1
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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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2
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Richardson JO. Nonadiabatic Tunneling in Chemical Reactions. J Phys Chem Lett 2024:7387-7397. [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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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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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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5
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Upadhyayula S, Pollak E. Uniform Semiclassical Instanton Rate Theory. J Phys Chem Lett 2023; 14:9892-9899. [PMID: 37906954 PMCID: PMC10641875 DOI: 10.1021/acs.jpclett.3c02779] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2023] [Revised: 10/17/2023] [Accepted: 10/19/2023] [Indexed: 11/02/2023]
Abstract
The instanton expression for the thermal transmission probability through a one-dimensional barrier is derived by using the uniform semiclassical energy-dependent transmission coefficient of Kemble. The resulting theory does not diverge at the "crossover temperature" but changes smoothly. The temperature-dependent energy of the instanton is the same as the barrier height when ℏβω‡ = π and not 2π as in the "standard" instanton theory. The concept of a crossover temperature between tunneling and thermal activation, based on the divergence of the instanton rate, is obsolete. The theory is improved by assuring that at high energy when the energy-dependent transmission coefficient approaches unity the integrand decays exponentially as dictated by the Boltzmann factor and not as a Gaussian. This ensures that at sufficiently high temperatures the uniform theory reduces to the classical. Application to Eckart barriers demonstrates that the uniform theory provides a good estimate of the numerically exact result over the whole temperature range.
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Affiliation(s)
- Sameernandan Upadhyayula
- Chemical and Biological Physics
Department Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Eli Pollak
- Chemical and Biological Physics
Department Weizmann Institute of Science, Rehovoth 76100, Israel
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6
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Mulvihill CR, Georgievskii Y, Klippenstein SJ. Quantum and anharmonic effects in non-adiabatic transition state theory. J Chem Phys 2023; 159:174104. [PMID: 37916591 DOI: 10.1063/5.0168612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Accepted: 09/25/2023] [Indexed: 11/03/2023] Open
Abstract
Quantitative descriptions of non-adiabatic transition rates at intermediate temperatures are challenging due to the simultaneous importance of quantum and anharmonic effects. In this paper, the interplay between quantum effects-for motion across or along the seam of crossing-and anharmonicity in the seam potential is considered within the weak coupling limit. The well-known expression for quantized 1-D motion across the seam (i.e., tunneling) in the linear terms approximation is derived in the thermal domain using the Lagrangian formalism, which is then applied to the case when tunneling is distributed along the seam of crossing (treating motion along the seam classically). For high-frequency quantum modes, a vibrationally adiabatic (VA) approach is developed that introduces to the non-adiabatic rate constant a factor associated with high-frequency wavefunction overlap; this approach treats the high-frequency motion along the seam quantum mechanically. To test these methodologies, the reaction N2O ↔ N2 + O(3P) was chosen. CCSD(T)-F12b/cc-pVTZ-F12 explorations of the 3A'-1A' seam of N2O revealed that seam anharmonicity has a strong effect on the rate constant (a factor of ∼20 at 2000 K). Several quantum effects were found to be significant at intermediate/lower temperatures, including the quantum N-N vibration that was coupled with seam anharmonicity using the VA approach. Finally, a 1-D approximation to non-adiabatic instanton theory is presented to estimate the validity limit of the linear terms model at low temperatures (∼250 K for N2O). We recommend that the assumptions built into many statistical theories for non-adiabatic reactions-harmonic behavior, classical motion, linear terms, and weak coupling-should be verified on a case-by-case basis.
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Affiliation(s)
- Clayton R Mulvihill
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Yuri Georgievskii
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Stephen J Klippenstein
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
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7
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Fang W, Heller ER, Richardson JO. Competing quantum effects in heavy-atom tunnelling through conical intersections. Chem Sci 2023; 14:10777-10785. [PMID: 37829019 PMCID: PMC10566476 DOI: 10.1039/d3sc03706a] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 09/07/2023] [Indexed: 10/14/2023] Open
Abstract
Thermally activated chemical reactions are typically understood in terms of overcoming potential-energy barriers. However, standard rate theories break down in the presence of a conical intersection (CI) because these processes are inherently nonadiabatic, invalidating the Born-Oppenheimer approximation. Moreover, CIs give rise to intricate nuclear quantum effects such as tunnelling and the geometric phase, which are neglected by standard trajectory-based simulations and remain largely unexplored in complex molecular systems. We present new semiclassical transition-state theories based on an extension of golden-rule instanton theory to describe nonadiabatic tunnelling through CIs and thus provide an intuitive picture for the reaction mechanism. We apply the method in conjunction with first-principles electronic-structure calculations to the electron transfer in the bis(methylene)-adamantyl cation. Our study reveals a strong competition between heavy-atom tunnelling and geometric-phase effects.
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Affiliation(s)
- Wei Fang
- Department of Chemistry, Fudan University Shanghai 200438 P. R. China
- 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
| | - Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zürich 8093 Zürich Switzerland
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8
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Heller ER, Richardson JO. Heavy‐Atom Quantum Tunnelling in Spin Crossovers of Nitrenes**. Angew Chem Int Ed Engl 2022; 61:e202206314. [PMID: 35698730 PMCID: PMC9540336 DOI: 10.1002/anie.202206314] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Indexed: 01/01/2023]
Abstract
We simulate two recent matrix‐isolation experiments at cryogenic temperatures, in which a nitrene undergoes spin crossover from its triplet state to a singlet state via quantum tunnelling. We detail the failure of the commonly applied weak‐coupling method (based on a linear approximation of the potentials) in describing these deep‐tunnelling reactions. The more rigorous approach of semiclassical golden‐rule instanton theory in conjunction with double‐hybrid density‐functional theory and multireference perturbation theory does, however, provide rate constants and kinetic isotope effects in good agreement with experiment. In addition, these calculations locate the optimal tunnelling pathways, which provide a molecular picture of the reaction mechanism. The reactions involve substantial heavy‐atom quantum tunnelling of carbon, nitrogen and oxygen atoms, which unexpectedly even continues to play a role 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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Lawrence JE, Richardson JO. Improved microcanonical instanton theory. Faraday Discuss 2022; 238:204-235. [PMID: 35929848 DOI: 10.1039/d2fd00063f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Canonical (thermal) instanton theory is now routinely applicable to complex gas-phase reactions and allows for the accurate description of tunnelling in highly non-separable systems. Microcanonical instanton theory is by contrast far less well established. Here, we demonstrate that the best established microcanonical theory [S. Chapman, B. C. Garrett and W. H. Miller, J. Chem. Phys., 1975, 63, 2710-2716], fails to accurately describe the deep-tunnelling regime for systems where the frequencies of the orthogonal modes change rapidly along the instanton path. By taking a first principles approach to the derivation of microcanonical instanton theory, we obtain an improved method, which accurately recovers the thermal instanton rate when integrated over energy. The resulting theory also correctly recovers the separable limit and can be thought of as an instanton generalisation of Rice-Ramsperger-Kassel-Marcus (RRKM) theory. When combined with the density-of-states approach [W. Fang, P. Winter and J. O. Richardson, J. Chem. Theory Comput., 2021, 17, 40-55], this new method can be straightforwardly applied to real molecular systems.
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10
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Heller ER, Richardson JO. Heavy‐Atom Quantum Tunnelling in Spin Crossovers of Nitrenes. Angew Chem Int Ed Engl 2022. [DOI: 10.1002/ange.202206314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Eric R Heller
- Eidgenossische Technische Hochschule Zurich Lab. Physical Chemistry SWITZERLAND
| | - Jeremy O Richardson
- Eidgenössische Technische Hochschule Zürich Lab. Physical Chemistry Vladimir-Prelog-Weg 2 8093 Zurich SWITZERLAND
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11
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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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12
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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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13
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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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14
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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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15
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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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16
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Ranya S, Ananth N. Multistate ring polymer instantons and nonadiabatic reaction rates. J Chem Phys 2020; 152:114112. [DOI: 10.1063/1.5132807] [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)
- Srinath Ranya
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Nandini Ananth
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
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17
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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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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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Vaillant CL, Thapa MJ, Vaníček J, Richardson JO. Semiclassical analysis of the quantum instanton approximation. J Chem Phys 2019; 151:144111. [DOI: 10.1063/1.5123800] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Christophe L. Vaillant
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Manish J. Thapa
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Jiří Vaníček
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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20
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Lawrence JE, Fletcher T, Lindoy LP, Manolopoulos DE. On the calculation of quantum mechanical electron transfer rates. J Chem Phys 2019; 151:114119. [DOI: 10.1063/1.5116800] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [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
| | - Theo Fletcher
- Department of Chemistry, University of Oxford, Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ, United Kingdom
| | - Lachlan P. Lindoy
- 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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21
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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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22
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Löhle A, Kästner J. Calculation of Reaction Rate Constants in the Canonical and Microcanonical Ensemble. J Chem Theory Comput 2018; 14:5489-5498. [DOI: 10.1021/acs.jctc.8b00565] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Andreas Löhle
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart,Germany
| | - Johannes Kästner
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart,Germany
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Jensen KT, Benson RL, Cardamone S, Thom AJW. Modeling Electron Transfers Using Quasidiabatic Hartree–Fock States. J Chem Theory Comput 2018; 14:4629-4639. [DOI: 10.1021/acs.jctc.8b00379] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Kristopher T. Jensen
- Department of Chemistry, University of Cambridge, Lensfield Rd, Cambridge, CB2 1TN, UK
| | - Raz L. Benson
- Department of Chemistry, University of Cambridge, Lensfield Rd, Cambridge, CB2 1TN, UK
| | - Salvatore Cardamone
- Department of Chemistry, University of Cambridge, Lensfield Rd, Cambridge, CB2 1TN, UK
| | - Alex J. W. Thom
- Department of Chemistry, University of Cambridge, Lensfield Rd, Cambridge, CB2 1TN, UK
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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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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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Cvitaš MT. Quadratic String Method for Locating Instantons in Tunneling Splitting Calculations. J Chem Theory Comput 2018; 14:1487-1500. [DOI: 10.1021/acs.jctc.7b00881] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Marko T. Cvitaš
- Department of Physical Chemistry, Ruđer Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia
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29
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An analysis of nonadiabatic ring-polymer molecular dynamics and its application to vibronic spectra. Chem Phys 2017. [DOI: 10.1016/j.chemphys.2016.09.036] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Richardson JO. Derivation of instanton rate theory from first principles. J Chem Phys 2016; 144:114106. [DOI: 10.1063/1.4943866] [Citation(s) in RCA: 67] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jeremy O. Richardson
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom and Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstr. 7, 91058 Erlangen, Germany
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31
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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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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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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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