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Nelson TR, White AJ, Bjorgaard JA, Sifain AE, Zhang Y, Nebgen B, Fernandez-Alberti S, Mozyrsky D, Roitberg AE, Tretiak S. Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials. Chem Rev 2020; 120:2215-2287. [PMID: 32040312 DOI: 10.1021/acs.chemrev.9b00447] [Citation(s) in RCA: 198] [Impact Index Per Article: 49.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.
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Affiliation(s)
- Tammie R Nelson
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
| | - Alexander J White
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
| | - Josiah A Bjorgaard
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
| | - Andrew E Sifain
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States.,U.S. Army Research Laboratory , Aberdeen Proving Ground , Maryland 21005 , United States
| | - Yu Zhang
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
| | - Benjamin Nebgen
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
| | | | - Dmitry Mozyrsky
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
| | - Adrian E Roitberg
- Department of Chemistry , University of Florida , Gainesville , Florida 32611 , United States
| | - Sergei Tretiak
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
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Carof A, Giannini S, Blumberger J. Detailed balance, internal consistency, and energy conservation in fragment orbital-based surface hopping. J Chem Phys 2018; 147:214113. [PMID: 29221382 DOI: 10.1063/1.5003820] [Citation(s) in RCA: 41] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
We have recently introduced an efficient semi-empirical non-adiabatic molecular dynamics method for the simulation of charge transfer/transport in molecules and molecular materials, denoted fragment orbital-based surface hopping (FOB-SH) [J. Spencer et al., J. Chem. Phys. 145, 064102 (2016)]. In this method, the charge carrier wavefunction is expanded in a set of charge localized, diabatic electronic states and propagated in the time-dependent potential due to classical nuclear motion. Here we derive and implement an exact expression for the non-adiabatic coupling vectors between the adiabatic electronic states in terms of nuclear gradients of the diabatic electronic states. With the non-adiabatic coupling vectors (NACVs) available, we investigate how different flavours of fewest switches surface hopping affect detailed balance, internal consistency, and total energy conservation for electron hole transfer in a molecular dimer with two electronic states. We find that FOB-SH satisfies detailed balance across a wide range of diabatic electronic coupling strengths provided that the velocities are adjusted along the direction of the NACV to satisfy total energy conservation upon a surface hop. This criterion produces the right fraction of energy-forbidden (frustrated) hops, which is essential for correct population of excited states, especially when diabatic couplings are on the order of the thermal energy or larger, as in organic semiconductors and DNA. Furthermore, we find that FOB-SH is internally consistent, that is, the electronic surface population matches the average quantum amplitudes, but only in the limit of small diabatic couplings. For large diabatic couplings, inconsistencies are observed as the decrease in excited state population due to frustrated hops is not matched by a corresponding decrease in quantum amplitudes. The derivation provided here for the NACV should be generally applicable to any electronic structure approach where the electronic Hamiltonian is constructed in a diabatic electronic state basis.
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Affiliation(s)
- Antoine Carof
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Samuele Giannini
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Jochen Blumberger
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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Church MS, Hele TJH, Ezra GS, Ananth N. Nonadiabatic semiclassical dynamics in the mixed quantum-classical initial value representation. J Chem Phys 2018; 148:102326. [DOI: 10.1063/1.5005557] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Matthew S. Church
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Timothy J. H. Hele
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Gregory S. Ezra
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Nandini Ananth
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
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Lu J, Zhou Z. Improved sampling and validation of frozen Gaussian approximation with surface hopping algorithm for nonadiabatic dynamics. J Chem Phys 2016; 145:124109. [DOI: 10.1063/1.4963107] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jianfeng Lu
- Department of Mathematics, Duke University, Box 90320, Durham, North Carolina 27708, USA
- Department of Physics and Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Zhennan Zhou
- Department of Mathematics, Duke University, Box 90320, Durham, North Carolina 27708, USA
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Kondorskiy AD, Nanbu S. Electronically nonadiabatic wave packet propagation using frozen Gaussian scattering. J Chem Phys 2015; 143:114103. [DOI: 10.1063/1.4930923] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alexey D. Kondorskiy
- P. N. Lebedev Physical Institute of the Russian Academy of Sciences, 53, Leninsky Prospekt, Moscow 119991, Russia
| | - Shinkoh Nanbu
- Department of Materials and Life Sciences, Faculty of Science and Technology, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan
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Herman MF. Improving the efficiency of Monte Carlo surface hopping calculations. J Phys Chem B 2014; 118:8026-33. [PMID: 24650188 DOI: 10.1021/jp501139s] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
A surface hopping method with a Monte Carlo procedure for deciding whether to hop at each step along the classical trajectories used in the semiclassical calculation is discussed. It is shown for a simple one-dimensional model problem that the numerical efficiency of the method can be improved by averaging over several copies of the sections of each trajectory that span the interaction regions. The use of Sobol sequences in the selection of the initial momentum for the trajectories is also explored. It is found that accurate results can be obtained with relatively small trajectory samples.
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Affiliation(s)
- Michael F Herman
- Department of Chemistry, Tulane University , New Orleans, Louisiana 70118, United States
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Herman MF. Analysis of a surface hopping expansion that includes hops in classically forbidden regions. Chem Phys 2014. [DOI: 10.1016/j.chemphys.2014.01.013] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Ananth N. Mapping variable ring polymer molecular dynamics: A path-integral based method for nonadiabatic processes. J Chem Phys 2013; 139:124102. [DOI: 10.1063/1.4821590] [Citation(s) in RCA: 102] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Dang PT, Herman MF. A justification for the use of approximate transition amplitudes in semiclassical surface hopping. Mol Phys 2011. [DOI: 10.1080/00268976.2011.575406] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Ananth N, Miller TF. Exact quantum statistics for electronically nonadiabatic systems using continuous path variables. J Chem Phys 2010; 133:234103. [DOI: 10.1063/1.3511700] [Citation(s) in RCA: 67] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
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Herman MF. The calculation of multidimensional semiclassical wave functions in the forbidden region using real valued coordinates. J Chem Phys 2010; 133:114108. [PMID: 20866127 DOI: 10.1063/1.3490087] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
A method that uses only real valued coordinates is presented for integrating the many dimensional semiclassical wave function into the forbidden region. The procedure first determines a surface of caustic points by running the set of trajectories that define the wave function in the allowed region. In the forbidden region, the momentum and the action integral are both complex functions of position, and their imaginary parts vanish on the caustic surface. The direction of the imaginary part of the momentum p(I) can be chosen to the perpendicular to the caustic surface at all points on that surface. Equations are derived for integrating the values of the real and imaginary parts of the momentum along the curves that follow the direction of p(I). The equations for the change in the action integral and the prefactor for the semiclassical wave function along these curves are also obtained, allowing for the determination of the semiclassical wave function in the forbidden region. Calculations are performed for a two dimensional problem, and the semiclassical wave function is found to be is excellent agreement with the results of exact quantum calculations.
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Affiliation(s)
- Michael F Herman
- Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, USA.
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Using semiclassical surface hopping for coupled partial wave calculations on systems with non-spherically symmetric potentials. Chem Phys 2010. [DOI: 10.1016/j.chemphys.2010.05.028] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Herman MF. A singularity free surface hopping expansion for the multistate wave function. J Chem Phys 2009; 131:214108. [PMID: 19968338 DOI: 10.1063/1.3268923] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A version of a surface hopping wave function for nonadiabatic multistate problems, which is free of turning point singularities, is derived and tested. The primitive semiclassical form of the particular surface hopping method considered has been shown to be highly accurate, even for classically forbidden processes. However, this semiclassical wave function displays the usual singular behavior at turning points and caustics in the classical motion. Numerical data has shown that this somewhat reduces its accuracy when the energy is near the crossing energy of the diabatic electronic surfaces. The singularity free version of this surface hopping wave function is derived by partitioning the x-axis into a large number of small steps for one dimensional problems. The adiabatic electronic energy surfaces are approximated to be linear functions within each step. The matching conditions required by the continuity of the wave function and its derivative at each step boundary provide the needed conditions to obtain the amplitudes for changes in electronic state and/or reflection of the trajectory for the motion of the nuclei. This leads to a form of the surface hopping wave function that is free of turning point singularities. The method is tested for a one dimensional model problem, and it is found to be highly accurate at all energies considered, even when the energy is near the crossing energy.
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Affiliation(s)
- Michael F Herman
- Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, USA.
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Liu J, Miller WH, Paesani F, Zhang W, Case DA. Quantum dynamical effects in liquid water: A semiclassical study on the diffusion and the infrared absorption spectrum. J Chem Phys 2009; 131:164509. [PMID: 19894958 DOI: 10.1063/1.3254372] [Citation(s) in RCA: 71] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jian Liu
- Department of Chemistry and K. S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720-1460, USA
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Shenvi N. Phase-space surface hopping: Nonadiabatic dynamics in a superadiabatic basis. J Chem Phys 2009; 130:124117. [DOI: 10.1063/1.3098321] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Dang PT, Herman MF. A semiclassical model for the calculation of nonadiabatic transition probabilities for classically forbidden transitions. J Chem Phys 2009; 130:054107. [PMID: 19206958 DOI: 10.1063/1.3066595] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
A semiclassical surface hopping model is presented for the calculation of nonadiabatic transition probabilities for the case in which the avoided crossing point is in the classically forbidden regions. The exact potentials and coupling are replaced with simple functional forms that are fitted to the values, evaluated at the turning point in the classical motion, of the Born-Oppenheimer potentials, the nonadiabatic coupling, and their first few derivatives. For the one-dimensional model considered, reasonably accurate results for transition probabilities are obtained down to around 10(-10). The possible extension of this model to many dimensional problems is discussed. The fact that the model requires only information at the turning point, a point that the trajectories encounter would be a significant advantage in many dimensional problems over Landau-Zener type models, which require information at the avoided crossing seam, which is in the forbidden region where the trajectories do not go.
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Affiliation(s)
- Phuong-Thanh Dang
- Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, USA
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Herman MF. Semiclassical nonadiabatic surface-hopping wave function expansion at low energies: hops in the forbidden region. J Phys Chem B 2008; 112:15966-72. [PMID: 19367994 DOI: 10.1021/jp804937q] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
The accuracy of a semiclassical surface-hopping expansion of the time-independent wave function for problems in which the nonadiabatic coupling is peaked in the classically forbidden regions is studied numerically for a one-dimensional curve-crossing problem. This surface-hopping expansion has recently been shown to satisfy the Schrodinger equation to all orders in h and all orders in the nonadiabatic coupling. It has also been found to provide very accurate transition probabilities for problems in which the crossing points of the diabatic energy surfaces are classically allowed. In the numerical study reported here, transition probabilities are evaluated for energies well below the crossing point energy. It is found that the expansion provides accurate results for transition probabilities as small as 10(-11).
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Affiliation(s)
- Michael F Herman
- Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, USA
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18
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Numerical studies concerning the efficiency of various techniques in time-independent surface hopping calculations. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2008.08.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Liu J, Miller WH. Linearized semiclassical initial value time correlation functions with maximum entropy analytic continuation. J Chem Phys 2008; 129:124111. [PMID: 19045010 DOI: 10.1063/1.2981065] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jian Liu
- Department of Chemistry and K. S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720-1460, USA
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Dunkel ER, Bonella S, Coker DF. Iterative linearized approach to nonadiabatic dynamics. J Chem Phys 2008; 129:114106. [DOI: 10.1063/1.2976441] [Citation(s) in RCA: 63] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Herman MF. Higher order phase corrected transition amplitudes for time dependent semiclassical surface hopping calculations. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2008.03.033] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Herman MF, Wu Y. An analysis through order ℏ2 of a surface hopping expansion of the nonadiabatic wave function. J Chem Phys 2008; 128:114105. [DOI: 10.1063/1.2837803] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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