a few. These dynamics involve nuclear degrees of freedom entangled with many electronic degrees of freedom (in the metal), and as such there is always the possibility for nonadiabatic phenomena to appear: the nuclei do not necessarily need to move slower than the electrons to break the Born-Oppenheimer (BO) approximation. In this Feature Article, we review a set of dynamical methods developed recently to deal with such nonadiabatic phenomena at a metal surface, methods that serve as alternatives to Tully's independent electron surface hopping (IESH) model. In the weak molecule-metal coupling regime, a classical master equation (CME) can be derived and a simple surface hopping approach is proposed to propagate nuclear and electronic dynamics stochastically. In the strong molecule-metal interaction regime, a Fokker-Planck equation can be derived for the nuclear dynamics, with electronic DoFs incorporated into the overall friction and random force. Lastly, a broadened classical master equation (BCME) can interpolate between the weak and strong molecule-metal interactions. Here, we briefly review these methods and the relevant benchmarking data, showing in particular how the methods can be used to calculate nonequilibrium transport properties. We highlight several open questions and pose several avenues for future study.
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Affiliation(s)
- Wenjie Dou
- Department of Chemistry , University of California, Berkeley , Berkeley , California 94720 , United States
| | - Joseph E Subotnik
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States
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12
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Subotnik J, Miao G, Bellonzi N, Teh HH, Dou W. A demonstration of consistency between the quantum classical Liouville equation and Berry’s phase and curvature for the case of complex Hamiltonians. J Chem Phys 2019; 151:074113. [DOI: 10.1063/1.5116210] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Nicole Bellonzi
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Hung-Hsuan Teh
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Wenjie Dou
- Department of Chemistry, University of California, Berkeley, California 94720, USA
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13
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Miao G, Subotnik J. Revisiting the Recoherence Problem in the Fewest Switches Surface Hopping Algorithm. J Phys Chem A 2019; 123:5428-5435. [DOI: 10.1021/acs.jpca.9b03188] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
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14
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Miao G, Bellonzi N, Subotnik J. An extension of the fewest switches surface hopping algorithm to complex Hamiltonians and photophysics in magnetic fields: Berry curvature and “magnetic” forces. J Chem Phys 2019; 150:124101. [DOI: 10.1063/1.5088770] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Nicole Bellonzi
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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15
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Li TE, Chen HT, Subotnik JE. Comparison of Different Classical, Semiclassical, and Quantum Treatments of Light–Matter Interactions: Understanding Energy Conservation. J Chem Theory Comput 2019; 15:1957-1973. [DOI: 10.1021/acs.jctc.8b01232] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Tao E. Li
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Hsing-Ta Chen
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
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16
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Miao G, Ouyang W, Subotnik J. A comparison of surface hopping approaches for capturing metal-molecule electron transfer: A broadened classical master equation versus independent electron surface hopping. J Chem Phys 2019; 150:041711. [PMID: 30709317 DOI: 10.1063/1.5050235] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Within a generalized Anderson-Holstein model, we investigate electron transfer rates using two different surface hopping algorithms: a broadened classical master equation (BCME) and independent electron surface hopping (IESH). We find that for large enough bandwidth and density of one electron states, and in the presence of external friction, the IESH results converge to the BCME results for impurity-bath model systems, recovering both relaxation rates and equilibrium populations. Without external friction, however, the BCME and IESH results can strongly disagree, and preliminary evidence suggests that IESH does not always recover the correct equilibrium state. Finally, we also demonstrate that adding an electronic thermostat to IESH does help drive the metallic substrate to the correct equilibrium state, but this improvement can sometimes come at the cost of worse short time dynamics. Overall, our results should be of use for all computational chemists looking to model either gas phase scattering or electrochemical dynamics at a metal interface.
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Affiliation(s)
- Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Wenjun Ouyang
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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17
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Gao LH, Xie BB, Fang WH. Theories and Applications of Mixed Quantum-Classical Non-adiabatic Dynamics. CHINESE J CHEM PHYS 2018. [DOI: 10.1063/1674-0068/31/cjcp1712234] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Affiliation(s)
- Liang-hui Gao
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Bin-bin Xie
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Wei-hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
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18
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Medders GR, Alguire EC, Jain A, Subotnik JE. Ultrafast Electronic Relaxation through a Conical Intersection: Nonadiabatic Dynamics Disentangled through an Oscillator Strength-Based Diabatization Framework. J Phys Chem A 2017; 121:1425-1434. [DOI: 10.1021/acs.jpca.6b12120] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Gregory R. Medders
- Department
of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Ethan C. Alguire
- Department
of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Amber Jain
- Department
of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Joseph E. Subotnik
- Department
of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
- Stanford
PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States
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19
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Jain A, Alguire E, Subotnik JE. An Efficient, Augmented Surface Hopping Algorithm That Includes Decoherence for Use in Large-Scale Simulations. J Chem Theory Comput 2016; 12:5256-5268. [PMID: 27715036 DOI: 10.1021/acs.jctc.6b00673] [Citation(s) in RCA: 94] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We propose and implement a highly efficient augmented surface hopping algorithm that (i) can be used for large simulations (with many nuclei and many electronic states) and (ii) includes the effects of decoherence without parametrization. Our protocol is based on three key modifications of the surface hopping methodology: (a) a novel separation of classical and quantum degrees of freedom that treats avoided and trivial crossings efficiently, (b) a multidimensional approximation of the time derivative matrix that avoids explicit construction of the derivative coupling at most time steps, and (c) an efficient approximation for the augmented fewest-switches surface hopping decoherence rate. We will show that this protocol can be several orders of magnitude more efficient than the traditional protocol for large multidimensional problems. Furthermore, the marginal cost for including decoherence effects is now negligible.
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Affiliation(s)
- Amber Jain
- Department of Chemistry, University of Pennsylvania , 231 South 34th Street, Philadelphia, Pennsylvania 19104, United States
| | - Ethan Alguire
- Department of Chemistry, University of Pennsylvania , 231 South 34th Street, Philadelphia, Pennsylvania 19104, United States
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania , 231 South 34th Street, Philadelphia, Pennsylvania 19104, United States
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20
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Subotnik JE, Jain A, Landry B, Petit A, Ouyang W, Bellonzi N. Understanding the Surface Hopping View of Electronic Transitions and Decoherence. Annu Rev Phys Chem 2016; 67:387-417. [DOI: 10.1146/annurev-physchem-040215-112245] [Citation(s) in RCA: 234] [Impact Index Per Article: 29.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
| | - Amber Jain
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
| | - Brian Landry
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
| | - Andrew Petit
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
| | - Wenjun Ouyang
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
| | - Nicole Bellonzi
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
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21
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Nakamura H, Nanbu S, Teranishi Y, Ohta A. Development of semiclassical molecular dynamics simulation method. Phys Chem Chem Phys 2016; 18:11972-85. [DOI: 10.1039/c5cp07655b] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Various quantum mechanical effects such as nonadiabatic transitions, quantum mechanical tunneling and coherence play crucial roles in a variety of chemical and biological systems.
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Affiliation(s)
- Hiroki Nakamura
- Institute of Molecular Science
- National Chiao Tung University
- Hsinchu
- 30010 Taiwan
| | - Shinkoh Nanbu
- Department of Materials and Life Science
- Sophia University
- Tokyo 102-8554
- Japan
| | | | - Ayumi Ohta
- Department of Materials and Life Science
- Sophia University
- Tokyo 102-8554
- Japan
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22
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Ouyang W, Dou W, Subotnik JE. Surface hopping with a manifold of electronic states. I. Incorporating surface-leaking to capture lifetimes. J Chem Phys 2015; 142:084109. [PMID: 25725714 DOI: 10.1063/1.4908032] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the incorporation of the surface-leaking (SL) algorithm into Tully's fewest-switches surface hopping (FSSH) algorithm to simulate some electronic relaxation induced by an electronic bath in conjunction with some electronic transitions between discrete states. The resulting SL-FSSH algorithm is benchmarked against exact quantum scattering calculations for three one-dimensional model problems. The results show excellent agreement between SL-FSSH and exact quantum dynamics in the wide band limit, suggesting the potential for a SL-FSSH algorithm. Discrepancies and failures are investigated in detail to understand the factors that will limit the reliability of SL-FSSH, especially the wide band approximation. Considering the easiness of implementation and the low computational cost, we expect this method to be useful in studying processes involving both a continuum of electronic states (where electronic dynamics are probabilistic) and processes involving only a few electronic states (where non-adiabatic processes cannot ignore short-time coherence).
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Affiliation(s)
- Wenjun Ouyang
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Wenjie Dou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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23
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Landry BR, Subotnik JE. Surface hopping outperforms secular Redfield theory when reorganization energies range from small to moderate (and nuclei are classical). J Chem Phys 2015; 142:104102. [PMID: 25770523 DOI: 10.1063/1.4913494] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
We evaluate the accuracy of Tully's surface hopping algorithm for the spin-boson model in the limit of small to moderate reorganization energy. We calculate transition rates between diabatic surfaces in the exciton basis and compare against exact results from the hierarchical equations of motion; we also compare against approximate rates from the secular Redfield equation and Ehrenfest dynamics. We show that decoherence-corrected surface hopping performs very well in this regime, agreeing with secular Redfield theory for very weak system-bath coupling and outperforming secular Redfield theory for moderate system-bath coupling. Surface hopping can also be extended beyond the Markovian limits of standard Redfield theory. Given previous work [B. R. Landry and J. E. Subotnik, J. Chem. Phys. 137, 22A513 (2012)] that establishes the accuracy of decoherence-corrected surface-hopping in the Marcus regime, this work suggests that surface hopping may well have a very wide range of applicability.
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Affiliation(s)
- Brian R Landry
- Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, Pennsylvania 19104, USA
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Dou W, Nitzan A, Subotnik JE. Surface hopping with a manifold of electronic states. II. Application to the many-body Anderson-Holstein model. J Chem Phys 2015; 142:084110. [DOI: 10.1063/1.4908034] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Wenjie Dou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Abraham Nitzan
- School of Chemistry, The Sackler Faculty of Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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Abstract
While individual Tully-style fewest switches surface hopping (FSSH) trajectories are stochastic and cannot be inverted in time, it is possible to reverse in time the dynamics of a swarm of FSSH trajectories. Here we show exactly how to invert such dynamics, and we investigate the stability of such time-reversed surface hopping dynamics. We demonstrate that FSSH trajectories can be inverted successfully for short time periods, but the time-reversed dynamics become unstable for long times with multiple hopping events. We argue that this instability of FSSH going backward in time can be correlated with the stability of the FSSH algorithm going forward in time.
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Affiliation(s)
- Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania , Philadelphia, Pennsylvania 19104, United States
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26
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White AJ, Gorshkov VN, Wang R, Tretiak S, Mozyrsky D. Semiclassical Monte Carlo: A first principles approach to non-adiabatic molecular dynamics. J Chem Phys 2014; 141:184101. [DOI: 10.1063/1.4900988] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Affiliation(s)
- Alexander J. White
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Nonlinear Studies (CNLS), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Vyacheslav N. Gorshkov
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- National Technical University of Ukraine, Kiev 03056, Ukraine
| | - Ruixi Wang
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Department of Chemistry, Wayne State University, 5101 Cass Avenue, Detroit, Michigan 48202, USA
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Nonlinear Studies (CNLS), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Integrated Nanotechnologies (CINT), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Dmitry Mozyrsky
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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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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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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29
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DOLTSINIS NIKOSL, MARX DOMINIK. FIRST PRINCIPLES MOLECULAR DYNAMICS INVOLVING EXCITED STATES AND NONADIABATIC TRANSITIONS. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2012. [DOI: 10.1142/s0219633602000257] [Citation(s) in RCA: 126] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Extensions of traditional molecular dynamics to excited electronic states and non-Born–Oppenheimer dynamics are reviewed focusing on applicability to chemical reactions of large molecules, possibly in condensed phases. The latter imposes restrictions on both the level of accuracy of the underlying electronic structure theory and the treatment of nonadiabaticity. This review, therefore, exclusively deals with ab initio "on the fly" molecular dynamics methods. For the same reason, mainly mixed quantum-classical approaches to nonadiabatic dynamics are considered.
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Affiliation(s)
- NIKOS L. DOLTSINIS
- Lehrstuhl für Theoretische Chemie, Ruhr–Universität Bochum, 44780 Bochum, Germany
| | - DOMINIK MARX
- Lehrstuhl für Theoretische Chemie, Ruhr–Universität Bochum, 44780 Bochum, Germany
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30
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Landry BR, Subotnik JE. Communication: Standard surface hopping predicts incorrect scaling for Marcus’ golden-rule rate: The decoherence problem cannot be ignored. J Chem Phys 2011; 135:191101. [DOI: 10.1063/1.3663870] [Citation(s) in RCA: 93] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
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31
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Subotnik JE. Fewest-Switches Surface Hopping and Decoherence in Multiple Dimensions. J Phys Chem A 2011; 115:12083-96. [DOI: 10.1021/jp206557h] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
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32
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Fujii M. Quantum and semiclassical theories for nonadiabatic transitions based on overlap integrals related to fast degrees of freedom. J Chem Phys 2011; 135:114102. [PMID: 21950845 DOI: 10.1063/1.3634025] [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
Alternative treatments of quantum and semiclassical theories for nonadiabatic dynamics are presented. These treatments require no derivative couplings and instead are based on overlap integrals between eigenstates corresponding to fast degrees of freedom, such as electronic states. Derived from mathematical transformations of the Schrödinger equation, the theories describe nonlocal characteristics of nonadiabatic transitions. The idea that overlap integrals can be used for nonadiabatic transitions stems from an article by Johnson and Levine [Chem. Phys. Lett. 13, 168 (1972)]. Furthermore, overlap integrals in path-integral form have been recently made available by Schmidt and Tully [J. Chem. Phys. 127, 094103 (2007)] to analyze nonadiabatic effects in thermal equilibrium systems. The present paper expands this idea to dynamic problems presented in path-integral form that involve nonadiabatic semiclassical propagators. Applications to one-dimensional nonadiabatic transitions have provided excellent results, thereby verifying the procedure. In principle these theories that are presented can be applied to multidimensional systems, although numerical costs could be quite expensive.
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Affiliation(s)
- Mikiya Fujii
- Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, 153-8902, Tokyo, Japan.
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33
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Subotnik JE, Shenvi N. Decoherence and surface hopping: When can averaging over initial conditions help capture the effects of wave packet separation? J Chem Phys 2011; 134:244114. [DOI: 10.1063/1.3603448] [Citation(s) in RCA: 66] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
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34
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Subotnik JE, Shenvi N. A new approach to decoherence and momentum rescaling in the surface hopping algorithm. J Chem Phys 2011; 134:024105. [PMID: 21241078 DOI: 10.1063/1.3506779] [Citation(s) in RCA: 203] [Impact Index Per Article: 15.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
As originally proposed, the fewest switches surface hopping (FSSH) algorithm does not allow for decoherence between wavefunction amplitudes on different adiabatic surfaces. In this paper, we propose an inexpensive correction to standard FSSH dynamics wherein we explicitly model the decoherence of nuclear wave packets on distinct electronic surfaces. Our augmented fewest switches surface hopping approach is conceptually simple and, thus far, it has allowed us to capture several key features of the exact quantum results. Two points in particular merit attention. First, we obtain the correct branching ratios when a quantum particle passes through more than one region of nonadiabatic coupling. Second, our formalism provides a new and natural approach for rescaling nuclear momenta after a surface hop. Both of these features should become increasingly important as surface hopping schemes are applied to higher-dimensional problems.
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Affiliation(s)
- Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
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35
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Subotnik JE. Augmented Ehrenfest dynamics yields a rate for surface hopping. J Chem Phys 2010; 132:134112. [DOI: 10.1063/1.3314248] [Citation(s) in RCA: 58] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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Nonadiabatic Chemical Dynamics: Comprehension and Control of Dynamics, and Manifestation of Molecular Functions. ADVANCES IN CHEMICAL PHYSICS 2008. [DOI: 10.1002/9780470259474.ch3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register]
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37
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Ananth N, Venkataraman C, Miller WH. Semiclassical description of electronically nonadiabatic dynamics via the initial value representation. J Chem Phys 2007; 127:084114. [PMID: 17764236 DOI: 10.1063/1.2759932] [Citation(s) in RCA: 88] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The initial value representation (IVR) of semiclassical (SC) theory is used in conjunction with the Meyer-Miller/Stock-Thoss description of electronic degrees of freedom in order to treat electronically nonadiabatic processes. It is emphasized that the classical equations of motion for the nuclear and electronic degrees of freedom that emerge in this description are precisely the Ehrenfest equations of motion (the force on the nuclei is the force averaged over the electronic wave function) but that the trajectories given by these equations of motion do not have the usual shortcomings of the traditional Ehrenfest model when they are used within the SC-IVR framework. For example, in the traditional Ehrenfest model (a mixed quantum-classical approach) the nuclear motion emerges from a nonadiabatic encounter on an average potential energy surface (a weighted average according to the population in the various electronic states), while the SC-IVR describes the correct correlation between electronic and nuclear dynamics, i.e., the nuclear motion is on one potential energy surface or the other depending on the electronic state. Calculations using forward-backward versions of SC-IVR theory are presented to illustrate this behavior. An even more approximate version of the SC-IVR, the linearized approximation (LSC-IVR), is slightly better than the traditional Ehrenfest model, but since it cannot describe quantum coherence effects, the LSC-IVR is also not able to describe the correct correlation between nuclear and electronic dynamics.
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Affiliation(s)
- Nandini Ananth
- Department of Chemistry, University of California, Berkeley, California 94720-1460, USA
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38
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Fernandez-Ramos A, Miller JA, Klippenstein SJ, Truhlar DG. Modeling the kinetics of bimolecular reactions. Chem Rev 2007; 106:4518-84. [PMID: 17091928 DOI: 10.1021/cr050205w] [Citation(s) in RCA: 393] [Impact Index Per Article: 23.1] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Antonio Fernandez-Ramos
- Departamento de Quimica Fisica, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
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39
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Kondorskiy A, Nakamura H. Semiclassical theory of electronically nonadiabatic chemical dynamics: incorporation of the Zhu-Nakamura theory into the frozen Gaussian propagation method. J Chem Phys 2006; 120:8937-54. [PMID: 15267829 DOI: 10.1063/1.1687679] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The title theory is developed by combining the Herman-Kluk semiclassical theory for adiabatic propagation on single potential-energy surface and the semiclassical Zhu-Nakamura theory for nonadiabatic transition. The formulation with use of natural mathematical principles leads to a quite simple expression for the propagator based on classical trajectories and simple formulas are derived for overall adiabatic and nonadiabatic processes. The theory is applied to electronically nonadiabatic photodissociation processes: a one-dimensional problem of H2+ in a cw (continuous wave) laser field and a two-dimensional model problem of H2O in a cw laser field. The theory is found to work well for the propagation duration of several molecular vibrational periods and wide energy range. Although the formulation is made for the case of laser induced nonadiabatic processes, it is straightforwardly applicable to ordinary electronically nonadiabatic chemical dynamics.
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Affiliation(s)
- A Kondorskiy
- Department of Theoretical Studies, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan
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40
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Oloyede P, Mil'nikov G, Nakamura H. Generalized trajectory surface hopping method based on the Zhu-Nakamura theory. J Chem Phys 2006; 124:144110. [PMID: 16626183 DOI: 10.1063/1.2187978] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
We present a generalized formulation of the trajectory surface hopping method applicable to a general multidimensional system. The method is based on the Zhu-Nakamura theory of a nonadiabatic transition and therefore includes the treatment of classically forbidden hops. The method uses a generalized recipe for the conservation of angular momentum after forbidden hops and an approximation for determining a nonadiabatic transition direction which is crucial when the coupling vector is unavailable. This method also eliminates the need for a rigorous location of the seam surface, thereby ensuring its applicability to a wide class of chemical systems. In a test calculation, we implement the method for the DH(2) (+) system, and it shows a remarkable agreement with the previous results of C. Zhu, H. Kamisaka, and H. Nakamura, [J. Chem. Phys. 116, 3234 (2002)]. We then apply it to a diatomic-in-molecule model system with a conical intersection, and the results compare well with exact quantum calculations. The successful application to the conical intersection system confirms the possibility of directly extending the present method to an arbitrary potential of general topology.
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Affiliation(s)
- Ponmile Oloyede
- Department of Functional Molecular Science, The Graduate University for Advanced Studies, Myodaiji, Okazaki 444-8585, Japan
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41
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Nangia S, Jasper AW, Miller TF, Truhlar DG. Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method. J Chem Phys 2006; 120:3586-97. [PMID: 15268520 DOI: 10.1063/1.1641019] [Citation(s) in RCA: 64] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The most widely used algorithm for Monte Carlo sampling of electronic transitions in trajectory surface hopping (TSH) calculations is the so-called anteater algorithm, which is inefficient for sampling low-probability nonadiabatic events. We present a new sampling scheme (called the army ants algorithm) for carrying out TSH calculations that is applicable to systems with any strength of coupling. The army ants algorithm is a form of rare event sampling whose efficiency is controlled by an input parameter. By choosing a suitable value of the input parameter the army ants algorithm can be reduced to the anteater algorithm (which is efficient for strongly coupled cases), and by optimizing the parameter the army ants algorithm may be efficiently applied to systems with low-probability events. To demonstrate the efficiency of the army ants algorithm, we performed atom-diatom scattering calculations on a model system involving weakly coupled electronic states. Fully converged quantum mechanical calculations were performed, and the probabilities for nonadiabatic reaction and nonreactive deexcitation (quenching) were found to be on the order of 10(-8). For such low-probability events the anteater sampling scheme requires a large number of trajectories ( approximately 10(10)) to obtain good statistics and converged semiclassical results. In contrast by using the new army ants algorithm converged results were obtained by running 10(5) trajectories. Furthermore, the results were found to be in excellent agreement with the quantum mechanical results. Sampling errors were estimated using the bootstrap method, which is validated for use with the army ants algorithm.
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Affiliation(s)
- Shikha Nangia
- Department of Chemistry, University of Minnesota, Minneapolis 55455-0431, USA.
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43
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Jones GA, Paddon-Row MN, Carpenter BK, Piotrowiak P. Symmetry-Forbidden vs Symmetry-Allowed Electron and Hole Transfer in Medium Sized Intramolecular Organic Donor−Acceptor Radical Ions. A Trajectory Surface Hopping Study. J Phys Chem A 2002. [DOI: 10.1021/jp0255839] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Affiliation(s)
- Garth A. Jones
- School of Chemistry, University of New South Wales, Sydney 2052, Australia
| | | | - Barry K. Carpenter
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853-1301
| | - Piotr Piotrowiak
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102
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44
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Jasper AW, Stechmann SN, Truhlar DG. Fewest-switches with time uncertainty: A modified trajectory surface-hopping algorithm with better accuracy for classically forbidden electronic transitions. J Chem Phys 2002. [DOI: 10.1063/1.1453404] [Citation(s) in RCA: 131] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
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45
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Zhu C, Kamisaka H, Nakamura H. New implementation of the trajectory surface hopping method with use of the Zhu–Nakamura theory. II. Application to the charge transfer processes in the 3D DH2+ system. J Chem Phys 2002. [DOI: 10.1063/1.1446032] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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46
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47
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Kamisaka H, Bian W, Nobusada K, Nakamura H. Accurate quantum dynamics of electronically nonadiabatic chemical reactions in the DH2+ system. J Chem Phys 2002. [DOI: 10.1063/1.1418252] [Citation(s) in RCA: 75] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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48
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Jasper AW, Hack MD, Chakraborty A, Truhlar DG, Piecuch P. Photodissociation of LiFH and NaFH van der Waals complexes: A semiclassical trajectory study. J Chem Phys 2001. [DOI: 10.1063/1.1407278] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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49
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Jasper AW, Hack MD, Truhlar DG. The treatment of classically forbidden electronic transitions in semiclassical trajectory surface hopping calculations. J Chem Phys 2001. [DOI: 10.1063/1.1377891] [Citation(s) in RCA: 83] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
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50
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Hack MD, Truhlar DG. A natural decay of mixing algorithm for non-Born–Oppenheimer trajectories. J Chem Phys 2001. [DOI: 10.1063/1.1368388] [Citation(s) in RCA: 83] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
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