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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. [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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2
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Fay TP. Extending non-adiabatic rate theory to strong electronic couplings in the Marcus inverted regime. J Chem Phys 2024; 161:014101. [PMID: 38949594 DOI: 10.1063/5.0218653] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2024] [Accepted: 06/12/2024] [Indexed: 07/02/2024] Open
Abstract
Electron transfer reactions play an essential role in many chemical and biological processes. Fermi's golden rule (GR), which assumes that the coupling between electronic states is small, has formed the foundation of electron transfer rate theory; however, in short range electron/energy transfer reactions, this coupling can become very large, and, therefore, Fermi's GR fails to make even qualitatively accurate rate predictions. In this paper, I present a simple modified GR theory to describe electron transfer in the Marcus inverted regime at arbitrarily large electronic coupling strengths. This theory is based on an optimal global rotation of the diabatic states, which makes it compatible with existing methods for calculating GR rates that can account for nuclear quantum effects with anharmonic potentials. Furthermore, the optimal GR (OGR) theory can also be combined with analytic theories for non-adiabatic rates, such as Marcus theory and Marcus-Levich-Jortner theory, offering clear physical insights into strong electronic coupling effects in non-adiabatic processes. OGR theory is also tested on a large set of spin-boson models and an anharmonic model against exact quantum dynamics calculations, where it performs well, correctly predicting rate turnover at large coupling strengths. Finally, an example application to a boron-dipyrromethane-anthracene photosensitizer reveals that strong coupling effects inhibit excited state charge recombination in this system, reducing the rate of this process by a factor of 4. Overall, OGR theory offers a new approach to calculating electron transfer rates at strong couplings, offering new physical insights into a range of non-adiabatic processes.
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Affiliation(s)
- Thomas P Fay
- Institut de Chimie Radicalaire, Aix-Marseille Université, Campus de Saint-Jérôme, Av. Esc. Normandie Niemen, 13397 Marseille, France
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3
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Lawrence JE, Mannouch JR, Richardson JO. A size-consistent multi-state mapping approach to surface hopping. J Chem Phys 2024; 160:244112. [PMID: 38940540 DOI: 10.1063/5.0208575] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2024] [Accepted: 06/05/2024] [Indexed: 06/29/2024] Open
Abstract
We develop a multi-state generalization of the recently proposed mapping approach to surface hopping (MASH) for the simulation of electronically nonadiabatic dynamics. This new approach extends the original MASH method to be able to treat systems with more than two electronic states. It differs from previous approaches in that it is size consistent and rigorously recovers the original two-state MASH in the appropriate limits. We demonstrate the accuracy of the method by applying it to a series of model systems for which exact benchmark results are available, and we find that the method is well suited to the simulation of photochemical relaxation processes.
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Affiliation(s)
- Joseph E Lawrence
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland
- Simons Center for Computational Physical Chemistry, New York University, New York, New York 10003, USA
- Department of Chemistry, New York University, New York, New York 10003, USA
| | - Jonathan R Mannouch
- Hamburg Center for Ultrafast Imaging, Universität Hamburg and the Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland
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4
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Fay TP, Limmer DT. Unraveling the mechanisms of triplet state formation in a heavy-atom free photosensitizer. Chem Sci 2024; 15:6726-6737. [PMID: 38725521 PMCID: PMC11077524 DOI: 10.1039/d4sc01369g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2024] [Accepted: 03/29/2024] [Indexed: 05/12/2024] Open
Abstract
Triplet excited state generation plays a pivotal role in photosensitizers, however the reliance on transition metals and heavy atoms can limit the utility of these systems. In this study, we demonstrate that an interplay of competing quantum effects controls the high triplet quantum yield in a prototypical boron dipyrromethene-anthracene (BD-An) donor-acceptor dyad photosensitizer, which is only captured by an accurate treatment of both inner and outer sphere reorganization energies. Our ab initio-derived model provides excellent agreement with experimentally measured spectra, triplet yields and excited state kinetic data, including the triplet lifetime. We find that rapid triplet state formation occurs primarily via high-energy triplet states through both spin-orbit coupled charge transfer and El-Sayed's rule breaking intersystem crossing, rather than direct spin-orbit coupled charge transfer to the lowest lying triplet state. Our calculations also reveal that competing effects of nuclear tunneling, electronic state recrossing, and electronic polarizability dictate the rate of non-productive ground state recombination. This study sheds light on the quantum effects driving efficient triplet formation in the BD-An system, and offers a promising simulation methodology for diverse photochemical systems.
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Affiliation(s)
- Thomas P Fay
- Department of Chemistry, University of California Berkeley CA 94720 USA
| | - David T Limmer
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Kavli Energy Nanoscience Institute Berkeley CA 94720 USA
- Chemical Science Division Lawrence Berkeley National Laboratory Berkeley CA 94720 USA
- Material Science Division Lawrence Berkeley National Laboratory Berkeley CA 94720 USA
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5
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Lawrence JE, Mannouch JR, Richardson JO. Recovering Marcus Theory Rates and Beyond without the Need for Decoherence Corrections: The Mapping Approach to Surface Hopping. J Phys Chem Lett 2024; 15:707-716. [PMID: 38214476 PMCID: PMC10823533 DOI: 10.1021/acs.jpclett.3c03197] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Revised: 12/22/2023] [Accepted: 01/05/2024] [Indexed: 01/13/2024]
Abstract
It is well-known that fewest-switches surface hopping (FSSH) fails to correctly capture the quadratic scaling of rate constants with diabatic coupling in the weak-coupling limit, as expected from Fermi's golden rule and Marcus theory. To address this deficiency, the most widely used approach is to introduce a "decoherence correction", which removes the inconsistency between the wave function coefficients and the active state. Here we investigate the behavior of a new nonadiabatic trajectory method, called the mapping approach to surface hopping (MASH), on systems that exhibit an incoherent rate behavior. Unlike FSSH, MASH hops between active surfaces deterministically and can never have an inconsistency between the wave function coefficients and the active state. We show that MASH not only can describe rates for intermediate and strong diabatic coupling but also can accurately reproduce the results of Marcus theory in the golden-rule limit, without the need for a decoherence correction. MASH is therefore a significant improvement over FSSH in the simulation of nonadiabatic reactions.
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Affiliation(s)
- Joseph E. Lawrence
- Department
of Chemistry and Applied Biosciences, ETH
Zurich, 8093 Zurich, Switzerland
| | - Jonathan R. Mannouch
- Hamburg
Center for Ultrafast Imaging, Universität
Hamburg and Max Planck Institute for the Structure and Dynamics of
Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Jeremy O. Richardson
- Department
of Chemistry and Applied Biosciences, ETH
Zurich, 8093 Zurich, Switzerland
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6
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Anderson MC, Schile AJ, Limmer DT. Nonadiabatic transition paths from quantum jump trajectories. J Chem Phys 2022; 157:164105. [DOI: 10.1063/5.0102891] [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
We present a means of studying rare reactive pathways in open quantum systems using transition path theory and ensembles of quantum jump trajectories. This approach allows for the elucidation of reactive paths for dissipative, nonadiabatic dynamics when the system is embedded in a Markovian environment. We detail the dominant pathways and rates of thermally activated processes and the relaxation pathways and photoyields following vertical excitation in a minimal model of a conical intersection. We find that the geometry of the conical intersection affects the electronic character of the transition state as defined through a generalization of a committor function for a thermal barrier crossing event. Similarly, the geometry changes the mechanism of relaxation following a vertical excitation. Relaxation in models resulting from small diabatic coupling proceeds through pathways dominated by pure dephasing, while those with large diabatic coupling proceed through pathways limited by dissipation. The perspective introduced here for the nonadiabatic dynamics of open quantum systems generalizes classical notions of reactive paths to fundamentally quantum mechanical processes.
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Affiliation(s)
- Michelle C. Anderson
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Addison J. Schile
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - David T. Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Kavli Energy NanoSciences Institute, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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7
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Runeson JE, Lawrence JE, Mannouch JR, Richardson JO. Explaining the Efficiency of Photosynthesis: Quantum Uncertainty or Classical Vibrations? J Phys Chem Lett 2022; 13:3392-3399. [PMID: 35404611 PMCID: PMC9036581 DOI: 10.1021/acs.jpclett.2c00538] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2022] [Accepted: 04/01/2022] [Indexed: 06/14/2023]
Abstract
Photosynthetic organisms are known to use a mechanism of vibrationally assisted exciton energy transfer to efficiently harvest energy from light. The importance of quantum effects in this mechanism is a long-standing topic of debate, which has traditionally focused on the role of excitonic coherences. Here, we address another recent claim: that the efficient energy transfer in the Fenna-Matthews-Olson complex relies on nuclear quantum uncertainty and would not function if the vibrations were classical. We present a counter-example to this claim, showing by trajectory-based simulations that a description in terms of quantum electrons and classical nuclei is indeed sufficient to describe the funneling of energy to the reaction center. We analyze and compare these findings to previous classical-nuclear approximations that predicted the absence of an energy funnel and conclude that the key difference and the reason for the discrepancy is the ability of the trajectories to properly account for Newton's third law.
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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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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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