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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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2
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Karmakar S, Thakur S, Jain A. Can classical mechanics sense conical intersection? J Chem Phys 2024; 160:124110. [PMID: 38526110 DOI: 10.1063/5.0197381] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2024] [Accepted: 03/05/2024] [Indexed: 03/26/2024] Open
Abstract
Conical intersection (CI) leads to fast electronic energy transfer. However, Hamm and Stock [Phys. Rev. Lett. 109, 173201 (2012)] showed the existence of a vibrational CI and its role in vibrational energy relaxation. In this paper, we further investigate the vibrational energy relaxation using an isolated model Hamiltonian system of four vibrational modes with two distinctively different timescales (two fast modes and two slow modes). We show that the excitation of the slow modes plays a crucial role in the energy relaxation mechanism. We also analyze the system from a mixed quantum-classical (surface hopping method) and a completely classical point of view. Notably, surface hopping and even classical simulations also capture fast energy relaxation, which is a signature of CI's existence.
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Affiliation(s)
- Sourav Karmakar
- Department of Chemistry, Indian Institute of Technology Bombay, Bombay, India
| | - Saumya Thakur
- Department of Chemistry, Indian Institute of Technology Bombay, Bombay, India
| | - Amber Jain
- Department of Chemistry, Indian Institute of Technology Bombay, Bombay, India
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3
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Zhao X, Merritt ICD, Lei R, Shu Y, Jacquemin D, Zhang L, Xu X, Vacher M, Truhlar DG. Nonadiabatic Coupling in Trajectory Surface Hopping: Accurate Time Derivative Couplings by the Curvature-Driven Approximation. J Chem Theory Comput 2023; 19:6577-6588. [PMID: 37772732 DOI: 10.1021/acs.jctc.3c00813] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/30/2023]
Abstract
Trajectory surface hopping (TSH) is a widely used mixed quantum-classical dynamics method that is used to simulate molecular dynamics with multiple electronic states. In TSH, time-derivative coupling is employed to propagate the electronic coefficients and in that way to determine when the electronic state on which the nuclear trajectory is propagated switches. In this work, we discuss nonadiabatic TSH dynamics algorithms employing the curvature-driven approximation and overlap-based time derivative couplings, and we report test calculations on six photochemical reactions where we compare the results to one another and to calculations employing analytic nonadiabatic coupling vectors. We correct previous published results thanks to a bug found in the software. We also provide additional, more detailed studies of the time-derivative couplings. Our results show good agreement between curvature-driven algorithms and overlap-based algorithms.
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Affiliation(s)
- Xiaorui Zhao
- Center for Combustion Energy, Tsinghua University, Beijing 100084, P. R. China
- School of Aerospace Engineering, Tsinghua University, Beijing 100084, P. R. China
| | | | - Ruiqing Lei
- Center for Combustion Energy, Tsinghua University, Beijing 100084, P. R. China
| | - Yinan Shu
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, Nantes F-44000, France
- Institut Universitaire de France (IUF), Paris 75005, France
| | - Linyao Zhang
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, P. R. China
| | - Xuefei Xu
- Center for Combustion Energy, Tsinghua University, Beijing 100084, P. R. China
- Department of Energy and Power Engineering, and Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Tsinghua University, Beijing 100084, P. R. China
| | - Morgane Vacher
- Nantes Université, CNRS, CEISAM UMR 6230, Nantes F-44000, France
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, 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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Shu Y, Zhang L, Chen X, Sun S, Huang Y, Truhlar DG. Nonadiabatic Dynamics Algorithms with Only Potential Energies and Gradients: Curvature-Driven Coherent Switching with Decay of Mixing and Curvature-Driven Trajectory Surface Hopping. J Chem Theory Comput 2022; 18:1320-1328. [PMID: 35104136 DOI: 10.1021/acs.jctc.1c01080] [Citation(s) in RCA: 23] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Direct dynamics by mixed quantum-classical nonadiabatic methods is an important tool for understanding processes involving multiple electronic states. Very often, the computational bottleneck of such direct simulation comes from electronic structure theory. For example, at every time step of a trajectory, nonadiabatic dynamics requires potential energy surfaces, their gradients, and the matrix elements coupling the surfaces. The need for the couplings can be alleviated by employing the time derivatives of the wave functions, which can be evaluated from overlaps of electronic wave functions at successive time steps. However, evaluation of overlap integrals is still expensive for large systems. In addition, for electronic structure methods for which the wave functions or the coupling matrix elements are not available, nonadiabatic dynamics algorithms become inapplicable. In this work, building on recent work by Baeck and An, we propose new nonadiabatic dynamics algorithms that only require adiabatic potential energies and their gradients. The new methods are named curvature-driven coherent switching with decay of mixing (κCSDM) and curvature-driven trajectory surface hopping (κTSH). We show how powerful these new methods are in terms of computation time and accuracy as compared to previous mixed quantum-classical nonadiabatic dynamics algorithms. The lowering of the computational cost will allow longer nonadiabatic trajectories and greater ensemble averaging to be affordable, and the ability to calculate the dynamics without electronic structure coupling matrix elements extends the dynamics capability to new classes of electronic structure methods.
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Affiliation(s)
- Yinan Shu
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA
| | - Linyao Zhang
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, P. R. China.,School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150001, P. R. China
| | - Xiye Chen
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, P. R. China.,School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150001, P. R. China
| | - Shaozeng Sun
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, P. R. China
| | - Yudong Huang
- School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150001, P. R. China
| | - Donald G Truhlar
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA
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6
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Shu Y, Zhang L, Mai S, Sun S, González L, Truhlar DG. Implementation of Coherent Switching with Decay of Mixing into the SHARC Program. J Chem Theory Comput 2020; 16:3464-3475. [DOI: 10.1021/acs.jctc.0c00112] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Yinan Shu
- Department of Chemistry and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Linyao Zhang
- Department of Chemistry and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, People’s Republic of China
| | - Sebastian Mai
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Str. 17, 1090, Vienna, Austria
| | - Shaozeng Sun
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, People’s Republic of China
| | - Leticia González
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Str. 17, 1090, Vienna, Austria
| | - Donald G. Truhlar
- Department of Chemistry and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
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7
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Shu Y, Zhang L, Varga Z, Parker KA, Kanchanakungwankul S, Sun S, Truhlar DG. Conservation of Angular Momentum in Direct Nonadiabatic Dynamics. J Phys Chem Lett 2020; 11:1135-1140. [PMID: 31958368 DOI: 10.1021/acs.jpclett.9b03749] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Direct nonadiabatic dynamics is used to study processes involving multiple electronic states from small molecules to materials. Compared with dynamics with fitted analytical potential energy surfaces, direct dynamics is more user-friendly in that it obtains all needed energies, gradients, and nonadiabatic couplings (NACs) by electronic structure calculations. However, the NAC that is usually used does not conserve angular momentum or the center of mass in widely used mixed quantum-classical nonadiabatic dynamics algorithms, in particular, trajectory surface hopping, semiclassical Ehrenfest, and coherent switching with decay of mixing. We show that by using a projection operator to remove the translational and rotational components of the originally computed NAC, one can restore the conservation.
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Affiliation(s)
- Yinan Shu
- Department of Chemistry and Supercomputing Institute , University of Minnesota , Minneapolis , Minnesota 55455-0431 , United States
| | - Linyao Zhang
- Department of Chemistry and Supercomputing Institute , University of Minnesota , Minneapolis , Minnesota 55455-0431 , United States
- School of Energy Science and Engineering , Harbin Institute of Technology , Harbin 150001 , P. R. China
| | - Zoltán Varga
- Department of Chemistry and Supercomputing Institute , University of Minnesota , Minneapolis , Minnesota 55455-0431 , United States
| | - Kelsey A Parker
- Department of Chemistry and Supercomputing Institute , University of Minnesota , Minneapolis , Minnesota 55455-0431 , United States
| | - Siriluk Kanchanakungwankul
- Department of Chemistry and Supercomputing Institute , University of Minnesota , Minneapolis , Minnesota 55455-0431 , United States
| | - Shaozeng Sun
- School of Energy Science and Engineering , Harbin Institute of Technology , Harbin 150001 , P. R. China
| | - Donald G Truhlar
- Department of Chemistry and Supercomputing Institute , University of Minnesota , Minneapolis , Minnesota 55455-0431 , United States
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8
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Abstract
Multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory is a rigorous and powerful method to simulate quantum dynamics in complex many-body systems. This approach extends the original MCTDH theory of Meyer, Manthe, and Cederbaum to include dynamically contracted layers in a recursive way, within which the equations of motion are determined from the Dirac-Frenkel variational principle. This paper presents the general derivation of the theory and analyzes the important features that make the ML-MCTDH method numerically efficient. Furthermore, we discuss the generalization of the theory to treat many-body identical particles (fermions or bosons) as well as calculating energy eigenstates via the improved relaxation method.
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Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, United States
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9
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de Andrés J, Lucas JM, Albertí M, Bofill JM, Belyaev A, Aguilar A. Crossed molecular beams study of inelastic non-adiabatic processes in gas phase collisions between sodium ions and ZnBr 2 molecules in the 0.10–3.50 keV energy range. J Chem Phys 2012; 137:154202. [DOI: 10.1063/1.4757967] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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10
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Khait YG, Theis D, Hoffmann MR. Nonadiabatic coupling terms for the GVVPT2 variant of multireference perturbation theory. Chem Phys 2012. [DOI: 10.1016/j.chemphys.2011.09.014] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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11
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Jambrina PG, Aoiz FJ, Eyles CJ, Herrero VJ, Sáez Rábanos V. Cumulative reaction probabilities and transition state properties: a study of the H+ + H2 and H+ + D2 proton exchange reactions. J Chem Phys 2009; 130:184303. [PMID: 19449917 DOI: 10.1063/1.3129343] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
Cumulative reaction probabilities (CRPs) have been calculated by accurate (converged, close coupling) quantum mechanical (QM), quasiclassical trajectory (QCT), and statistical QCT (SQCT) methods for the H(+) + H(2) and H(+) + D(2) reactions at collision energies up to 1.2 eV and total angular momentum J = 0-4. A marked resonance structure is found in the QM CRP, most especially for the H(3)(+) system and J = 0. When the CRPs are resolved in their ortho and para contributions, a clear steplike structure is found associated with the opening of internal states of reactants and products. The comparison of the QCT results with those of the other methods evinces the occurrence of two transition states, one at the entrance and one at the exit. At low J values, except for the quantal resonance structure and the lack of quantization in the product channel, the agreement between QM and QCT is very good. The SQCT model, that reflects the steplike structure associated with the opening of initial and final states accurately, clearly tends to overestimate the value of the CRP as the collision energy increases. This effect seems more marked for the H(+) + D(2) isotopic variant. For sufficiently high J values, the growth of the centrifugal barrier leads to an increase in the threshold of the CRP. At these high J values the discrepancy between SQCT and QCT becomes larger and is magnified with growing collision energy. The total CRPs calculated with the QCT and SQCT methods allowed the determination of the rate constant for the H(+) + D(2) reaction. It was found that the rate, in agreement with experiment, decreases with temperature as expected for an endothermic reaction. In the range of temperatures between 200 and 500 K the differences between SQCT and QCT rate results are relatively minor. Although exact QM calculations are formidable for an exact determination of the k(T), it can be reliably expected that their value will lie between those given by the dynamical and statistical trajectory methods.
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Affiliation(s)
- P G Jambrina
- Departamento de Química Física, Universidad de Salamanca, 37008 Salamanca, Spain
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12
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Fink RF, Piancastelli MN, Grum-Grzhimailo AN, Ueda K. Angular distribution of Auger electrons from fixed-in-space and rotating C 1s-->2pi photoexcited CO: theory. J Chem Phys 2009; 130:014306. [PMID: 19140614 DOI: 10.1063/1.3042153] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The one-center approach for molecular Auger decay is applied to predict the angular distribution of Auger electrons from rotating and fixed-in-space molecules. For that purpose, phase shifts between the Auger decay amplitudes have been incorporated in the atomic model. The approach is applied to the resonant Auger decay of the photoexcited C 1s-->2pi resonance in carbon monoxide. It is discussed how the symmetry of the final ionic state is related to features in the angular distributions and a parametrization for the molecular frame Auger electron angular distribution is suggested. The angular distribution of Auger electrons after partial orientation of the molecule by the sigma-->pi-excitation process is also calculated and compared to available experimental and theoretical data. The results of the one-center approach are at least of the same quality as the available theoretical data even though the latter stem from a much more sophisticated method. As the one-center approximation can be applied with low computational demand even to extended systems, the present approach opens a way to describe the angular distribution of Auger electrons in a wide variety of applications.
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Affiliation(s)
- R F Fink
- Institute of Organic Chemistry, University of Würzburg, D-97074 Würzburg, Germany.
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13
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Decoherence in Combined Quantum Mechanical and Classical Mechanical Methods for Dynamics as Illustrated for Non-Born–Oppenheimer Trajectories. QUANTUM DYNAMICS OF COMPLEX MOLECULAR SYSTEMS 2007. [DOI: 10.1007/978-3-540-34460-5_9] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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14
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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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15
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Zhu C, Jasper AW, Truhlar DG. Non-Born-Oppenheimer trajectories with self-consistent decay of mixing. J Chem Phys 2006; 120:5543-57. [PMID: 15267430 DOI: 10.1063/1.1648306] [Citation(s) in RCA: 132] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
A semiclassical trajectory method, called the self-consistent decay of mixing (SCDM) method, is presented for the treatment of electronically nonadiabatic dynamics. The SCDM method is a modification of the semiclassical Ehrenfest (SE) method (also called the semiclassical time-dependent self-consistent-field method) that solves the problem of unphysical mixed final states by including decay-of-mixing terms in the equations for the evolution of the electronic state populations. These terms generate a force, called the decoherent force (or dephasing force), that drives the electronic component of each trajectory toward a pure state. Results for several mixed quantum-classical methods, in particular the SCDM, SE, and natural-decay-of-mixing methods and several trajectory surface hopping methods, are compared to the results of accurate quantum mechanical calculations for 12 cases involving five different fully dimensional triatomic model systems. The SCDM method is found to be the most accurate of the methods tested. The method should be useful for the simulation of photochemical reactions.
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Affiliation(s)
- Chaoyuan Zhu
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA
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16
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Li J, Woywod C, Vallet V, Meier C. Investigation of the dynamics of two coupled oscillators with mixed quantum-classical methods. J Chem Phys 2006; 124:184105. [PMID: 16709095 DOI: 10.1063/1.2196408] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The dynamics of two coupled oscillators can become quite complex if anharmonic potential energy functions are employed. This type of system therefore represents a good model for an investigation of the performance of mixed quantum-classical methods. In this work, the motion of two coupled particles with a mass ratio of one to ten is studied with three different mixed quantum-classical methods in the presence of anharmonic potential terms for a comparison with exact quantum mechanical calculations. The mixed quantum-classical approaches include the multitrajectory Ehrenfest, the mixed quantum-classical Bohmian (MQCB), and the so-called coupled Schrödinger equations (CSE) formalisms. The analysis shows that while the description of a weakly anharmonic system by the Ehrenfest and MQCB schemes is accurate if proper sampling techniques are applied, both approximations break down rapidly if the anharmonic terms are increased. The performance of the simple CSE prescription, which corresponds to a reduction of the full two-dimensional wave function to two one-dimensional wave functions representing two quantum oscillators coupled via the potential energy in a classical fashion, decreases if the width of the initial wave packet is enlarged. The dependence of the CSE method on the diffuseness of the initial wave packet is therefore opposite to that of the MQCB method, which is more accurate for wide wave packets. Overall, the multitrajectory Ehrenfest ansatz is found to be most successful in reproducing the exact quantum results.
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Affiliation(s)
- Jingrui Li
- Theoretical Chemistry, Department of Chemistry, Technical University Munich, D-85747 Garching, Germany.
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17
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Jasper AW, Truhlar DG. Conical intersections and semiclassical trajectories: Comparison to accurate quantum dynamics and analyses of the trajectories. J Chem Phys 2005; 122:44101. [PMID: 15740229 DOI: 10.1063/1.1829031] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Semiclassical trajectory methods are tested for electronically nonadiabatic systems with conical intersections. Five triatomic model systems are presented, and each system features two electronic states that intersect via a seam of conical intersections (CIs). Fully converged, full-dimensional quantum mechanical scattering calculations are carried out for all five systems at energies that allow for electronic de-excitation via the seam of CIs. Several semiclassical trajectory methods are tested against the accurate quantum mechanical results. For four of the five model systems, the diabatic representation is the preferred (most accurate) representation for semiclassical trajectories, as correctly predicted by the Calaveras County criterion. Four surface hopping methods are tested and have overall relative errors of 40%-60%. The semiclassical Ehrenfest method has an overall error of 66%, and the self-consistent decay of mixing (SCDM) and coherent switches with decay of mixing (CSDM) methods are the most accurate methods overall with relative errors of approximately 32%. Furthermore, the CSDM method is less representation dependent than both the SCDM and the surface hopping methods, making it the preferred semiclassical trajectory method. Finally, the behavior of semiclassical trajectories near conical intersections is discussed.
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Affiliation(s)
- Ahren W Jasper
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, MN 55455-0431, USA
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18
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Thoss M, Wang H. SEMICLASSICAL DESCRIPTION OF MOLECULAR DYNAMICS BASED ON INITIAL-VALUE REPRESENTATION METHODS. Annu Rev Phys Chem 2004; 55:299-332. [PMID: 15117255 DOI: 10.1146/annurev.physchem.55.091602.094429] [Citation(s) in RCA: 137] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Recent progress in the development of semiclassical methods to describe quantum effects in molecular dynamics is reviewed. Focusing on rigorous semiclassical methods that are based on the initial-value representation of the semiclassical propagator, we discuss several promising schemes that have been developed in the past few years to extend the applicability of semiclassical approaches to complex molecular systems. In particular, integral-filtering techniques and forward-backward methods are surveyed. Furthermore, recently proposed approaches that allow the semiclassical description of nonadiabatic molecular dynamics are discussed. The potential and efficiency of these methods is illustrated by selected applications.
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Affiliation(s)
- Michael Thoss
- Theoretische Chemie, Technische Universitat Munchen, D-85747 Garching, Germany.
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19
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Abstract
To predict the branching between energetically allowed product channels, chemists often rely on statistical transition state theories or exact quantum scattering calculations on a single adiabatic potential energy surface. The potential energy surface gives the energetic barriers to each chemical reaction and allows prediction of the reaction rates. Yet, chemical reactions evolve on a single potential energy surface only if, in simple terms, the electronic wavefunction can evolve from the reactant electronic configuration to the product electronic configuration on a time scale that is fast compared to the nuclear dynamics through the transition state. The experiments reviewed here investigate how the breakdown of the Born-Oppenheimer approximation at a barrier along an adiabatic reaction coordinate can alter the dynamics of and the expected branching between molecular dissociation pathways. The work reviewed focuses on three questions that have come to the forefront with recent theory and experiments: Which classes of chemical reactions evidence dramatic nonadiabatic behavior that influences the branching between energetically allowed reaction pathways? How do the intramolecular distance and orientation between the electronic orbitals involved influence the nonadiabaticity in the reaction? How can the detailed nuclear dynamics mediate the effective nonadiabatic coupling encountered in a chemical reaction?
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Affiliation(s)
- L J Butler
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
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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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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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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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Zhu C, Nobusada K, Nakamura H. New implementation of the trajectory surface hopping method with use of the Zhu–Nakamura theory. J Chem Phys 2001. [DOI: 10.1063/1.1386811] [Citation(s) in RCA: 73] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
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Wang H, Thoss M, Miller WH. Systematic convergence in the dynamical hybrid approach for complex systems: A numerically exact methodology. J Chem Phys 2001. [DOI: 10.1063/1.1385561] [Citation(s) in RCA: 152] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Thoss M, Wang H, Miller WH. Self-consistent hybrid approach for complex systems: Application to the spin-boson model with Debye spectral density. J Chem Phys 2001. [DOI: 10.1063/1.1385562] [Citation(s) in RCA: 209] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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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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Hack MD, Wensmann AM, Truhlar DG, Ben-Nun M, Martı́nez TJ. Comparison of full multiple spawning, trajectory surface hopping, and converged quantum mechanics for electronically nonadiabatic dynamics. J Chem Phys 2001. [DOI: 10.1063/1.1377030] [Citation(s) in RCA: 126] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
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Hack MD, Truhlar DG. Electronically nonadiabatic trajectories: Continuous surface switching II. J Chem Phys 2001. [DOI: 10.1063/1.1342224] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
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Kaledin AL, Heaven MC, Morokuma K. Theoretical prediction of the rate constant for I+O[sub 2](a [sup 1]Δ[sub g]) electronic energy transfer: A surface-hopping trajectory study. J Chem Phys 2001. [DOI: 10.1063/1.1330205] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Topaler MS, Hack MD, Allison TC, Liu YP, Mielke SL, Schwenke DW, Truhlar DG. Validation of trajectory surface hopping methods against accurate quantum mechanical dynamics and semiclassical analysis of electronic-to-vibrational energy transfer. J Chem Phys 1997. [DOI: 10.1063/1.473931] [Citation(s) in RCA: 59] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
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Errea LF, Gorfinkiel JD, Kryachko ES, Macı́as A, Méndez L, Riera A. Ab initiopotential energy surfaces and nonadiabatic couplings involved in Be4++H2electron rearrangement. J Chem Phys 1997. [DOI: 10.1063/1.473033] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kassner C, Stuhl F, Luo M, Lehner M, Fink R, Jungen M. On the vacuum ultraviolet radical photolysis CH2(1 3B1)+hν→CH(A 2Δ)+H(1 2S): A combined experimental and theoretical investigation. J Chem Phys 1996. [DOI: 10.1063/1.472303] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Tawa GJ, Mielke SL, Truhlar DG, Schwenke DW. Algebraic variational and propagation formalisms for quantal dynamics calculations of electronic‐to‐vibrational, rotational energy transfer and application to the quenching of the 3pstate of sodium by hydrogen molecules. J Chem Phys 1994. [DOI: 10.1063/1.467140] [Citation(s) in RCA: 56] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
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Dong K, Gislason EA, Sizun M. A trajectory surface-hopping study of chemical reaction and collision-induced dissociation in the HD++He system. Chem Phys 1994. [DOI: 10.1016/0301-0104(93)e0374-5] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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