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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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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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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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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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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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Fang JH, Fan WB, Yang H, Song JN, Li YL. Rate coefficients and kinetic isotope effects of Cl+XCl→XCl+Cl (X=H, D, Mu) reactions from ring polymer molecular dynamics. CHINESE J CHEM PHYS 2021. [DOI: 10.1063/1674-0068/cjcp2007117] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Jun-hua Fang
- Department of Chemistry, Shanghai University, Shanghai 200444, China
| | - Wen-bin Fan
- Department of Physics, International Center for Quantum and Molecular Structures, and Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University, Shanghai 200444, China
| | - Hui Yang
- Department of Physics, International Center for Quantum and Molecular Structures, and Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University, Shanghai 200444, China
| | - Jia-ning Song
- Department of Physics, International Center for Quantum and Molecular Structures, and Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University, Shanghai 200444, China
| | - Yong-le Li
- Department of Physics, International Center for Quantum and Molecular Structures, and Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University, Shanghai 200444, China
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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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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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Campos-Gonzalez-Angulo JA, Yuen-Zhou J. Polaritonic normal modes in transition state theory. J Chem Phys 2020; 152:161101. [DOI: 10.1063/5.0007547] [Citation(s) in RCA: 43] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Affiliation(s)
| | - Joel Yuen-Zhou
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
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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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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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