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Sanz García J, Maskri R, Mitrushchenkov A, Joubert-Doriol L. Optimizing Conical Intersections without Explicit Use of Non-Adiabatic Couplings. J Chem Theory Comput 2024; 20:5643-5654. [PMID: 38888629 DOI: 10.1021/acs.jctc.4c00326] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/20/2024]
Abstract
We present two alternative methods for optimizing minimum energy conical intersection (MECI) molecular geometries without knowledge of the derivative coupling (DC). These methods are based on the utilization of Lagrange multipliers: (i) one method uses an approximate calculation of the DC, while the other (ii) do not require the DC. Both methods use the fact that information on the DC is contained in the Hessian of the squared energy difference. Tests done on a set of small molecular systems, in comparison with other methods, show the ability of the proposed methods to optimize MECIs. Finally, we apply the methods to the furimamide molecule, to optimize and characterize its S1/S2 MECI, and to optimizing the S0/S1 MECI of the silver trimer.
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Affiliation(s)
- Juan Sanz García
- Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS, UMR 8208, MSME, F-77454 Marne-la-Vallée, France
| | - Rosa Maskri
- Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS, UMR 8208, MSME, F-77454 Marne-la-Vallée, France
| | - Alexander Mitrushchenkov
- Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS, UMR 8208, MSME, F-77454 Marne-la-Vallée, France
| | - Loïc Joubert-Doriol
- Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS, UMR 8208, MSME, F-77454 Marne-la-Vallée, France
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2
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Xu J, Hao J, Bu C, Meng Y, Xiao H, Zhang M, Li C. XMECP: Reaching State-of-the-Art MECP Optimization in Multiscale Complex Systems. J Chem Theory Comput 2024; 20:3590-3600. [PMID: 38651739 DOI: 10.1021/acs.jctc.4c00033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
The Python-based program, XMECP, is developed for realizing robust, efficient, and state-of-the-art minimum energy crossing point (MECP) optimization in multiscale complex systems. This article introduces the basic capabilities of the XMECP program by theoretically investigating the MECP mechanism of several example systems including (1) the photosensitization mechanism of benzophenone, (2) photoinduced proton-coupled electron transfer in the cytosine-guanine base pair in DNA, (3) the spin-flip process in oxygen activation catalyzed by an iron-containing 2-oxoglutarate-dependent oxygenase (Fe/2OGX), and (4) the photochemical pathway of flavoprotein adjusted by the intensity of an external electric field. MECPs related to multistate reaction and multistate reactivity in large-scale complex biochemical systems can be well-treated by workflows suggested by the XMECP program. The branching plane updating the MECP optimization algorithm is strongly recommended as it provides derivative coupling vector (DCV) with explicit calculation and can equivalently evaluate contributions from non-QM residues to DCV, which can be nonadiabatic coupling or spin-orbit coupling in different cases. In the discussed QM/MM examples, we also found that the influence on the QM region by DCV can occur through noncovalent interactions and decay with distance. In the example of DNA base pairs, the nonadiabatic coupling occurs across the π-π stacking structure formed in the double-helix system. In contrast to general intuition, in the example of Fe/2OGX, the central ferrous and oxygen part contribute little to the spin-orbit coupling; however, a nearby arginine residue, which is treated by molecular mechanics in the QM/MM method, contributes significantly via two hydrogen bonds formed with α-ketoglutarate (α-KG). This indicates that the arginine residue plays a significant role in oxygen activation, driving the initial triplet state toward the productive quintet state, which is more than the previous knowledge that the arginine residue can bind α-KG at the reaction site by hydrogen bonds.
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Affiliation(s)
- Jiawei Xu
- State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, Fujian, P. R. China
- School of Chemical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China
| | - Jian Hao
- State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, Fujian, P. R. China
- School of Chemical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China
| | - Caijie Bu
- State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, Fujian, P. R. China
- College of Chemistry and Materials Science, Fujian Normal University, Fuzhou 350117, Fujian, P. R. China
| | - Yajie Meng
- State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, Fujian, P. R. China
- School of Chemical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China
| | - Han Xiao
- State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, Fujian, P. R. China
| | - Minyi Zhang
- State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, Fujian, P. R. China
| | - Chunsen Li
- State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, Fujian, P. R. China
- School of Chemical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Xiamen University, Xiamen 361005, Fujian, P. R. China
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Wang TY, Neville SP, Schuurman MS. Machine Learning Seams of Conical Intersection: A Characteristic Polynomial Approach. J Phys Chem Lett 2023; 14:7780-7786. [PMID: 37615964 PMCID: PMC10494228 DOI: 10.1021/acs.jpclett.3c01649] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 08/15/2023] [Indexed: 08/25/2023]
Abstract
The machine learning of potential energy surfaces (PESs) has undergone rapid progress in recent years. The vast majority of this work, however, has been focused on the learning of ground state PESs. To reliably extend machine learning protocols to excited state PESs, the occurrence of seams of conical intersections between adiabatic electronic states must be correctly accounted for. This introduces a serious problem, for at such points, the adiabatic potentials are not differentiable to any order, complicating the application of standard machine learning methods. We show that this issue may be overcome by instead learning the coordinate-dependent coefficients of the characteristic polynomial of a simple decomposition of the potential matrix. We demonstrate that, through this approach, quantitatively accurate machine learning models of seams of conical intersection may be constructed.
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Affiliation(s)
- Tzu Yu Wang
- Department
of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Simon P. Neville
- National
Research Council Canada, 100 Sussex Dr., Ottawa, Ontario K1A 0R6, Canada
| | - Michael S. Schuurman
- Department
of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
- National
Research Council Canada, 100 Sussex Dr., Ottawa, Ontario K1A 0R6, Canada
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4
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Zhao X, Shu Y, Zhang L, Xu X, Truhlar DG. Direct Nonadiabatic Dynamics of Ammonia with Curvature-Driven Coherent Switching with Decay of Mixing and with Fewest Switches with Time Uncertainty: An Illustration of Population Leaking in Trajectory Surface Hopping Due to Frustrated Hops. J Chem Theory Comput 2023; 19:1672-1685. [PMID: 36877830 DOI: 10.1021/acs.jctc.2c01260] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/08/2023]
Abstract
Mixed quantum-classical nonadiabatic dynamics is a widely used approach to simulate molecular dynamics involving multiple electronic states. There are two main categories of mixed quantum-classical nonadiabatic dynamics algorithms, namely, trajectory surface hopping (TSH) in which the trajectory propagates on a single potential energy surface, interrupted by hops, and self-consistent-potential (SCP) methods, such as semiclassical Ehrenfest, in which propagation occurs on a mean-field surface without hops. In this work, we will illustrate an example of severe population leaking in TSH. We emphasize that such leaking is a combined effect of frustrated hops and long-time simulations that drive the final excited-state population toward zero as a function of time. We further show that such leaking can be alleviated-but not eliminated-by the fewest switches with time uncertainty TSH algorithm (here implemented in the SHARC program); the time uncertainty algorithm slows down the leaking process by a factor of 4.1. The population leaking is not present in coherent switching with decay of mixing (CSDM), which is an SCP method with non-Markovian decoherence included. Another result in this paper is that we find very similar results with the original CSDM algorithm, with time-derivative CSDM (tCSDM), and with curvature-driven CSDM (κCSDM). Not only do we find good agreement for electronically nonadiabatic transition probabilities but also we find good agreement of the norms of the effective nonadiabatic couplings (NACs) that are derived from the curvature-driven time-derivative couplings as implemented in κCSDM with the time-dependent norms of the nonadiabatic coupling vectors computed by state-averaged complete-active-space self-consistent field theory.
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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
| | - Yinan Shu
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - 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
| | - Donald G Truhlar
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
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5
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Richardson JO. Machine learning of double-valued nonadiabatic coupling vectors around conical intersections. J Chem Phys 2023; 158:011102. [PMID: 36610946 DOI: 10.1063/5.0133191] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
In recent years, machine learning has had an enormous success in fitting ab initio potential-energy surfaces to enable efficient simulations of molecules in their ground electronic state. In order to extend this approach to excited-state dynamics, one must not only learn the potentials but also nonadiabatic coupling vectors (NACs). There is a particular difficulty in learning NACs in systems that exhibit conical intersections, as due to the geometric-phase effect, the NACs may be double-valued and are, thus, not suitable as training data for standard machine-learning techniques. In this work, we introduce a set of auxiliary single-valued functions from which the NACs can be reconstructed, thus enabling a reliable machine-learning approach.
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6
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Carpenter BK, Ellison GB, Nimlos MR, Scheer AM. A Conical Intersection Influences the Ground State Rearrangement of Fulvene to Benzene. J Phys Chem A 2022; 126:1429-1447. [PMID: 35191307 DOI: 10.1021/acs.jpca.2c00038] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The rearrangement of fulvene to benzene is believed to play an important role in the formation of soot during hydrocarbon combustion. Previous work has identified two possible mechanisms for the rearrangement─a unimolecular path and a hydrogen-atom-assisted, bimolecular path. Computational results to date have suggested that the unimolecular mechanism faces a barrier of about 74 kcal/mol, which makes it unable to compete with the bimolecular mechanism under typical combustion conditions. This computed barrier is about 10 kcal/mol higher than the experimental value, which is an unusually large discrepancy for modern electronic structure theory. In the present work, we have reinvestigated the unimolecular mechanism computationally, and we have found a second transition state that is approximately 10 kcal/mol lower in energy than the previously identified one and, therefore, in excellent agreement with the experimental value. The existence of two transition states for the same rearrangement arises because there is a conical intersection between the two lowest singlet states which occurs in the vicinity of the reaction coordinates. The two possible paths around the cone on the lower adiabatic surface give rise to the two distinct saddle points. The lower barrier for the unimolecular mechanism now makes it competitive with the bimolecular one, according to our calculations. In support of this conclusion, we have reanalyzed some previous experimental results on anisole pyrolysis, which leads to benzene as a significant product and have shown that the unimolecular and bimolecular mechanisms for fulvene → benzene must be occurring competitively in that system. Finally, we have identified that similar conical intersections arise during the isomerizations of benzofulvene and isobenzofulvene to naphthalene.
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Affiliation(s)
- Barry K Carpenter
- School of Chemistry, Cardiff University, Main Building, Park PL, Cardiff CF10 3AT, U.K
| | - G Barney Ellison
- Department of Chemistry, University of Colorado, Boulder, Colorado 80309, United States
| | - Mark R Nimlos
- National Renewable Energy Laboratory, 15013 Denver West Parkway, Golden, Colorado 80401, United States
| | - Adam M Scheer
- Recurve Inc., 4014 South Lemay Avenue, Unit 22, Fort Collins, Colorado 80525, United States
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Westermayr J, Marquetand P. Machine learning and excited-state molecular dynamics. MACHINE LEARNING-SCIENCE AND TECHNOLOGY 2020. [DOI: 10.1088/2632-2153/ab9c3e] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
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Westermayr J, Gastegger M, Marquetand P. Combining SchNet and SHARC: The SchNarc Machine Learning Approach for Excited-State Dynamics. J Phys Chem Lett 2020; 11:3828-3834. [PMID: 32311258 PMCID: PMC7246974 DOI: 10.1021/acs.jpclett.0c00527] [Citation(s) in RCA: 86] [Impact Index Per Article: 21.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2020] [Accepted: 04/20/2020] [Indexed: 05/26/2023]
Abstract
In recent years, deep learning has become a part of our everyday life and is revolutionizing quantum chemistry as well. In this work, we show how deep learning can be used to advance the research field of photochemistry by learning all important properties-multiple energies, forces, and different couplings-for photodynamics simulations. We simplify such simulations substantially by (i) a phase-free training skipping costly preprocessing of raw quantum chemistry data; (ii) rotationally covariant nonadiabatic couplings, which can either be trained or (iii) alternatively be approximated from only ML potentials, their gradients, and Hessians; and (iv) incorporating spin-orbit couplings. As the deep-learning method, we employ SchNet with its automatically determined representation of molecular structures and extend it for multiple electronic states. In combination with the molecular dynamics program SHARC, our approach termed SchNarc is tested on two polyatomic molecules and paves the way toward efficient photodynamics simulations of complex systems.
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Affiliation(s)
- Julia Westermayr
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
| | - Michael Gastegger
- Machine
Learning Group, Technical University of
Berlin, 10587 Berlin, Germany
| | - Philipp Marquetand
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
- Vienna
Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
- Data
Science @ Uni Vienna, University of Vienna, Währinger Str. 29, 1090 Vienna, Austria
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9
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Gómez S, Heindl M, Szabadi A, González L. From Surface Hopping to Quantum Dynamics and Back. Finding Essential Electronic and Nuclear Degrees of Freedom and Optimal Surface Hopping Parameters. J Phys Chem A 2019; 123:8321-8332. [DOI: 10.1021/acs.jpca.9b06103] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Sandra Gómez
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, 1010 Vienna, Austria
| | - Moritz Heindl
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, 1010 Vienna, Austria
| | - András Szabadi
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, 1010 Vienna, Austria
| | - Leticia González
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, 1010 Vienna, Austria
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Aldaz C, Kammeraad JA, Zimmerman PM. Discovery of conical intersection mediated photochemistry with growing string methods. Phys Chem Chem Phys 2018; 20:27394-27405. [PMID: 30357173 PMCID: PMC6532651 DOI: 10.1039/c8cp04703k] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
Conical intersections (CIs) are important features of photochemistry that determine yields and selectivity. Traditional CI optimizers require significant human effort and chemical intuition, which typically restricts searching to only a small region of the CI space. Herein, a systematic approach utilizing the growing string method is introduced to locate multiple CIs. Unintuitive MECI are found using driving coordinates that can be generated using a combinatorial search, and subsequent optimization allows reaction pathways, transition states, products, and seam-space pathways to be located. These capabilities are demonstrated by application to two prototypical photoisomerization reactions and the dimerization of butadiene. In total, many reaction pathways were uncovered, including the elusive stilbene hula-twist mechanism, and a previously unidentified product in butadiene dimerization. Overall, these results suggest that growing string methods provide a predictive strategy for exploring photochemistry.
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Affiliation(s)
- Cody Aldaz
- Department of Chemistry, University of Michigan, Ann Arbor, MI 48109, USA.
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11
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Gonon B, Perveaux A, Gatti F, Lauvergnat D, Lasorne B. On the applicability of a wavefunction-free, energy-based procedure for generating first-order non-adiabatic couplings around conical intersections. J Chem Phys 2018; 147:114114. [PMID: 28938825 DOI: 10.1063/1.4991635] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
The primal definition of first-order non-adiabatic couplings among electronic states relies on the knowledge of how electronic wavefunctions vary with nuclear coordinates. However, the non-adiabatic coupling between two electronic states can be obtained in the vicinity of a conical intersection from energies only, as this vector spans the branching plane along which degeneracy is lifted to first order. The gradient difference and derivative coupling are responsible of the two-dimensional cusp of a conical intersection between both potential-energy surfaces and can be identified to the non-trivial eigenvectors of the second derivative of the square energy difference, as first pointed out in Köppel and Schubert [Mol. Phys. 104(5-7), 1069 (2006)]. Such quantities can always be computed in principle for the cost of two numerical Hessians in the worst-case scenario. Analytic-derivative techniques may help in terms of accuracy and efficiency but also raise potential traps due to singularities and ill-defined derivatives at degeneracies. We compare here two approaches, one fully numerical, the other semianalytic, where analytic gradients are available but Hessians are not, and investigate their respective conditions of applicability. Benzene and 3-hydroxychromone are used as illustrative application cases. It is shown that non-adiabatic couplings can thus be estimated with decent accuracy in regions of significant size around conical intersections. This procedure is robust and could be useful in the context of on-the-fly non-adiabatic dynamics or be used for producing model representations of intersecting potential energy surfaces with complete obviation of the electronic wavefunctions.
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Affiliation(s)
- Benjamin Gonon
- Institut Charles Gerhardt Montpellier (UMR 5253), CNRS, Université de Montpellier, F-34095 Montpellier, France
| | - Aurelie Perveaux
- Institut Charles Gerhardt Montpellier (UMR 5253), CNRS, Université de Montpellier, F-34095 Montpellier, France
| | - Fabien Gatti
- Institut Charles Gerhardt Montpellier (UMR 5253), CNRS, Université de Montpellier, F-34095 Montpellier, France
| | - David Lauvergnat
- Laboratoire de Chimie Physique (UMR 8000), CNRS, Université Paris-Sud/Paris-Saclay, F-91405 Orsay, France
| | - Benjamin Lasorne
- Institut Charles Gerhardt Montpellier (UMR 5253), CNRS, Université de Montpellier, F-34095 Montpellier, France
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12
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Morrison AF, Herbert JM. Analytic derivative couplings and first-principles exciton/phonon coupling constants for an ab initio Frenkel-Davydov exciton model: Theory, implementation, and application to compute triplet exciton mobility parameters for crystalline tetracene. J Chem Phys 2017; 146:224110. [DOI: 10.1063/1.4985607] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Adrian F. Morrison
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - John M. Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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