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Richardson JO. Nonadiabatic Tunneling in Chemical Reactions. J Phys Chem Lett 2024; 15:7387-7397. [PMID: 38995660 DOI: 10.1021/acs.jpclett.4c01098] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/13/2024]
Abstract
Quantum tunneling can have a dramatic effect on chemical reaction rates. In nonadiabatic reactions such as electron transfers or spin crossovers, nuclear tunneling effects can be even stronger than for adiabatic proton transfers. Ring-polymer instanton theory enables molecular simulations of tunneling in full dimensionality and has been shown to be far more reliable than commonly used separable approximations. First-principles instanton calculations predict significant nonadiabatic tunneling of heavy atoms even at room temperature and give excellent agreement with experimental measurements for the intersystem crossing of two nitrenes in cryogenic matrix isolation, the spin-forbidden relaxation of photoexcited thiophosgene in the gas phase, and singlet oxygen deactivation in water at ambient conditions. Finally, an outlook of further theoretical developments is discussed.
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Affiliation(s)
- Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland
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2
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London N, Bu S, Johnson B, Ananth N. Mean-Field Ring Polymer Rates Using a Population Dividing Surface. J Phys Chem A 2024; 128:5730-5739. [PMID: 38976564 DOI: 10.1021/acs.jpca.4c00005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/10/2024]
Abstract
Mean-field ring polymer molecular dynamics offers a computationally efficient method for the simulation of reaction rates in multilevel systems. Previous work has established that, to model a nonadiabatic state-to-state reaction accurately, it is necessary to ensure reactive trajectories form kinked ring polymer configurations at the dividing surface. Building on this idea, we introduce a population difference coordinate and a reactive flux expression modified to only include contributions from kinked configurations. We test the accuracy of the resulting mean-field rate theory on a series of linear vibronic coupling model systems. We demonstrate that this new kMF-RP rate approach is efficient to implement and quantitatively accurate for models over a wide range of driving forces, coupling strengths, and temperatures.
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Affiliation(s)
- Nathan London
- Department of Chemistry, Cornell University, Ithaca, New York 14853, United States
| | - Siyu Bu
- Department of Chemistry, Cornell University, Ithaca, New York 14853, United States
| | - Britta Johnson
- Department of Chemistry, Cornell University, Ithaca, New York 14853, United States
| | - Nandini Ananth
- Department of Chemistry, Cornell University, Ithaca, New York 14853, United States
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3
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Ansari IM, Heller ER, Trenins G, Richardson JO. Heavy-atom tunnelling in singlet oxygen deactivation predicted by instanton theory with branch-point singularities. Nat Commun 2024; 15:4335. [PMID: 38773078 DOI: 10.1038/s41467-024-48463-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2023] [Accepted: 04/29/2024] [Indexed: 05/23/2024] Open
Abstract
The reactive singlet state of oxygen (O2) can decay to the triplet ground state nonradiatively in the presence of a solvent. There is a controversy about whether tunnelling is involved in this nonadiabatic spin-crossover process. Semiclassical instanton theory provides a reliable and practical computational method for elucidating the reaction mechanism and can account for nuclear quantum effects such as zero-point energy and multidimensional tunnelling. However, the previously developed instanton theory is not directly applicable to this system because of a branch-point singularity which appears in the flux correlation function. Here we derive a new instanton theory for cases dominated by the singularity, leading to a new picture of tunnelling in nonadiabatic processes. Together with multireference electronic-structure theory, this provides a rigorous framework based on first principles that we apply to calculate the decay rate of singlet oxygen in water. The results indicate a new reaction mechanism that is 27 orders of magnitude faster at room temperature than the classical process through the minimum-energy crossing point. We find significant heavy-atom tunnelling contributions as well as a large temperature-dependent H2O/D2O kinetic isotope effect of approximately 20, in excellent agreement with experiment.
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Affiliation(s)
- Imaad M Ansari
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093, Zürich, Switzerland
| | - Eric R Heller
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093, Zürich, Switzerland
- Department of Chemistry, University of California, Berkeley, 94720, Berkeley, USA
| | - George Trenins
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093, Zürich, Switzerland
- MPI for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761, Hamburg, Germany
| | - Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093, Zürich, Switzerland.
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4
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Pollak E. A personal perspective of the present status and future challenges facing thermal reaction rate theory. J Chem Phys 2024; 160:150902. [PMID: 38639316 DOI: 10.1063/5.0199557] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2024] [Accepted: 03/06/2024] [Indexed: 04/20/2024] Open
Abstract
Reaction rate theory has been at the center of physical chemistry for well over one hundred years. The evolution of the theory is not only of historical interest. Reliable and accurate computation of reaction rates remains a challenge to this very day, especially in view of the development of quantum chemistry methods, which predict the relevant force fields. It is still not possible to compute the numerically exact rate on the fly when the system has more than at most a few dozen anharmonic degrees of freedom, so one must consider various approximate methods, not only from the practical point of view of constructing numerical algorithms but also on conceptual and formal levels. In this Perspective, I present some of the recent analytical results concerning leading order terms in an ℏ2m series expansion of the exact rate and their implications on various approximate theories. A second aspect has to do with the crossover temperature between tunneling and thermal activation. Using a uniform semiclassical transmission probability rather than the "primitive" semiclassical theory leads to the conclusion that there is no divergence problem associated with a "crossover temperature." If one defines a semiclassical crossover temperature as the point at which the tunneling energy of the instanton equals the barrier height, then it is a factor of two higher than its previous estimate based on the "primitive" semiclassical approximation. In the low temperature tunneling regime, the uniform semiclassical theory as well as the "primitive" semiclassical theory were based on the classical Euclidean action of a periodic orbit on the inverted potential. The uniform semiclassical theory wrongly predicts that the "half-point," which is the energy at which the transmission probability equals 1/2, for any barrier potential, is always the barrier energy. We describe here how augmenting the Euclidean action with constant terms of order ℏ2 can significantly improve the accuracy of the semiclassical theory and correct this deficiency. This also leads to a deep connection with and improvement of vibrational perturbation theory. The uniform semiclassical theory also enables an extension of the quantum version of Kramers' turnover theory to temperatures below the "crossover temperature." The implications of these recent advances on various approximate methods used to date are discussed at length, leading to the conclusion that reaction rate theory will continue to challenge us both on conceptual and practical levels for years to come.
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Affiliation(s)
- Eli Pollak
- Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel
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Ansari IM, Heller ER, Trenins G, Richardson JO. Instanton theory for Fermi's golden rule and beyond. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20200378. [PMID: 35341312 PMCID: PMC8958279 DOI: 10.1098/rsta.2020.0378] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2021] [Accepted: 09/22/2021] [Indexed: 05/29/2023]
Abstract
Instanton theory provides a semiclassical approximation for computing quantum tunnelling effects in complex molecular systems. It is typically applied to proton-transfer reactions for which the Born-Oppenheimer approximation is valid. However, many processes in physics, chemistry and biology, such as electron transfers, are non-adiabatic and are correctly described instead using Fermi's golden rule. In this work, we discuss how instanton theory can be generalized to treat these reactions in the golden-rule limit. We then extend the theory to treat fourth-order processes such as bridge-mediated electron transfer and apply the method to simulate an electron moving through a model system of three coupled quantum dots. By comparison with benchmark quantum calculations, we demonstrate that the instanton results are much more reliable than alternative approximations based on superexchange-mediated effective coupling or a classical sequential mechanism. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.
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Affiliation(s)
| | - Eric R. Heller
- Laboratory of Physical Chemistry, ETH, Zürich, Switzerland
| | - George Trenins
- Laboratory of Physical Chemistry, ETH, Zürich, Switzerland
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6
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Trenins G, Richardson JO. Nonadiabatic instanton rate theory beyond the golden-rule limit. J Chem Phys 2022; 156:174115. [DOI: 10.1063/5.0088518] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Fermi's golden rule describes the leading-order behaviour of the reaction rate as a function of the diabatic coupling. Its asymptotic (ℏ →0) limit is the semiclassical golden-rule instanton rate theory, which rigorously approximates nuclear quantum effects, lends itself to efficient numerical computation and gives physical insight into reaction mechanisms. However the golden rule by itself becomes insufficient as the strength of the diabatic coupling increases, so higher-order terms must be additionally considered. In this work we give a first-principles derivation of the next-order term beyond the golden rule, represented as a sum of three components. Two of them lead to new instanton pathways that extend the golden-rule case and, among other factors, account for the effects of recrossing on the full rate. The remaining component derives from the equilibrium partition function and accounts for changes in potential energy around the reactant and product wells due to diabatic coupling. The new semiclassical theory demands little computational effort beyond a golden-rule instanton calculation. It makes it possible to rigorously assess the accuracy of the golden-rule approximation and sets the stage for future work on general semiclassical nonadiabatic rate theories.
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Affiliation(s)
- George Trenins
- ETH Zurich Department of Chemistry and Applied Biosciences, Switzerland
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7
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Tinnin J, Bhandari S, Zhang P, Geva E, Dunietz BD, Sun X, Cheung MS. Correlating Interfacial Charge Transfer Rates with Interfacial Molecular Structure in the Tetraphenyldibenzoperiflanthene/C 70 Organic Photovoltaic System. J Phys Chem Lett 2022; 13:763-769. [PMID: 35040657 DOI: 10.1021/acs.jpclett.1c03618] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Organic photovoltaics (OPV) is an emerging solar cell technology that offers vast advantages such as low-cost manufacturing, transparency, and solution processability. However, because the performance of OPV devices is still disappointing compared to their inorganic counterparts, better understanding of how controlling the molecular-level morphology can impact performance is needed. To this end, one has to overcome significant challenges that stem from the complexity and heterogeneity of the underlying electronic structure and molecular morphology. In this Letter, we address this challenge in the context of the DBP/C70 OPV system by employing a modular workflow that combines recent advances in electronic structure, molecular dynamics, and rate theory. We show how the wide range of interfacial pairs can be classified into four types of interfacial donor-acceptor geometries and find that the least populated interfacial geometry gives rise to the fastest charge transfer (CT) rates.
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Affiliation(s)
- Jacob Tinnin
- Department of Physics, University of Houston, 617 Science & Research Building 1, Houston, Texas 77204, United States
- Center for Theoretical Biological Physics, Rice University, 6500 Main St., BioScience Research Collaborative, Suite 1005G, Houston, Texas 77030-1402, United States
| | - Srijana Bhandari
- Department of Chemistry and Biochemistry, Kent State University, 1175 Risman Drive, Kent, Ohio 44242, United States
- Department of Chemistry, Case Western Reserve University, 10800 Euclid Avenue, Cleveland, Ohio 44106, United States
| | - Pengzhi Zhang
- Department of Physics, University of Houston, 617 Science & Research Building 1, Houston, Texas 77204, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, 930 North University Avenue, Ann Arbor, Michigan 48109, United States
| | - Barry D Dunietz
- Department of Chemistry and Biochemistry, Kent State University, 1175 Risman Drive, Kent, Ohio 44242, United States
| | - Xiang Sun
- Division of Arts and Sciences, NYU Shanghai, 1555 Century Avenue, Shanghai 200122, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- Department of Chemistry, New York University, New York, New York 10003, United States
| | - Margaret S Cheung
- Department of Physics, University of Houston, 617 Science & Research Building 1, Houston, Texas 77204, United States
- Center for Theoretical Biological Physics, Rice University, 6500 Main St., BioScience Research Collaborative, Suite 1005G, Houston, Texas 77030-1402, United States
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, 902 Battelle Blvd, Richland, Washington 99354, United States
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8
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Heller ER, Richardson JO. Spin Crossover of Thiophosgene via Multidimensional Heavy-Atom Quantum Tunneling. J Am Chem Soc 2021; 143:20952-20961. [PMID: 34846871 DOI: 10.1021/jacs.1c10088] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
The spin-crossover reaction of thiophosgene has drawn broad attention from both experimenters and theoreticians as a prime example of radiationless intramolecular decay via intersystem crossing. Despite multiple attempts over 20 years, theoretical predictions have typically been orders of magnitude in error relative to the experimentally measured triplet lifetime. We address the T1 → S0 transition by the first application of semiclassical golden-rule instanton theory in conjunction with on-the-fly electronic-structure calculations based on multireference perturbation theory. Our first-principles approach provides excellent agreement with the experimental rates. This was only possible because instanton theory goes beyond previous methods by locating the optimal tunneling pathway in full dimensionality and thus captures "corner cutting" effects. Since the reaction is situated in the Marcus inverted regime, the tunneling mechanism can be interpreted in terms of two classical trajectories, one traveling forward and one backward in imaginary time, which are connected by particle-antiparticle creation and annihilation events. The calculated mechanism indicates that the spin crossover is sped up by many orders of magnitude due to multidimensional quantum tunneling of the carbon atom even at room temperature.
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Affiliation(s)
- Eric R Heller
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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9
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Cui B, Craven GT, Nitzan A. Heat transport induced by electron transfer: A general temperature quantum calculation. J Chem Phys 2021; 155:194104. [PMID: 34800951 DOI: 10.1063/5.0068303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Electron transfer dominates chemical processes in biological, inorganic, and material chemistry. Energetic aspects of such phenomena, in particular, the energy transfer associated with the electron transfer process, have received little attention in the past but are important in designing energy conversion devices. This paper generalizes our earlier work in this direction, which was based on the semiclassical Marcus theory of electron transfer. It provides, within a simple model, a unified framework that includes the deep (nuclear) tunneling limit of electron transfer and the associated heat transfer when the donor and acceptor sites are seated in environments characterized by different local temperatures. The electron transfer induced heat conduction is shown to go through a maximum at some intermediate average temperature where quantum effects are already appreciable, and it approaches zero when the average temperature is very high (the classical limit) or very low (deep tunneling).
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Affiliation(s)
- Bingyu Cui
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Galen T Craven
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
| | - Abrahan Nitzan
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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10
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Breuil G, Mangaud E, Lasorne B, Atabek O, Desouter-Lecomte M. Funneling dynamics in a phenylacetylene trimer: Coherent excitation of donor excitonic states and their superposition. J Chem Phys 2021; 155:034303. [PMID: 34293889 DOI: 10.1063/5.0056351] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
Funneling dynamics in conjugated dendrimers has raised great interest in the context of artificial light-harvesting processes. Photoinduced relaxation has been explored by time-resolved spectroscopy and simulations, mainly by semiclassical approaches or referring to open quantum systems methods, within the Redfield approximation. Here, we take the benefit of an ab initio investigation of a phenylacetylene trimer, and in the spirit of a divide-and-conquer approach, we focus on the early dynamics of the hierarchy of interactions. We build a simplified but realistic model by retaining only bright electronic states and selecting the vibrational domain expected to play the dominant role for timescales shorter than 500 fs. We specifically analyze the role of the in-plane high-frequency skeletal vibrational modes involving the triple bonds. Open quantum system non-adiabatic dynamics involving conical intersections is conducted by separating the electronic subsystem from the high-frequency tuning and coupling vibrational baths. This partition is implemented within a robust non-perturbative and non-Markovian method, here the hierarchical equations of motion. We will more precisely analyze the coherent preparation of donor states or of their superposition by short laser pulses with different polarizations. In particular, we extend the π-pulse strategy for the creation of a superposition to a V-type system. We study the relaxation induced by the high-frequency vibrational collective modes and the transitory dissymmetry, which results from the creation of a superposition of electronic donor states.
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Affiliation(s)
- Gabriel Breuil
- ICGM, Univ Montpellier, CNRS, ENSCM, Montpellier, France
| | - Etienne Mangaud
- MSME, Université Gustave Eiffel, UPEC, CNRS, F-77454 Marne-La-Vallée, France
| | | | - Osman Atabek
- Institut des Sciences Moléculaires, Université Paris-Saclay-CNRS, UMR8214, F-91400 Orsay, France
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11
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Lawrence JE, Manolopoulos DE. An improved path-integral method for golden-rule rates. J Chem Phys 2020; 153:154113. [PMID: 33092388 DOI: 10.1063/5.0022535] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a simple method for the calculation of reaction rates in the Fermi golden-rule limit, which accurately captures the effects of tunneling and zero-point energy. The method is based on a modification of the recently proposed golden-rule quantum transition state theory (GR-QTST) of Thapa, Fang, and Richardson [J. Chem. Phys. 150, 104107 (2019)]. While GR-QTST is not size consistent, leading to the possibility of unbounded errors in the rate, our modified method has no such issue and so can be reliably applied to condensed phase systems. Both methods involve path-integral sampling in a constrained ensemble; the two methods differ, however, in the choice of constraint functional. We demonstrate numerically that our modified method is as accurate as GR-QTST for the one-dimensional model considered by Thapa and co-workers. We then study a multidimensional spin-boson model, for which our method accurately predicts the true quantum rate, while GR-QTST breaks down with an increasing number of boson modes in the discretization of the spectral density. Our method is able to accurately predict reaction rates in the Marcus inverted regime without the need for the analytic continuation required by Wolynes theory.
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Affiliation(s)
- Joseph E Lawrence
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - David E Manolopoulos
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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12
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Lawrence JE, Manolopoulos DE. Confirming the role of nuclear tunneling in aqueous ferrous–ferric electron transfer. J Chem Phys 2020; 153:154114. [DOI: 10.1063/5.0022678] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Affiliation(s)
- Joseph E. Lawrence
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - David E. Manolopoulos
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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13
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Heller ER, Richardson JO. Semiclassical instanton formulation of Marcus–Levich–Jortner theory. J Chem Phys 2020; 152:244117. [DOI: 10.1063/5.0013521] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Eric R. Heller
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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14
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Lawrence JE, Manolopoulos DE. A general non-adiabatic quantum instanton approximation. J Chem Phys 2020; 152:204117. [DOI: 10.1063/5.0009109] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joseph E. Lawrence
- Department of Chemistry, University of Oxford, Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - David E. Manolopoulos
- Department of Chemistry, University of Oxford, Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, United Kingdom
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15
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Heller ER, Richardson JO. Instanton formulation of Fermi’s golden rule in the Marcus inverted regime. J Chem Phys 2020; 152:034106. [DOI: 10.1063/1.5137823] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Eric R. Heller
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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16
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Fang W, Zarotiadis RA, Richardson JO. Revisiting nuclear tunnelling in the aqueous ferrous–ferric electron transfer. Phys Chem Chem Phys 2020; 22:10687-10698. [DOI: 10.1039/c9cp06841d] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
We find that golden-rule quantum transition-state theory predicts nearly an order of magnitude less tunnelling than some of the previous estimates. This may indicate that the spin-boson model of electron transfer is not valid in the quantum regime.
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Affiliation(s)
- Wei Fang
- Laboratory of Physical Chemistry
- ETH Zürich
- 8093 Zürich
- Switzerland
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17
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Mangaud E, Lasorne B, Atabek O, Desouter-Lecomte M. Statistical distributions of the tuning and coupling collective modes at a conical intersection using the hierarchical equations of motion. J Chem Phys 2019; 151:244102. [DOI: 10.1063/1.5128852] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Etienne Mangaud
- Physicochimie des Electrolytes et des Nanosystèmes Interfaciaux-UMR 8234 Sorbonne Université, F-75252 Paris, France and Laboratoire Collisions Agrégats Réactivité (IRSAMC), Université Toulouse III Paul Sabatier, UMR 5589, F-31062 Toulouse, France
| | - Benjamin Lasorne
- Institut Charles Gerhardt Montpellier (ICGM), Université de Montpellier, CNRS, ENSCM, F-34095 Montpellier, France
| | - Osman Atabek
- Institut des Sciences Moléculaires d’Orsay (ISMO), Université Paris-Saclay, CNRS, F-91405 Orsay, France
| | - Michèle Desouter-Lecomte
- Institut de Chimie Physique (ICP), Université Paris-Saclay, CNRS, F-91405 Orsay, France and Département de Chimie, Université de Liège, Sart Tilman, B6, B-4000 Liège, Belgium
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18
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Fang W, Thapa MJ, Richardson JO. Nonadiabatic quantum transition-state theory in the golden-rule limit. II. Overcoming the pitfalls of the saddle-point and semiclassical approximations. J Chem Phys 2019; 151:214101. [DOI: 10.1063/1.5131092] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Wei Fang
- Laboratory of Physical Chemistry, ETH Zurich, 8093 Zurich, Switzerland
| | - Manish J. Thapa
- Laboratory of Physical Chemistry, ETH Zurich, 8093 Zurich, Switzerland
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19
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Thapa MJ, Fang W, Richardson JO. Nonadiabatic quantum transition-state theory in the golden-rule limit. I. Theory and application to model systems. J Chem Phys 2019; 150:104107. [DOI: 10.1063/1.5081108] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Manish J. Thapa
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Wei Fang
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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20
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Mandal A, Shakib FA, Huo P. Investigating photoinduced proton coupled electron transfer reaction using quasi diabatic dynamics propagation. J Chem Phys 2018; 148:244102. [DOI: 10.1063/1.5030634] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Arkajit Mandal
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - Farnaz A. Shakib
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
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21
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Hsieh CY, Cao J. A unified stochastic formulation of dissipative quantum dynamics. II. Beyond linear response of spin baths. J Chem Phys 2018; 148:014104. [PMID: 29306289 DOI: 10.1063/1.5018726] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We use the "generalized hierarchical equation of motion" proposed in Paper I [C.-Y. Hsieh and J. Cao, J. Chem. Phys. 148, 014103 (2018)] to study decoherence in a system coupled to a spin bath. The present methodology allows a systematic incorporation of higher-order anharmonic effects of the bath in dynamical calculations. We investigate the leading order corrections to the linear response approximations for spin bath models. Two kinds of spin-based environments are considered: (1) a bath of spins discretized from a continuous spectral density and (2) a bath of localized nuclear or electron spins. The main difference resides with how the bath frequency and the system-bath coupling parameters are distributed in an environment. When discretized from a continuous spectral density, the system-bath coupling typically scales as ∼1/NB where NB is the number of bath spins. This scaling suppresses the non-Gaussian characteristics of the spin bath and justifies the linear response approximations in the thermodynamic limit. For the nuclear/electron spin bath models, system-bath couplings are directly deduced from spin-spin interactions and do not necessarily obey the 1/NB scaling. It is not always possible to justify the linear response approximations in this case. Furthermore, if the spin-spin Hamiltonian is highly symmetrical, there exist additional constraints that generate highly non-Markovian and persistent dynamics that is beyond the linear response treatments.
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Affiliation(s)
- Chang-Yu Hsieh
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
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Xu YY, Chen B, Liu J. Achieving the classical Carnot efficiency in a strongly coupled quantum heat engine. Phys Rev E 2018; 97:022130. [PMID: 29548214 DOI: 10.1103/physreve.97.022130] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2017] [Indexed: 11/07/2022]
Abstract
Generally, the efficiency of a heat engine strongly coupled with a heat bath is less than the classical Carnot efficiency. Through a model-independent method, we show that the classical Carnot efficiency is achieved in a strongly coupled quantum heat engine. First, we present the first law of quantum thermodynamics in strong coupling. Then, we show how to achieve the Carnot cycle and the classical Carnot efficiency at strong coupling. We find that this classical Carnot efficiency stems from the fact that the heat released in a nonequilibrium process is balanced by the absorbed heat. We also analyze the restrictions in the achievement of the Carnot cycle. The first restriction is that there must be two corresponding intervals of the controllable parameter in which the corresponding entropies of the work substance at the hot and cold temperatures are equal, and the second is that the entropy of the initial and final states in a nonequilibrium process must be equal. Through these restrictions, we obtain the positive work conditions, including the usual one in which the hot temperature should be higher than the cold, and a new one in which there must be an entropy interval at the hot temperature overlapping that at the cold. We demonstrate our result through a paradigmatic model-a two-level system in which a work substance strongly interacts with a heat bath. In this model, we find that the efficiency may abruptly decrease to zero due to the first restriction, and that the second restriction results in the control scheme becoming complex.
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Affiliation(s)
- Y Y Xu
- Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - B Chen
- Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - J Liu
- Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming 650500, China
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23
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Mattiat J, Richardson JO. Effects of tunnelling and asymmetry for system-bath models of electron transfer. J Chem Phys 2018; 148:102311. [PMID: 29544261 DOI: 10.1063/1.5001116] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We apply the newly derived nonadiabatic golden-rule instanton theory to asymmetric models describing electron-transfer in solution. The models go beyond the usual spin-boson description and have anharmonic free-energy surfaces with different values for the reactant and product reorganization energies. The instanton method gives an excellent description of the behaviour of the rate constant with respect to asymmetry for the whole range studied. We derive a general formula for an asymmetric version of the Marcus theory based on the classical limit of the instanton and find that this gives significant corrections to the standard Marcus theory. A scheme is given to compute this rate based only on equilibrium simulations. We also compare the rate constants obtained by the instanton method with its classical limit to study the effect of tunnelling and other quantum nuclear effects. These quantum effects can increase the rate constant by orders of magnitude.
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Affiliation(s)
- Johann Mattiat
- Laboratory of Physical Chemistry, ETH Zurich, 8093 Zurich, Switzerland
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24
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Lawrence JE, Manolopoulos DE. Analytic continuation of Wolynes theory into the Marcus inverted regime. J Chem Phys 2018; 148:102313. [DOI: 10.1063/1.5002894] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joseph E. Lawrence
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - David E. Manolopoulos
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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25
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Mangaud E, Meier C, Desouter-Lecomte M. Analysis of the non-Markovianity for electron transfer reactions in an oligothiophene-fullerene heterojunction. Chem Phys 2017. [DOI: 10.1016/j.chemphys.2017.07.011] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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26
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Pelzer KM, Vázquez-Mayagoitia Á, Ratcliff LE, Tretiak S, Bair RA, Gray SK, Van Voorhis T, Larsen RE, Darling SB. Molecular dynamics and charge transport in organic semiconductors: a classical approach to modeling electron transfer. Chem Sci 2017; 8:2597-2609. [PMID: 28553494 PMCID: PMC5431633 DOI: 10.1039/c6sc04547b] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2016] [Accepted: 01/03/2017] [Indexed: 11/21/2022] Open
Abstract
Organic photovoltaics (OPVs) are a promising carbon-neutral energy conversion technology, with recent improvements pushing power conversion efficiencies over 10%. A major factor limiting OPV performance is inefficiency of charge transport in organic semiconducting materials (OSCs). Due to strong coupling with lattice degrees of freedom, the charges form polarons, localized quasi-particles comprised of charges dressed with phonons. These polarons can be conceptualized as pseudo-atoms with a greater effective mass than a bare charge. We propose that due to this increased mass, polarons can be modeled with Langevin molecular dynamics (LMD), a classical approach with a computational cost much lower than most quantum mechanical methods. Here we present LMD simulations of charge transfer between a pair of fullerene molecules, which commonly serve as electron acceptors in OSCs. We find transfer rates consistent with experimental measurements of charge mobility, suggesting that this method may provide quantitative predictions of efficiency when used to simulate materials on the device scale. Our approach also offers information that is not captured in the overall transfer rate or mobility: in the simulation data, we observe exactly when and why intermolecular transfer events occur. In addition, we demonstrate that these simulations can shed light on the properties of polarons in OSCs. Much remains to be learned about these quasi-particles, and there are no widely accepted methods for calculating properties such as effective mass and friction. Our model offers a promising approach to exploring mass and friction as well as providing insight into the details of polaron transport in OSCs.
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Affiliation(s)
- Kenley M Pelzer
- Center for Nanoscale Materials , Argonne National Laboratory , 9700 Cass Ave., Lemont , IL 60439 , USA . ; Tel: +1-630-252-7020
- Materials Science Division , Argonne National Laboratory , 9700 Cass Ave, Lemont , IL 60439 , USA
| | - Álvaro Vázquez-Mayagoitia
- Argonne Leadership Computing Facility , Argonne National Laboratory , 9700 Cass Ave. , Lemont , IL 60439 , USA
| | - Laura E Ratcliff
- Argonne Leadership Computing Facility , Argonne National Laboratory , 9700 Cass Ave. , Lemont , IL 60439 , USA
| | - Sergei Tretiak
- Theoretical Division , Center for Nonlinear Studies , Center for Integrated Nanotechnologies , Los Alamos National Laboratory , Los Alamos , NM 87545 , USA
| | - Raymond A Bair
- Mathematics and Computer Science Division , Argonne National Laboratory , 9700 Cass Ave. , Argonne , IL 60439 , USA
- Computation Institute , University of Chicago , 5735 S. Ellis Ave. , Chicago , IL 60637 , USA
- Computer, Environment, and Life Sciences , Argonne National Laboratory , 9700 Cass Ave. , Lemont , IL 60439 , USA
| | - Stephen K Gray
- Center for Nanoscale Materials , Argonne National Laboratory , 9700 Cass Ave., Lemont , IL 60439 , USA . ; Tel: +1-630-252-7020
- Computation Institute , University of Chicago , 5735 S. Ellis Ave. , Chicago , IL 60637 , USA
| | - Troy Van Voorhis
- Department of Chemistry , Massachusetts Institute of Technology , 77 Massachusetts Ave , Cambridge , MA 02139 , USA
| | - Ross E Larsen
- Computational Science Center , National Renewable Energy Laboratory , 15301 Denver W. Parkway, Golden , CO 80401 , USA
| | - Seth B Darling
- Center for Nanoscale Materials , Argonne National Laboratory , 9700 Cass Ave., Lemont , IL 60439 , USA . ; Tel: +1-630-252-7020
- Institute for Molecular Engineering , University of Chicago , 5747 S. Ellis Ave. , Chicago , IL 60637 , USA
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27
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Iles-Smith J, Dijkstra AG, Lambert N, Nazir A. Energy transfer in structured and unstructured environments: Master equations beyond the Born-Markov approximations. J Chem Phys 2016; 144:044110. [DOI: 10.1063/1.4940218] [Citation(s) in RCA: 82] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Affiliation(s)
- Jake Iles-Smith
- Controlled Quantum Dynamics Theory, Imperial College London, London SW7 2PG, United Kingdom
- Photon Science Institute and School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
- Department of Photonics Engineering, DTU Fotonik, Ørsteds Plads, 2800 Kongens Lyngby, Denmark
| | - Arend G. Dijkstra
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | | | - Ahsan Nazir
- Photon Science Institute and School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
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28
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Kretchmer JS, Miller III TF. Kinetically-constrained ring-polymer molecular dynamics for non-adiabatic chemistries involving solvent and donor–acceptor dynamical effects. Faraday Discuss 2016; 195:191-214. [DOI: 10.1039/c6fd00143b] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We investigate the performance of the recently developed kinetically-constrained ring polymer molecular dynamics (KC-RPMD) method for the description of model condensed-phase electron transfer (ET) reactions in which solvent and donor–acceptor dynamics play an important role. Comparison of KC-RPMD with results from Golden-Rule rate theories and numerically exact quantum dynamics calculations demonstrates that KC-RPMD accurately captures the combination of electronic- and nuclear-dynamical effects throughout the Marcus (intermediate solvent friction) and Zusman (large solvent friction) regimes of ET. It is also demonstrated that KC-RPMD accurately describes systems in which the magnitude of the diabatic coupling depends on the position of a dynamical donor–acceptor mode. In addition to these successes, however, we present an unsurprising failure of KC-RPMD to capture the enhancement of the ET rate in the low solvent friction regime associated with nuclear coherence effects. In this analysis, we re-visit several aspects of the original KC-RPMD formulation, including the form of the kinetic constraint and the choice of the mass of the auxiliary electronic variable. In particular, we introduce a Langevin bath for the auxiliary electronic variable to correct for its unphysically low coupling with the nuclear degrees of freedom. This work demonstrates that the KC-RPMD method is well suited for the direct simulation of non-adiabatic donor–acceptor chemistries associated with many complex systems, including those for which solvent dynamics plays an important role in the reaction mechanism.
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Affiliation(s)
- Joshua S. Kretchmer
- Division of Chemistry and Chemical Engineering
- California Institute of Technology
- Pasadena
- USA
| | - Thomas F. Miller III
- Division of Chemistry and Chemical Engineering
- California Institute of Technology
- Pasadena
- USA
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29
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Richardson JO. Microcanonical and thermal instanton rate theory for chemical reactions at all temperatures. Faraday Discuss 2016; 195:49-67. [DOI: 10.1039/c6fd00119j] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Semiclassical instanton theory is used to study the quantum effects of tunnelling and delocalization in molecular systems. An analysis of the approximations involved in the method is presented based on a recent first-principles derivation of instanton rate theory [J. Chem. Phys., 2016,144, 114106]. It is known that the standard instanton method is unable to accurately compute thermal rates near the crossover temperature. The causes of this problem are identified and an improved method is proposed, whereby an instanton approximation to the microcanonical rate is defined and integrated numerically to obtain a thermal rate at any temperature. No new computational algorithms are required, but only data analysis of a number of standard instanton calculations.
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Affiliation(s)
- Jeremy O. Richardson
- Department of Chemistry
- Durham University
- Durham
- UK
- Laboratory of Physical Chemistry
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30
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Duke JR, Ananth N. Mean field ring polymer molecular dynamics for electronically nonadiabatic reaction rates. Faraday Discuss 2016; 195:253-268. [DOI: 10.1039/c6fd00123h] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a mean field ring polymer molecular dynamics method to calculate the rate of electron transfer (ET) in multi-state, multi-electron condensed-phase processes. Our approach involves calculating a transition state theory (TST) estimate to the rate using an exact path integral in discrete electronic states and continuous Cartesian nuclear coordinates. A dynamic recrossing correction to the TST rate is then obtained from real-time dynamics simulations using mean field ring polymer molecular dynamics. We employ two different reaction coordinates in our simulations and show that, despite the use of mean field dynamics, the use of an accurate dividing surface to compute TST rates allows us to achieve remarkable agreement with Fermi's golden rule rates for nonadiabatic ET in the normal regime of Marcus theory. Further, we show that using a reaction coordinate based on electronic state populations allows us to capture the turnover in rates for ET in the Marcus inverted regime.
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Affiliation(s)
- Jessica Ryan Duke
- Department of Chemistry and Chemical Biology
- Cornell University
- Ithaca
- USA
| | - Nandini Ananth
- Department of Chemistry and Chemical Biology
- Cornell University
- Ithaca
- USA
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31
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Mangaud E, de la Lande A, Meier C, Desouter-Lecomte M. Electron transfer within a reaction path model calibrated by constrained DFT calculations: application to mixed-valence organic compounds. Phys Chem Chem Phys 2015; 17:30889-903. [PMID: 26041466 DOI: 10.1039/c5cp01194a] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The quantum dynamics of electron transfer in mixed-valence organic compounds is investigated using a reaction path model calibrated by constrained density functional theory (cDFT). Constrained DFT is used to define diabatic states relevant for describing the electron transfer, to obtain equilibrium structures for each of these states and to estimate the electronic coupling between them. The harmonic analysis at the diabatic minima yields normal modes forming the dissipative bath coupled to the electronic states. In order to decrease the system-bath coupling, an effective one dimensional vibronic Hamiltonian is constructed by partitioning the modes into a linear reaction path which connects both equilibrium positions and a set of secondary vibrational modes, coupled to this reaction coordinate. Using this vibronic model Hamiltonian, dissipative quantum dynamics is carried out using Redfield theory, based on a spectral density which is determined from the cDFT results. In a first benchmark case, the model is applied to a series of mixed-valence organic compounds formed by two 1,4-dimethoxy-3-methylphenylene fragments linked by an increasing number of phenylene bridges. This allows us to examine the coherent electron transfer in extreme situations leading to a ground adiabatic state with or without a barrier and therefore to the trapping of the charge or to an easy delocalization.
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Affiliation(s)
- E Mangaud
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, IRSAMC, Université Toulouse III Paul Sabatier, Bât. 3R1b4, 118 route de Narbonne, F-31062, Toulouse, France. and Laboratoire de Chimie Physique, UMR 8000, Université Paris-Sud, Bât. 349, 15 avenue Jean Perrin, F-91405 Orsay, France
| | - A de la Lande
- Laboratoire de Chimie Physique, UMR 8000, Université Paris-Sud, Bât. 349, 15 avenue Jean Perrin, F-91405 Orsay, France
| | - C Meier
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, IRSAMC, Université Toulouse III Paul Sabatier, Bât. 3R1b4, 118 route de Narbonne, F-31062, Toulouse, France.
| | - M Desouter-Lecomte
- Laboratoire de Chimie Physique, UMR 8000, Université Paris-Sud, Bât. 349, 15 avenue Jean Perrin, F-91405 Orsay, France and Département de Chimie, Université de Liège, Sart Tilman, B6, B-4000 Liège, Belgium
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32
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Richardson JO. Ring-polymer instanton theory of electron transfer in the nonadiabatic limit. J Chem Phys 2015; 143:134116. [DOI: 10.1063/1.4932362] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jeremy O. Richardson
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstraße 7/B2, 91058 Erlangen, Germany
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33
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Richardson JO, Bauer R, Thoss M. Semiclassical Green’s functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit. J Chem Phys 2015; 143:134115. [DOI: 10.1063/1.4932361] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jeremy O. Richardson
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstraße 7/B2, 91058 Erlangen, Germany
| | - Rainer Bauer
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstraße 7/B2, 91058 Erlangen, Germany
| | - Michael Thoss
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstraße 7/B2, 91058 Erlangen, Germany
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34
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Richardson JO, Thoss M. Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory. J Chem Phys 2014; 141:074106. [DOI: 10.1063/1.4892865] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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35
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Rossi M, Ceriotti M, Manolopoulos DE. How to remove the spurious resonances from ring polymer molecular dynamics. J Chem Phys 2014; 140:234116. [DOI: 10.1063/1.4883861] [Citation(s) in RCA: 133] [Impact Index Per Article: 13.3] [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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Chenel A, Mangaud E, Burghardt I, Meier C, Desouter-Lecomte M. Exciton dissociation at donor-acceptor heterojunctions: Dynamics using the collective effective mode representation of the spin-boson model. J Chem Phys 2014; 140:044104. [DOI: 10.1063/1.4861853] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
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37
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Huo P, Miller TF, Coker DF. Communication: Predictive partial linearized path integral simulation of condensed phase electron transfer dynamics. J Chem Phys 2013; 139:151103. [DOI: 10.1063/1.4826163] [Citation(s) in RCA: 59] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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38
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Kryvohuz M. On the derivation of semiclassical expressions for quantum reaction rate constants in multidimensional systems. J Chem Phys 2013; 138:244114. [DOI: 10.1063/1.4811221] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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39
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Huo P, Coker DF. Influence of environment induced correlated fluctuations in electronic coupling on coherent excitation energy transfer dynamics in model photosynthetic systems. J Chem Phys 2012; 136:115102. [DOI: 10.1063/1.3693019] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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40
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Menzeleev AR, Ananth N, Miller TF. Direct simulation of electron transfer using ring polymer molecular dynamics: comparison with semiclassical instanton theory and exact quantum methods. J Chem Phys 2011; 135:074106. [PMID: 21861555 DOI: 10.1063/1.3624766] [Citation(s) in RCA: 93] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The use of ring polymer molecular dynamics (RPMD) for the direct simulation of electron transfer (ET) reaction dynamics is analyzed in the context of Marcus theory, semiclassical instanton theory, and exact quantum dynamics approaches. For both fully atomistic and system-bath representations of condensed-phase ET, we demonstrate that RPMD accurately predicts both ET reaction rates and mechanisms throughout the normal and activationless regimes of the thermodynamic driving force. Analysis of the ensemble of reactive RPMD trajectories reveals the solvent reorganization mechanism for ET that is anticipated in the Marcus rate theory, and the accuracy of the RPMD rate calculation is understood in terms of its exact description of statistical fluctuations and its formal connection to semiclassical instanton theory for deep-tunneling processes. In the inverted regime of the thermodynamic driving force, neither RPMD nor a related formulation of semiclassical instanton theory capture the characteristic turnover in the reaction rate; comparison with exact quantum dynamics simulations reveals that these methods provide inadequate quantization of the real-time electronic-state dynamics in the inverted regime.
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Affiliation(s)
- Artur R Menzeleev
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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41
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Nan G, Shi Q, Shuai Z, Li Z. Influences of molecular packing on the charge mobility of organic semiconductors: from quantum charge transfer rate theory beyond the first-order perturbation. Phys Chem Chem Phys 2011; 13:9736-46. [DOI: 10.1039/c1cp00001b] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
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42
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Toutounji M. Algebraic approach to electronic spectroscopy and dynamics. J Chem Phys 2008; 128:164103. [DOI: 10.1063/1.2903748] [Citation(s) in RCA: 22] [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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43
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Gladkikh V, Burshtein AI, Rips I. Variation of the resonant transfer rate when passing from nonadiabatic to adiabatic electron transfer. J Phys Chem A 2007; 109:4983-8. [PMID: 16833848 DOI: 10.1021/jp044311y] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Two competing theories are used for bridging the gap between the nonadiabatic and the deeply adiabatic electron transfer between symmetric parabolic wells. For the high friction limit, a simple analytic interpolation is proposed as a reasonable alternative to them, well-fitted to the results of numerical simulations. It provides a continuous description of the electron transfer rate in the whole range of variation of the nonadiabatic coupling between the diabatic states. For lower friction, the original theories are used for the same goal. With an increase in coupling, the cusped barrier transforms into the parabolic one. Correspondingly, the pre-exponent of the Arrhenius transfer rate first increases with coupling, then levels off approaching the "dynamic solvent effect" plateau but finally reduces reaching the limit of the adiabatic Kramers theory for the parabolic barrier. These changes proceeding with a reduction in the particle separation affect significantly the spatial dependence of the total transfer rate. When approaching the contact distance, the exact rate becomes smaller than in the theory of dynamical solvent effects and much smaller than predicted by perturbation theory (golden rule), conventionally used in photochemistry and electrochemistry.
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Affiliation(s)
- V Gladkikh
- Chemical Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel
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44
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Basilevsky MV, Davidovich GV, Titov SV, Voronin AI. Non-Markovian modification of the golden rule rate expression. J Chem Phys 2006; 125:194513. [PMID: 17129129 DOI: 10.1063/1.2364498] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The reformulation of the standard golden rule approach considered in this paper for treating reactive tunneling reduces the computation of the reaction rate to a derivation of band shapes for energy levels of reactant and product states. This treatment is based on the assumption that the medium environment is actively involved as a partner in the energy exchange with the reactive subsystem but its reorganization effect is negligible. Starting from the quantum relaxation equation for the density matrix, the required band shapes are represented in terms of the spectral density function, exhibiting the continuum spectrum inherent to the interaction between the reactants and the medium in the total reactive system. The simplest Lorentzian spectral bands, obtained under Redfield approximation, proved to be unsatisfactory because they produced a divergent rate expression at low temperature. The problem is resolved by invoking a refined spectral band shape, which behaves as Lorentzian one at the band center but decays exponentially at its tails. The corresponding closed non-Markovian rate expression is derived and investigated taking as an example the photochemical H-transfer reaction between fluorene and acridine proceeding in the fluorene molecular crystal. The kinetics in this reactive system was thoroughly studied experimentally in a wide temperature range [B. Prass et al., Ber. Bunsenges. Phys. Chem. 102, 498 (1998)].
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Affiliation(s)
- M V Basilevsky
- Photochemistry Center, Russian Academy of Sciences, ul. Novatorov 7a, Moscow 119421, Russia.
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45
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Abstract
Trajectories of duration tau joining two points q(0) and q(1) in the configuration space of a classical system satisfy Hamilton's principle: they are stationary points of the classical action. The second variation (fluctuations) of the action around the stationary point signals whether the latter is or not a minimum and delivers the density in trajectory space around the points q(0) and q(1). This concept of density of paths is of great importance in semiclassical quantum theory, where it weights the contribution to the propagator from the single classical trajectories. In this paper, two algorithms based on the concepts of molecular dynamics simulation are introduced for computing the density of paths, also called van Vleck [Proc. Natl. Acad. Sci. U.S.A. 14, 178 (1928)] determinant. Examples for realistic systems are presented, together with a suggestion about possible applications in the field of rare events in physics and chemistry.
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Affiliation(s)
- Daniele Passerone
- Institute of Organic Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland.
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46
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Ishida T. Polarizable Solute in Polarizable and Flexible Solvents: Simulation Study of Electron Transfer Reaction Systems. J Phys Chem B 2005; 109:18558-64. [PMID: 16853390 DOI: 10.1021/jp052268o] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A polarizable solute model, based on the empirical valence bond approach, is developed and applied to electron transfer (ET) reactions in polarizable and flexible water solvents. The polarization effect is investigated in comparison with a nonpolarizable solute and solvent model. With free energy curves constructed by a molecular dynamics simulation, the activation energy barrier and the reorganization energy related to ET processes are investigated. The present simulation results show that the activation energy barrier becomes larger in the polarizable model than in the nonpolarizable model and that this makes the ET rate slower than that with the nonpolarizable model. It is shown that the effect of the electronic energy difference of solute molecule on free energy profiles is remarkable and that, corresponding to this effect, the reorganization energy is significantly modified. These results indicate that the process of solvent polarization by the polarized solute to enhance the solute-solvent interaction is a key factor and that treating the polarization of both solute and solvent at the same time is essential. Also, the polarization effect on the diffusive motion of the solute molecule in the polarization solvent is studied. The polarized solute molecule shows slower diffusive motion compared with that in the nonpolarizable model.
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Affiliation(s)
- Tateki Ishida
- Department of Computational Molecular Science, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan
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47
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Abstract
We compute the quantum rate constant based on two extended stationary phase approximations to the imaginary-time formulation of the quantum rate theory. The optimized stationary phase approximation to the imaginary-time flux-flux correlation function employs the optimized quadratic reference system to overcome the inaccuracy of the quadratic expansion in the standard stationary phase approximation, and yields favorable agreements with instanton results for both adiabatic and nonadiabatic processes in dissipative and nondissipative systems. The integrated stationary phase approximation to the two-dimensional barrier free energy is particularly useful for adiabatic processes and demonstrates consistent results with the imaginary-time flux-flux correlation function approach. Our stationary phase methods do not require calculation of tunneling paths or stability matrices, and work equally well in the high-temperature and the low-temperature regimes. The numerical results suggest their general applicability for calibration of imaginary-time methods and for the calculation of quantum rate constants in systems with a large number of degrees of freedom.
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Affiliation(s)
- Shilong Yang
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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48
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Abstract
Variational approach based on the diabatic variational transition state theory optimization is extended and applied to the calculation of the radiationless transition rate for asymmetric high-barrier normal and inverted crossings. Scaling argument is employed to derive an analytic expression for the renormalized frequency as a function of the asymmetry of the crossing and of the dissipation strength for the particular case of Ohmic dissipation (Debye relaxation). The effect of the asymmetry of the crossing on the physical parameters and on the radiationless transition rate is explored. The effective adiabaticity parameter increases with the increasing asymmetry of the crossing in the normal region and decreases with the increasing asymmetry in the inverted region. The physical behavior of the radiationless transition rate in the normal and inverted regions is qualitatively different in the strong dissipation (Smoluchowski) limit. In the inverted region the rate exhibits stretched exponential decay as a function of the dissipation strength reflecting adiabatic suppression in the strong dissipation limit. The accuracy of the approach decreases with the increasing (decreasing) asymmetry of the crossing in the normal (inverted) region and breaks down in the activationless case.
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Affiliation(s)
- Ilya Rips
- Department of Sciences, Holon Academic Institute of Technology, Holon 58102, Israel.
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Liao JL, Voth GA. Numerical approaches for computing nonadiabatic electron transfer rate constants. J Chem Phys 2002. [DOI: 10.1063/1.1474584] [Citation(s) in RCA: 8] [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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50
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Jang S, Cao J. Nonadiabatic instanton calculation of multistate electron transfer reaction rate: Interference effects in three and four states systems. J Chem Phys 2001. [DOI: 10.1063/1.1371262] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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