1
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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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2
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Sayer T, Montoya-Castillo A. Generalized quantum master equations can improve the accuracy of semiclassical predictions of multitime correlation functions. J Chem Phys 2024; 161:011101. [PMID: 38949578 DOI: 10.1063/5.0219205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2024] [Accepted: 06/12/2024] [Indexed: 07/02/2024] Open
Abstract
Multitime quantum correlation functions are central objects in physical science, offering a direct link between the experimental observables and the dynamics of an underlying model. While experiments such as 2D spectroscopy and quantum control can now measure such quantities, the accurate simulation of such responses remains computationally expensive and sometimes impossible, depending on the system's complexity. A natural tool to employ is the generalized quantum master equation (GQME), which can offer computational savings by extending reference dynamics at a comparatively trivial cost. However, dynamical methods that can tackle chemical systems with atomistic resolution, such as those in the semiclassical hierarchy, often suffer from poor accuracy, limiting the credence one might lend to their results. By combining work on the accuracy-boosting formulation of semiclassical memory kernels with recent work on the multitime GQME, here we show for the first time that one can exploit a multitime semiclassical GQME to dramatically improve both the accuracy of coarse mean-field Ehrenfest dynamics and obtain orders of magnitude efficiency gains.
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Affiliation(s)
- Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
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3
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Bañuelos JL, Borguet E, Brown GE, Cygan RT, DeYoreo JJ, Dove PM, Gaigeot MP, Geiger FM, Gibbs JM, Grassian VH, Ilgen AG, Jun YS, Kabengi N, Katz L, Kubicki JD, Lützenkirchen J, Putnis CV, Remsing RC, Rosso KM, Rother G, Sulpizi M, Villalobos M, Zhang H. Oxide- and Silicate-Water Interfaces and Their Roles in Technology and the Environment. Chem Rev 2023; 123:6413-6544. [PMID: 37186959 DOI: 10.1021/acs.chemrev.2c00130] [Citation(s) in RCA: 19] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Interfacial reactions drive all elemental cycling on Earth and play pivotal roles in human activities such as agriculture, water purification, energy production and storage, environmental contaminant remediation, and nuclear waste repository management. The onset of the 21st century marked the beginning of a more detailed understanding of mineral aqueous interfaces enabled by advances in techniques that use tunable high-flux focused ultrafast laser and X-ray sources to provide near-atomic measurement resolution, as well as by nanofabrication approaches that enable transmission electron microscopy in a liquid cell. This leap into atomic- and nanometer-scale measurements has uncovered scale-dependent phenomena whose reaction thermodynamics, kinetics, and pathways deviate from previous observations made on larger systems. A second key advance is new experimental evidence for what scientists hypothesized but could not test previously, namely, interfacial chemical reactions are frequently driven by "anomalies" or "non-idealities" such as defects, nanoconfinement, and other nontypical chemical structures. Third, progress in computational chemistry has yielded new insights that allow a move beyond simple schematics, leading to a molecular model of these complex interfaces. In combination with surface-sensitive measurements, we have gained knowledge of the interfacial structure and dynamics, including the underlying solid surface and the immediately adjacent water and aqueous ions, enabling a better definition of what constitutes the oxide- and silicate-water interfaces. This critical review discusses how science progresses from understanding ideal solid-water interfaces to more realistic systems, focusing on accomplishments in the last 20 years and identifying challenges and future opportunities for the community to address. We anticipate that the next 20 years will focus on understanding and predicting dynamic transient and reactive structures over greater spatial and temporal ranges as well as systems of greater structural and chemical complexity. Closer collaborations of theoretical and experimental experts across disciplines will continue to be critical to achieving this great aspiration.
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Affiliation(s)
- José Leobardo Bañuelos
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, United States
| | - Eric Borguet
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States
| | - Gordon E Brown
- Department of Earth and Planetary Sciences, The Stanford Doerr School of Sustainability, Stanford University, Stanford, California 94305, United States
| | - Randall T Cygan
- Department of Soil and Crop Sciences, Texas A&M University, College Station, Texas 77843, United States
| | - James J DeYoreo
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Patricia M Dove
- Department of Geosciences, Department of Chemistry, Department of Materials Science and Engineering, Virginia Tech, Blacksburg, Virginia 24060, United States
| | - Marie-Pierre Gaigeot
- Université Paris-Saclay, Univ Evry, CNRS, LAMBE UMR8587, 91025 Evry-Courcouronnes, France
| | - Franz M Geiger
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Julianne M Gibbs
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2Canada
| | - Vicki H Grassian
- Department of Chemistry and Biochemistry, University of California, San Diego, California 92093, United States
| | - Anastasia G Ilgen
- Geochemistry Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Young-Shin Jun
- Department of Energy, Environmental & Chemical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, United States
| | - Nadine Kabengi
- Department of Geosciences, Georgia State University, Atlanta, Georgia 30303, United States
| | - Lynn Katz
- Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| | - James D Kubicki
- Department of Earth, Environmental & Resource Sciences, The University of Texas at El Paso, El Paso, Texas 79968, United States
| | - Johannes Lützenkirchen
- Karlsruher Institut für Technologie (KIT), Institut für Nukleare Entsorgung─INE, Eggenstein-Leopoldshafen 76344, Germany
| | - Christine V Putnis
- Institute for Mineralogy, University of Münster, Münster D-48149, Germany
| | - Richard C Remsing
- Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Kevin M Rosso
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Gernot Rother
- Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Marialore Sulpizi
- Department of Physics, Ruhr Universität Bochum, NB6, 65, 44780, Bochum, Germany
| | - Mario Villalobos
- Departamento de Ciencias Ambientales y del Suelo, LANGEM, Instituto De Geología, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico
| | - Huichun Zhang
- Department of Civil and Environmental Engineering, Case Western Reserve University, Cleveland, Ohio 44106, United States
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4
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Montoya-Castillo A, Markland TE. A derivation of the conditions under which bosonic operators exactly capture fermionic structure and dynamics. J Chem Phys 2023; 158:094112. [PMID: 36889969 DOI: 10.1063/5.0138664] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/15/2023] Open
Abstract
The dynamics of many-body fermionic systems are important in problems ranging from catalytic reactions at electrochemical surfaces to transport through nanojunctions and offer a prime target for quantum computing applications. Here, we derive the set of conditions under which fermionic operators can be exactly replaced by bosonic operators that render the problem amenable to a large toolbox of dynamical methods while still capturing the correct dynamics of n-body operators. Importantly, our analysis offers a simple guide on how one can exploit these simple maps to calculate nonequilibrium and equilibrium single- and multi-time correlation functions essential in describing transport and spectroscopy. We use this to rigorously analyze and delineate the applicability of simple yet effective Cartesian maps that have been shown to correctly capture the correct fermionic dynamics in select models of nanoscopic transport. We illustrate our analytical results with exact simulations of the resonant level model. Our work provides new insights as to when one can leverage the simplicity of bosonic maps to simulate the dynamics of many-electron systems, especially those where an atomistic representation of nuclear interactions becomes essential.
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Affiliation(s)
| | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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5
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Lyu N, Mulvihill E, Soley MB, Geva E, Batista VS. Tensor-Train Thermo-Field Memory Kernels for Generalized Quantum Master Equations. J Chem Theory Comput 2023; 19:1111-1129. [PMID: 36719350 DOI: 10.1021/acs.jctc.2c00892] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
The generalized quantum master equation (GQME) approach provides a rigorous framework for deriving the exact equation of motion for any subset of electronic reduced density matrix elements (e.g., the diagonal elements). In the context of electronic dynamics, the memory kernel and inhomogeneous term of the GQME introduce the implicit coupling to nuclear motion and dynamics of electronic density matrix elements that are projected out (e.g., the off-diagonal elements), allowing for efficient quantum dynamics simulations. Here, we focus on benchmark quantum simulations of electronic dynamics in a spin-boson model system described by various types of GQMEs. Exact memory kernels and inhomogeneous terms are obtained from short-time quantum-mechanically exact tensor-train thermo-field dynamics (TT-TFD) simulations and are compared with those obtained from an approximate linearized semiclassical method, allowing for assessment of the accuracy of these approximate memory kernels and inhomogeneous terms. Moreover, we have analyzed the computational cost of the full and reduced-dimensionality GQMEs. The scaling of the computational cost is dependent on several factors, sometimes with opposite scaling trends. The TT-TFD memory kernels can provide insights on the main sources of inaccuracies of GQME approaches when combined with approximate input methods and pave the road for the development of quantum circuits that implement GQMEs on digital quantum computers.
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Affiliation(s)
- Ningyi Lyu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Ellen Mulvihill
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Micheline B Soley
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States.,Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States.,Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States.,Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
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6
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Sayer T, Montoya-Castillo A. Compact and complete description of non-Markovian dynamics. J Chem Phys 2023; 158:014105. [PMID: 36610963 DOI: 10.1063/5.0132614] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
Generalized master equations provide a theoretically rigorous framework to capture the dynamics of processes ranging from energy harvesting in plants and photovoltaic devices to qubit decoherence in quantum technologies and even protein folding. At their center is the concept of memory. The explicit time-nonlocal description of memory is both protracted and elaborate. When physical intuition is at a premium, one would desire a more compact, yet complete, description. Here, we demonstrate how and when the time-convolutionless formalism constitutes such a description. In particular, by focusing on the dissipative dynamics of the spin-boson and Frenkel exciton models, we show how to: easily construct the time-local generator from reference reduced dynamics, elucidate the dependence of its existence on the system parameters and the choice of reduced observables, identify the physical origin of its apparent divergences, and offer analysis tools to diagnose their severity and circumvent their deleterious effects. We demonstrate that, when applicable, the time-local approach requires as little information as the more commonly used time-nonlocal scheme, with the important advantages of providing a more compact description, greater algorithmic simplicity, and physical interpretability. We conclude by introducing the discrete-time analog and a straightforward protocol to employ it in cases where the reference dynamics have limited resolution. The insights we present here offer the potential for extending the reach of dynamical methods, reducing both their cost and conceptual complexity.
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Affiliation(s)
- Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
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7
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Amati G, Saller MAC, Kelly A, Richardson JO. Quasiclassical approaches to the generalized quantum master equation. J Chem Phys 2022; 157:234103. [PMID: 36550031 DOI: 10.1063/5.0124028] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
The formalism of the generalized quantum master equation (GQME) is an effective tool to simultaneously increase the accuracy and the efficiency of quasiclassical trajectory methods in the simulation of nonadiabatic quantum dynamics. The GQME expresses correlation functions in terms of a non-Markovian equation of motion, involving memory kernels that are typically fast-decaying and can therefore be computed by short-time quasiclassical trajectories. In this paper, we study the approximate solution of the GQME, obtained by calculating the kernels with two methods: Ehrenfest mean-field theory and spin-mapping. We test the approaches on a range of spin-boson models with increasing energy bias between the two electronic levels and place a particular focus on the long-time limits of the populations. We find that the accuracy of the predictions of the GQME depends strongly on the specific technique used to calculate the kernels. In particular, spin-mapping outperforms Ehrenfest for all the systems studied. The problem of unphysical negative electronic populations affecting spin-mapping is resolved by coupling the method with the master equation. Conversely, Ehrenfest in conjunction with the GQME can predict negative populations, despite the fact that the populations calculated from direct dynamics are positive definite.
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Affiliation(s)
- Graziano Amati
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | | | - Aaron Kelly
- The Hamburg Center for Ultrafast Imaging, Universität Hamburg, Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, 22761 Hamburg, Germany
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8
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Mulvihill E, Geva E. Simulating the dynamics of electronic observables via reduced-dimensionality generalized quantum master equations. J Chem Phys 2022; 156:044119. [DOI: 10.1063/5.0078040] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Affiliation(s)
- Ellen Mulvihill
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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9
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Lai Y, Geva E. On simulating the dynamics of electronic populations and coherences via quantum master equations based on treating off-diagonal electronic coupling terms as a small perturbation. J Chem Phys 2021; 155:204101. [PMID: 34852488 DOI: 10.1063/5.0069313] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Quantum master equations provide a general framework for describing the dynamics of electronic observables within a complex molecular system. One particular family of such equations is based on treating the off-diagonal coupling terms between electronic states as a small perturbation within the framework of second-order perturbation theory. In this paper, we show how different choices of projection operators, as well as whether one starts out with the time-convolution or the time-convolutionless forms of the generalized quantum master equation, give rise to four different types of such off-diagonal quantum master equations (OD-QMEs), namely, time-convolution and time-convolutionless versions of a Pauli-type OD-QME for only the electronic populations and an OD-QME for the full electronic density matrix (including both electronic populations and coherences). The fact that those OD-QMEs are given in terms of the interaction picture makes it non-trivial to obtain Schrödinger picture electronic coherences from them. To address this, we also extend a procedure for extracting Schrödinger picture electronic coherences from interaction picture populations recently introduced by Trushechkin in the context of time-convolutionless Pauli-type OD-QME to the other three types of OD-QMEs. The performance of the aforementioned four types of OD-QMEs is explored in the context of the Garg-Onuchic-Ambegaokar benchmark model for charge transfer in the condensed phase across a relatively wide parameter range. The results show that time-convolution OD-QMEs can be significantly more accurate than their time-convolutionless counterparts, particularly in the case of Pauli-type OD-QMEs, and that rather accurate Schrödinger picture coherences can be obtained from interaction picture electronic inputs.
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Affiliation(s)
- Yifan Lai
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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10
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Brian D, Sun X. Generalized quantum master equation: A tutorial review and recent advances. CHINESE J CHEM PHYS 2021. [DOI: 10.1063/1674-0068/cjcp2109157] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Dominikus Brian
- Division of Arts and Sciences, NYU Shanghai, Shanghai 200122, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Department of Chemistry, New York University, New York 10003, USA
| | - Xiang Sun
- Division of Arts and Sciences, NYU Shanghai, Shanghai 200122, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Department of Chemistry, New York University, New York 10003, USA
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200241, China
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11
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Mulvihill E, Geva E. A Road Map to Various Pathways for Calculating the Memory Kernel of the Generalized Quantum Master Equation. J Phys Chem B 2021; 125:9834-9852. [PMID: 34424700 DOI: 10.1021/acs.jpcb.1c05719] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The generalized quantum master equation (GQME) provides a powerful framework for simulating electronic energy, charge, and coherence transfer dynamics in molecular systems. Within this framework, the effect of the nuclear degrees of freedom on the time evolution of the electronic reduced density matrix is fully captured by a memory kernel superoperator. However, the actual memory kernel depends on the choice of projection operator and is therefore not unique. Furthermore, calculating the memory kernel can be done in multiple ways that use different forms of projection-free inputs. Although the electronic dynamics is invariant to those choices when quantum-mechanically exact projection-free inputs are used, this is not the case when they are obtained via more feasible semiclassical or mixed quantum-classical approximate methods. Furthermore, the accuracy and numerical stability of the resulting electronic dynamics has been observed to be sensitive to the above-mentioned choices when approximate methods are used to calculate the projection-free inputs. In this article, we provide a systematic road map to 30 possible pathways for calculating the memory kernel and highlight how they are related as well as the ways in which they differ. We also compare the performance of different pathways in the context of the spin-boson benchmark model, with the projection-free inputs obtained via a mapping Hamiltonian linearized semiclassical method. In this case, we find that expressing the memory kernel with an exponential operator where the projection operator precedes the Liouvillian yields the most accurate and most numerically stable results.
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Affiliation(s)
- Ellen Mulvihill
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan48109, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan48109, United States
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12
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Santoro F, Green JA, Martinez-Fernandez L, Cerezo J, Improta R. Quantum and semiclassical dynamical studies of nonadiabatic processes in solution: achievements and perspectives. Phys Chem Chem Phys 2021; 23:8181-8199. [PMID: 33875988 DOI: 10.1039/d0cp05907b] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
We concisely review the main methodological approaches to model nonadiabatic dynamics in isotropic solutions and their applications. Three general classes of models are identified as the most used to include solvent effects in the simulations. The first model describes the solvent as a set of harmonic collective modes coupled to the solute degrees of freedom, and the second as a continuum, while the third explicitly includes solvent molecules in the calculations. The issues related to the use of these models in semiclassical and quantum dynamical simulations are discussed, as well as the main limitations and perspectives of each approach.
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Affiliation(s)
- Fabrizio Santoro
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR), SS di Pisa, Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy.
| | - James A Green
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Biostrutture e Bioimmagini (IBB-CNR), via Mezzocannone 16, I-80136 Napoli, Italy.
| | - Lara Martinez-Fernandez
- Departamento de Química, Facultad de Ciencias and Institute for Advanced Research in Chemistry (IADCHEM), Universidad Autónoma de Madrid, Campus de Excelencia UAM-CSIC, 28049 Madrid, Spain
| | - Javier Cerezo
- Departamento de Química, Facultad de Ciencias and Institute for Advanced Research in Chemistry (IADCHEM), Universidad Autónoma de Madrid, Campus de Excelencia UAM-CSIC, 28049 Madrid, Spain
| | - Roberto Improta
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Biostrutture e Bioimmagini (IBB-CNR), via Mezzocannone 16, I-80136 Napoli, Italy.
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13
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Cao S, Montoya-Castillo A, Wang W, Markland TE, Huang X. On the advantages of exploiting memory in Markov state models for biomolecular dynamics. J Chem Phys 2021; 153:014105. [PMID: 32640825 DOI: 10.1063/5.0010787] [Citation(s) in RCA: 31] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
Biomolecular dynamics play an important role in numerous biological processes. Markov State Models (MSMs) provide a powerful approach to study these dynamic processes by predicting long time scale dynamics based on many short molecular dynamics (MD) simulations. In an MSM, protein dynamics are modeled as a kinetic process consisting of a series of Markovian transitions between different conformational states at discrete time intervals (called "lag time"). To achieve this, a master equation must be constructed with a sufficiently long lag time to allow interstate transitions to become truly Markovian. This imposes a major challenge for MSM studies of proteins since the lag time is bound by the length of relatively short MD simulations available to estimate the frequency of transitions. Here, we show how one can employ the generalized master equation formalism to obtain an exact description of protein conformational dynamics both at short and long time scales without the time resolution restrictions imposed by the MSM lag time. Using a simple kinetic model, alanine dipeptide, and WW domain, we demonstrate that it is possible to construct these quasi-Markov State Models (qMSMs) using MD simulations that are 5-10 times shorter than those required by MSMs. These qMSMs only contain a handful of metastable states and, thus, can greatly facilitate the interpretation of mechanisms associated with protein dynamics. A qMSM opens the door to the study of conformational changes of complex biomolecules where a Markovian model with a few states is often difficult to construct due to the limited length of available MD simulations.
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Affiliation(s)
- Siqin Cao
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | | | - Wei Wang
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Xuhui Huang
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
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14
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Chatterjee S, Makri N. Real-Time Path Integral Methods, Quantum Master Equations, and Classical vs Quantum Memory. J Phys Chem B 2019; 123:10470-10482. [DOI: 10.1021/acs.jpcb.9b08429] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sambarta Chatterjee
- Department of Chemistry, University of Illinois, 505 South Mathews Avenue, Urbana, Illinois 61801, United States
| | - Nancy Makri
- Department of Chemistry, University of Illinois, 505 South Mathews Avenue, Urbana, Illinois 61801, United States
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15
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Pfalzgraff WC, Montoya-Castillo A, Kelly A, Markland TE. Efficient construction of generalized master equation memory kernels for multi-state systems from nonadiabatic quantum-classical dynamics. J Chem Phys 2019; 150:244109. [DOI: 10.1063/1.5095715] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- William C. Pfalzgraff
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
- Department of Chemistry, Chatham University, Pittsburgh, Pennsylvania 15232, USA
| | | | - Aaron Kelly
- Department of Chemistry, Dalhousie University, Halifax, Nova Scotia B3H 4R2, Canada
| | - Thomas E. Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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16
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Chowdhury SN, Huo P. State dependent ring polymer molecular dynamics for investigating excited nonadiabatic dynamics. J Chem Phys 2019; 150:244102. [DOI: 10.1063/1.5096276] [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)
- Sutirtha N. Chowdhury
- 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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17
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Kelly A. Mean field theory of thermal energy transport in molecular junctions. J Chem Phys 2019; 150:204107. [DOI: 10.1063/1.5089885] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Aaron Kelly
- Department of Chemistry, Dalhousie University, Halifax, Nova Scotia B3H 4R2, Canada
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18
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Agostini F, Curchod BFE. Different flavors of nonadiabatic molecular dynamics. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2019. [DOI: 10.1002/wcms.1417] [Citation(s) in RCA: 42] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Federica Agostini
- Laboratoire de Chimie Physique UMR 8000 CNRS/University Paris‐Sud Orsay France
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19
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Mandal A, Sandoval C. JS, Shakib FA, Huo P. Quasi-Diabatic Propagation Scheme for Direct Simulation of Proton-Coupled Electron Transfer Reaction. J Phys Chem A 2019; 123:2470-2482. [DOI: 10.1021/acs.jpca.9b00077] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Affiliation(s)
- Arkajit Mandal
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
| | - Juan S. Sandoval C.
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
| | - Farnaz A. Shakib
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
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20
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Amadei A, Aschi M. Theoretical-computational modeling of charge transfer and intersystem crossing reactions in complex chemical systems. RSC Adv 2018; 8:27900-27918. [PMID: 35542751 PMCID: PMC9083445 DOI: 10.1039/c8ra03900c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2018] [Accepted: 07/23/2018] [Indexed: 11/21/2022] Open
Abstract
In this paper we present a theoretical-computational methodology specifically aimed at describing processes involving internal conversion or intersystem crossing, from atomistic (semiclassical) simulations and, hence, very suitable for treating complex atomic-molecular systems. The core of the presented approach is the evaluation of the diabatic perturbed energy surfaces of a portion of the whole system, treated at the quantum level and therefore preventively selected, in semi-classical interaction with the atomic-molecular environment. Subsequently, the estimation of the coupling between the diabatic surfaces and the inclusion of the obtained observables within a properly designed kinetic model allows the reconstruction of the whole phenomenology directly comparable to the experimental (typically kinetic) data. Application to two systems has demonstrated that the proposed approach can represent a valuable tool, somewhat complementary to other methods based on explicit quantum-dynamical approaches, for the theoretical-computational investigations of large and complex atomic-molecular systems.
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Affiliation(s)
- Andrea Amadei
- Dipartimento di Scienze e Tecnologie Chimiche, Universita' di Roma 'Tor Vergata' Roma Italy +390672594905
| | - Massimiliano Aschi
- Dipartimento di Scienze Fisiche e Chimiche, Universita' di L'Aquila L'Aquila Italy +390862433775
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21
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Affiliation(s)
- Timothy J. H. Hele
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, USA
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22
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Montoya-Castillo A, Reichman DR. Approximate but accurate quantum dynamics from the Mori formalism. II. Equilibrium time correlation functions. J Chem Phys 2017; 146:084110. [DOI: 10.1063/1.4975388] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - David R. Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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23
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Mavros MG, Hait D, Van Voorhis T. Condensed phase electron transfer beyond the Condon approximation. J Chem Phys 2016; 145:214105. [DOI: 10.1063/1.4971166] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Michael G. Mavros
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
| | - Diptarka Hait
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
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24
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Montoya-Castillo A, Reichman DR. Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics. J Chem Phys 2016; 144:184104. [DOI: 10.1063/1.4948408] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Affiliation(s)
| | - David R. Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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25
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Kelly A, Montoya-Castillo A, Wang L, Markland TE. Generalized quantum master equations in and out of equilibrium: When can one win? J Chem Phys 2016; 144:184105. [DOI: 10.1063/1.4948612] [Citation(s) in RCA: 42] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Affiliation(s)
- Aaron Kelly
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | | | - Lu Wang
- Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Thomas E. Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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26
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White A, Tretiak S, Mozyrsky D. Coupled wave-packets for non-adiabatic molecular dynamics: a generalization of Gaussian wave-packet dynamics to multiple potential energy surfaces. Chem Sci 2016; 7:4905-4911. [PMID: 30155138 PMCID: PMC6018303 DOI: 10.1039/c6sc01319h] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2016] [Accepted: 04/21/2016] [Indexed: 12/24/2022] Open
Abstract
Coupled wave-packets for non-adiabatic dynamics is a new method for simulation of molecular dynamics on coupled potential energy surfaces, which efficiency and correctly accounts for decoherence and interferences effects.
Accurate simulation of the non-adiabatic dynamics of molecules in excited electronic states is key to understanding molecular photo-physical processes. Here we present a novel method, based on a semi-classical approximation, that is as efficient as the commonly used mean field Ehrenfest or ad hoc surface hopping methods and properly accounts for interference and decoherence effects. This novel method is an extension of Heller's thawed Gaussian wave-packet dynamics that includes coupling between potential energy surfaces. By studying several standard test problems we demonstrate that the accuracy of the method can be systematically improved while maintaining high efficiency. The method is suitable for investigating the role of quantum coherence in the non-adiabatic dynamics of many-atom molecules.
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Affiliation(s)
- Alexander White
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , NM , USA . ; ; .,Center for Nonlinear Studies , USA
| | - Sergei Tretiak
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , NM , USA . ; ; .,Center for Nonlinear Studies , USA.,Center for Integrated Nanotechnologies , USA
| | - Dmitry Mozyrsky
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , NM , USA . ; ;
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27
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Hele TJH, Ananth N. Deriving the exact nonadiabatic quantum propagator in the mapping variable representation. Faraday Discuss 2016; 195:269-289. [DOI: 10.1039/c6fd00106h] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and discrete electronic states. The resulting Liouvillian is a Moyal series that, when suitably approximated, can allow for the use of classical dynamics to efficiently model large systems. We demonstrate that different truncations of the exact Liouvillian lead to existing approximate semiclassical and mixed quantum–classical methods and we derive an associated error term for each method. Furthermore, by combining the imaginary-time path-integral representation of the Boltzmann operator with the exact Liouvillian, we obtain an analytic expression for thermal quantum real-time correlation functions. These results provide a rigorous theoretical foundation for the development of accurate and efficient classical-like dynamics to compute observables such as electron transfer reaction rates in complex quantized systems.
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Affiliation(s)
| | - Nandini Ananth
- Department of Chemistry and Chemical Biology
- Cornell University
- Ithaca
- USA
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