1
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Richardson JO. Nonadiabatic Tunneling in Chemical Reactions. J Phys Chem Lett 2024; 15:7387-7397. [PMID: 38995660 DOI: 10.1021/acs.jpclett.4c01098] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/13/2024]
Abstract
Quantum tunneling can have a dramatic effect on chemical reaction rates. In nonadiabatic reactions such as electron transfers or spin crossovers, nuclear tunneling effects can be even stronger than for adiabatic proton transfers. Ring-polymer instanton theory enables molecular simulations of tunneling in full dimensionality and has been shown to be far more reliable than commonly used separable approximations. First-principles instanton calculations predict significant nonadiabatic tunneling of heavy atoms even at room temperature and give excellent agreement with experimental measurements for the intersystem crossing of two nitrenes in cryogenic matrix isolation, the spin-forbidden relaxation of photoexcited thiophosgene in the gas phase, and singlet oxygen deactivation in water at ambient conditions. Finally, an outlook of further theoretical developments is discussed.
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Affiliation(s)
- Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland
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2
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Fang W, Zhu YC, Cheng Y, Hao YP, Richardson JO. Robust Gaussian Process Regression Method for Efficient Tunneling Pathway Optimization: Application to Surface Processes. J Chem Theory Comput 2024; 20:3766-3778. [PMID: 38708859 PMCID: PMC11099967 DOI: 10.1021/acs.jctc.4c00158] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2024] [Revised: 04/17/2024] [Accepted: 04/17/2024] [Indexed: 05/07/2024]
Abstract
Simulation of surface processes is a key part of computational chemistry that offers atomic-scale insights into mechanisms of heterogeneous catalysis, diffusion dynamics, and quantum tunneling phenomena. The most common theoretical approaches involve optimization of reaction pathways, including semiclassical tunneling pathways (called instantons). The computational effort can be demanding, especially for instanton optimizations with an ab initio electronic structure. Recently, machine learning has been applied to accelerate reaction-pathway optimization, showing great potential for a wide range of applications. However, previous methods still suffer from numerical and efficiency issues and were not designed for condensed-phase reactions. We propose an improved framework based on Gaussian process regression for general transformed coordinates, which has improved efficiency and numerical stability, and we propose a descriptor that combines internal and Cartesian coordinates suitable for modeling surface processes. We demonstrate with 11 instanton optimizations in three representative systems that the improved approach makes ab initio instanton optimization significantly cheaper, such that it becomes not much more expensive than a classical transition-state theory rate calculation.
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Affiliation(s)
- Wei Fang
- Department
of Chemistry, Shanghai Key Laboratory of Molecular Catalysis and Innovative
Materials, Fudan University, Shanghai 200438, P. R. China
- Laboratory
of Physical Chemistry, ETH Zürich, Zürich 8093, Switzerland
- State
Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical
Computational Chemistry, Dalian Institute
of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, P. R. China
| | - Yu-Cheng Zhu
- State
Key Laboratory for Artificial Microstructure and Mesoscopic Physics,
Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing 100871, China
| | - Yihan Cheng
- State
Key Laboratory for Artificial Microstructure and Mesoscopic Physics,
Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing 100871, China
| | - Yi-Ping Hao
- State
Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical
Computational Chemistry, Dalian Institute
of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, P. R. China
| | - Jeremy O. Richardson
- Department
of Chemistry and Applied Biosciences, ETH
Zürich, Zürich 8093, Switzerland
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3
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Lv D, Chen X, Jiang N, Wang G, Zeng X, Fang W, Li W, Zhou M. A rotational spectroscopy study of microsolvation effects on intramolecular proton transfer in trifluoroacetylacetone-(H 2O) 1-3. Phys Chem Chem Phys 2024; 26:12530-12536. [PMID: 38619876 DOI: 10.1039/d4cp01061b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/17/2024]
Abstract
Trifluoroacetylacetone (TFAA) has two enol forms, which can switch to each other via proton transfer. While much attention has been paid to their conformational preferences, the influence of microsolvation on regulating the proton position remains unexplored. Herein, we report the rotational spectra of trifluoroacetylacetone-(water)n (n = 1-3) investigated by chirped pulse Fourier transform microwave spectroscopy in the 2-8 GHz frequency range. Two conformers were identified for both TFAA-H2O and TFAA-(H2O)2, while only one conformer was characterized for TFAA-(H2O)3. The results indicate that water binding on the CH3 side stabilizes the enolF form, whereas water binding on the CF3 side stabilizes the enolH form. The enolF form predominates over the enolH form in these hydrated complexes, which contrasts with the fact that only enolH exists in isolated TFAA. EnolH becomes preferred only when water inserts itself into the intramolecular hydrogen bond. Instanton theory calculations reveal that the proton transfer reaction is dominated by quantum tunneling at low temperatures, leading to the stable existence of only one enol form in each configuration of the hydrated clusters.
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Affiliation(s)
- Dingding Lv
- Department of Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Fudan University, Songhu Rd. 2005, 200438 Shanghai, China.
| | - Xinlei Chen
- Department of Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Fudan University, Songhu Rd. 2005, 200438 Shanghai, China.
| | - Ningjing Jiang
- Department of Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Fudan University, Songhu Rd. 2005, 200438 Shanghai, China.
| | - Guanjun Wang
- Department of Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Fudan University, Songhu Rd. 2005, 200438 Shanghai, China.
| | - Xiaoqing Zeng
- Department of Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Fudan University, Songhu Rd. 2005, 200438 Shanghai, China.
| | - Wei Fang
- Department of Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Fudan University, Songhu Rd. 2005, 200438 Shanghai, China.
| | - Weixing Li
- Department of Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Fudan University, Songhu Rd. 2005, 200438 Shanghai, China.
| | - Mingfei Zhou
- Department of Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Fudan University, Songhu Rd. 2005, 200438 Shanghai, China.
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4
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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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5
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Claveau EE, Heller ER, Richardson JO, Miliordos E. Methane against Methanol: The Tortoise and the Hare of the Oxidation Race. J Phys Chem Lett 2023; 14:8749-8754. [PMID: 37738098 DOI: 10.1021/acs.jpclett.3c02274] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/24/2023]
Abstract
The selective partial oxidation of methane to methanol has been a major chemistry challenge over the past several decades. The reason for this is that the weaker C-H bond of the desired product (methanol) is readily activated by the same catalyst used to activate the stronger C-H bond of methane. Quantum chemical calculations reveal how hydrogen-bonding interactions with the catalyst as well as other electronic and geometric effects slow the unwanted methanol oxidation reaction. Thus, the oxidation of methane (the tortoise in Aesop's fable) becomes faster than methanol (Aesop's hare), increasing the selectivity toward the desired product. Activation barriers are calculated for two different mechanisms (2+2 and radical), and reaction rates for the oxidation of the two molecules are obtained using semiclassical instanton theory to include tunneling effects for the proton transfers. The tunneling effects are shown to accelerate all reactions substantially but do not dramatically affect the selectivity.
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Affiliation(s)
- Emily E Claveau
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849, United States
| | - Eric R Heller
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, United States
| | - Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
| | - Evangelos Miliordos
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849, United States
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6
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Suzuki K, Kanno M, Koseki S, Kono H. A Structure-Based Gaussian Expansion for Quantum Reaction Dynamics in Molecules: Application to Hydrogen Tunneling in Malonaldehyde. J Phys Chem A 2023; 127:4152-4165. [PMID: 37129441 DOI: 10.1021/acs.jpca.2c09088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
We developed an approximate method for quantum reaction dynamics simulations, namely, a structure-based Gaussian (SBG) expansion approach, where SBG bases for the expansion of the wave function Ψ, expressed by a product of single-atom Cartesian Gaussians centered at the positions of respective nuclei, are mainly placed around critical structures on reaction pathways such as on the intrinsic reaction coordinate (IRC) through a transition state. In the present approach, the "pseudo-lattice points" at which SBGs are deployed are selected in a perturbative manner so as to make moderate the expansion length. We first applied the SBG idea to a two-dimensional quadruple-well model and obtained accurate tunneling splitting values between the lowest four states. We then applied it to hydrogen tunneling in malonaldehyde and achieved a tunneling splitting of 27.1 cm-1 with only 875 SBGs at the MP2/6-31G(d,p) level of theory, in good agreement with 25 cm-1 by the more elaborate multiconfiguration time-dependent Hartree method. Reasonable results were also obtained for singly and doubly deuterated malonaldehyde. We analyzed the tunneling states by utilizing expansion coefficients of individual SBGs and found that 40-45% of the SBGs in Ψ are nonplanar structures and SBGs away from the IRC contribute a little to hydrogen transfer.
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Affiliation(s)
- Kazuma Suzuki
- Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
| | - Manabu Kanno
- Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
| | - Shiro Koseki
- Department of Chemistry, Graduate School of Science, Osaka Prefecture University, Osaka 599-8531, Japan
| | - Hirohiko Kono
- Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
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7
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Wang HD, Fu YL, Fu B, Fang W, Zhang DH. A highly accurate full-dimensional ab initio potential surface for the rearrangement of methylhydroxycarbene (H 3C-C-OH). Phys Chem Chem Phys 2023; 25:8117-8127. [PMID: 36876923 DOI: 10.1039/d3cp00312d] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/25/2023]
Abstract
We report here a full-dimensional machine learning global potential surface (PES) for the rearrangement of methylhydroxycarbene (H3C-C-OH, 1t). The PES is trained with the fundamental invariant neural network (FI-NN) method on 91 564 ab initio energies calculated at the UCCSD(T)-F12a/cc-pVTZ level of theory, covering three possible product channels. FI-NN PES has the correct symmetry properties with respect to permutation of four identical hydrogen atoms and is suitable for dynamics studies of the 1t rearrangement. The averaged root mean square error (RMSE) is 11.4 meV. Six important reaction pathways, as well as the energies and vibrational frequencies at the stationary geometries on these pathways are accurately preproduced by our FI-NN PES. To demonstrate the capacity of the PES, we calculated the rate coefficient of hydrogen migration in -CH3 (path A) and hydrogen migration of -OH (path B) with instanton theory on this PES. Our calculations predicted the half-life of 1t to be 95 min, which is excellent in agreement with experimental observations.
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Affiliation(s)
- Heng-Ding Wang
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China.
| | - Yan-Lin Fu
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China.
| | - Bina Fu
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China.
| | - Wei Fang
- Fudan University, Shanghai, 200032, China.
| | - Dong H Zhang
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China.
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8
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Jelenfi DP, Schneiker A, Tajti A, Magyarfalvi G, Tarczay G. Polyaromatic hydrocarbons with an imperfect aromatic system as catalysts of interstellar H 2 formation. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2142168] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Dávid P. Jelenfi
- Hevesy György PhD School of Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
- Institute of Chemistry, Laboratory of Theoretical Chemistry, ELTE – Eötvös Loránd University, Budapest, Hungary
| | - Anita Schneiker
- Hevesy György PhD School of Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
- Institute of Chemistry, Laboratory of Molecular Spectroscopy, ELTE – Eötvös Loránd University, Budapest, Hungary
| | - Attila Tajti
- Institute of Chemistry, Laboratory of Theoretical Chemistry, ELTE – Eötvös Loránd University, Budapest, Hungary
| | - Gábor Magyarfalvi
- Institute of Chemistry, Laboratory of Molecular Spectroscopy, ELTE – Eötvös Loránd University, Budapest, Hungary
| | - György Tarczay
- Institute of Chemistry, Laboratory of Molecular Spectroscopy, ELTE – Eötvös Loránd University, Budapest, Hungary
- MTA-ELTE Lendület Laboratory Astrochemistry Research Group, Budapest, Hungary
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9
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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] [Key Words] [Grants] [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 ChemistryETH Zürich8093ZürichSwitzerland
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10
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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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11
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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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12
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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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13
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Han E, Fang W, Stamatakis M, Richardson JO, Chen J. Quantum Tunnelling Driven H 2 Formation on Graphene. J Phys Chem Lett 2022; 13:3173-3181. [PMID: 35362977 DOI: 10.1021/acs.jpclett.2c00520] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
It is commonly believed that it is unfavorable for adsorbed H atoms on carbonaceous surfaces to form H2 without the help of incident H atoms. Using ring-polymer instanton theory to describe multidimensional tunnelling effects, combined with ab initio electronic structure calculations, we find that these quantum-mechanical simulations reveal a qualitatively different picture. Recombination of adsorbed H atoms, which was believed to be irrelevant at low temperature due to high barriers, is enabled by deep tunnelling, with reaction rates enhanced by tens of orders of magnitude. Furthermore, we identify a new path for H recombination that proceeds via multidimensional tunnelling but would have been predicted to be unfeasible by a simple one-dimensional description of the reaction. The results suggest that hydrogen molecule formation at low temperatures are rather fast processes that should not be ignored in experimental settings and natural environments with graphene, graphite, and other planar carbon segments.
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Affiliation(s)
- Erxun Han
- School of Physics, Peking University, Beijing 100871, China
- Interdisciplinary Institute of Light-Element Quantum Materials and Research Center for Light-Element Advanced Materials, Peking University, Beijing 100871, People's Republic of China
| | - Wei Fang
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, P. R. China
- Department of Chemistry, Fudan University, Shanghai 200438, China
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Michail Stamatakis
- Thomas Young Centre and Department of Chemical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
| | | | - Ji Chen
- School of Physics, Peking University, Beijing 100871, China
- Interdisciplinary Institute of Light-Element Quantum Materials and Research Center for Light-Element Advanced Materials, Peking University, Beijing 100871, People's Republic of China
- Frontiers Science Center for Nano-Optoelectronics, Peking University, Beijing 100871, People's Republic of China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, People's Republic of China
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14
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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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15
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Cheng YH, Zhu YC, Kang W, Li X, Fang W. Determination of concerted or stepwise mechanism of hydrogen tunneling from isotope effects: Departure between experiment and theory. J Chem Phys 2022; 156:124304. [DOI: 10.1063/5.0085010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Isotope substitution is an important experimental technique that offers deep insight into reaction mechanisms, as the measured kinetic isotope effects (KIEs) can be directly compared with theory. For multiple proton transfer processes, there are two types of mechanisms: stepwise transfer and concerted transfer. The Bell-Limbach model provides a simple theory to determine whether the proton transfer mechanism is stepwise or concerted from KIEs. Recent STM experiments have studied the proton switching process in water tetramers on NaCl(001). Theoretical studies predict that this process occurs via a concerted mechanism, however, the experimental KIEs resemble the Bell-Limbach model for stepwise tunneling, raising question on the underlying mechanism or the validity of the model. We study this system using ab initio instanton theory, and in addition to thermal rates, we also considered microcanonical rates, as well as tunneling splittings. Instanton theory predicts a concerted mechanism, and the KIEs for tunneling rates (both thermal and microcanonical) upon deuteration are consistent with the Bell-Limbach model for concerted tunneling, but could not explain the experiments. For tunneling splittings, partial and full deuteration changes the size of it in a similar fashion to how it changes the rates. We further examined the Bell-Limbach model in another system, porphycene, which has both stepwise and concerted tunneling pathways. The KIEs predicted by instanton theory are again consistent with the Bell-Limbach model. This study highlights differences between KIEs in stepwise and concerted tunneling, and the discrepancy between theory and recent STM experiments. New theory/experiments are desired to settle this problem.
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Affiliation(s)
| | | | - Wei Kang
- Center for Applied Physics and Technology, Peking University, China
| | | | - Wei Fang
- Dalian Institute of Chemical Physics, China
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16
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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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17
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Li SJ, Fang W, Richardson JO, Fang DC. Tunnelling assisted hydrogen elimination mechanisms of FeCl 3/TEMPO. Chem Commun (Camb) 2021; 58:565-568. [PMID: 34909806 DOI: 10.1039/d1cc06035j] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
Metal-TEMPO hybrids are a family of novel and promising catalysts for aerobic oxidation of alcohols, yet the underlying mechanisms have not been understood theoretically. Using density functional theory, we probe the hydrogen abstraction mechanisms of FeCl3/TEMPO on two characteristic substrates, 9,10-dihydroanthracene and benzyl alcohol. We found that the low spin state of FeCl3/TEMPO is more favourable, and that the N atom is the preferred hydrogen acceptor. Moreover, dispersion interactions assist the reaction, as well as nuclear tunnelling, which even at room temperature can speed up the process by almost two orders of magnitude. We also predict that pronounced kinetic isotope effects (KIE) could be observed due to tunnelling. Our findings provide insights into improving the substrate scope and the development of new transformations for the FeCl3/TEMPO system.
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Affiliation(s)
- Shi-Jun Li
- College of Chemistry, Beijing Normal University, Beijing 100875, P. R. China. .,Green Catalysis Center, and College of Chemistry, Zhengzhou University, 100 Science Avenue, Zhengzhou, Henan, 450001, P. R. China
| | - Wei Fang
- Laboratory for Physical Chemistry, ETH Zurich, Zurich 8093, Switzerland. .,State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, P. R. China
| | | | - De-Cai Fang
- College of Chemistry, Beijing Normal University, Beijing 100875, P. R. China.
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18
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Fang W, Winter P, Richardson JO. Microcanonical Tunneling Rates from Density-of-States Instanton Theory. J Chem Theory Comput 2020; 17:40-55. [PMID: 33351621 DOI: 10.1021/acs.jctc.0c01118] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Semiclassical instanton theory is a form of quantum transition-state theory which can be applied to the computation of thermal reaction rates in complex molecular systems including quantum tunneling effects. There have been a number of attempts to extend the theory to treat microcanonical rates. However, the previous formulations are either computationally unfeasible for large systems due to an explicit sum over states or they involve extra approximations, which make them less reliable. We propose a robust and practical microcanonical formulation called density-of-states instanton theory, which avoids the sum over states altogether. In line with the semiclassical approximations inherent to the instanton approach, we employ the stationary-phase approximation to the inverse Laplace transform to obtain the densities of states. This can be evaluated using only post-processing of the data available from a small set of instanton calculations, such that our approach remains computationally efficient. We show that the new formulation predicts results that agree well with quantum scattering theory for an atom-diatom reaction and with experiments for a photoexcited unimolecular hydrogen transfer in a Criegee intermediate. When the thermal rate is evaluated from a Boltzmann average over our new microcanonical formalism, it can overcome some problems of conventional instanton theory. In particular, it predicts a smooth transition at the crossover temperature and is able to describe bimolecular reactions with pre-reactive complexes such as CH3OH + OH.
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Affiliation(s)
- Wei Fang
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Pierre Winter
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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19
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Jahr E, Laude G, Richardson JO. Instanton theory of tunneling in molecules with asymmetric isotopic substitutions. J Chem Phys 2020; 153:094101. [PMID: 32891112 DOI: 10.1063/5.0021831] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We consider quantum tunneling in asymmetric double-well systems for which the local minima in the two wells have the same energy, but the frequencies differ slightly. In a molecular context, this situation can arise if the symmetry is broken by isotopic substitutions. We derive a generalization of instanton theory for these asymmetric systems, leading to a semiclassical expression for the tunneling matrix element and hence the energy-level splitting. We benchmark the method using a set of one- and two-dimensional models, for which the results compare favorably with numerically exact quantum calculations. Using the ring-polymer instanton approach, we apply the method to compute the level splittings in various isotopomers of malonaldehyde in full dimensionality and analyze the relative contributions from the zero-point energy difference and tunneling effects.
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Affiliation(s)
- Elena Jahr
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Gabriel Laude
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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20
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Laude G, Calderini D, Welsch R, Richardson JO. Calculations of quantum tunnelling rates for muonium reactions with methane, ethane and propane. Phys Chem Chem Phys 2020; 22:16843-16854. [PMID: 32666960 DOI: 10.1039/d0cp01346c] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Thermal rate constants for Mu + CH4, Mu + C2H6 and Mu + C3H8 and their equivalent reactions with H were evaluated with ab initio instanton rate theory. The potential-energy surfaces are fitted using Gaussian process regression to high-level electronic-structure calculations evaluated around the tunnelling pathway. This method was able to successfully reproduce various experimental measurements for the rate constant of these reactions. However, it was not able to reproduce the faster-than-expected rate of Mu + C3H8 at 300 K reported by Fleming et al. [Phys. Chem. Chem. Phys., 2015, 17, 19901 and Phys. Chem. Chem. Phys., 2020, 22, 6326]. Analysis of our results indicates that the kinetic isotope effect at this temperature is not significantly influenced by quantum tunnelling. We consider many possible factors for the discrepancy between theory and experiment but conclude that in each case, the instanton approximation is unlikely to be the cause of the error. This is in part based on the good agreement we find between the instanton predictions and new multiconfigurational time-dependent Hartree (MCTDH) calculations for Mu + CH4 using the same potential-energy surface. Further experiments will therefore be needed to resolve this issue.
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Affiliation(s)
- Gabriel Laude
- Laboratory of Physical Chemistry, ETH Zürich, Switzerland.
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21
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Heller ER, Richardson JO. Semiclassical instanton formulation of Marcus–Levich–Jortner theory. J Chem Phys 2020; 152:244117. [DOI: 10.1063/5.0013521] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Eric R. Heller
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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22
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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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23
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Abstract
The diffusion of water molecules and clusters across the surfaces of materials is important to a wide range of processes. Interestingly, experiments have shown that on certain substrates, water dimers can diffuse more rapidly than water monomers. Whilst explanations for anomalously fast diffusion have been presented for specific systems, the general underlying physical principles are not yet established. We investigate this through a systematic ab initio study of water monomer and dimer diffusion on a range of surfaces. Calculations reveal different mechanisms for fast water dimer diffusion, which is found to be more widespread than previously anticipated. The key factors affecting diffusion are the balance of water-water versus water-surface bonding and the ease with which hydrogen-bond exchange can occur (either through a classical over-the-barrier process or through quantum-mechanical tunnelling). We anticipate that the insights gained will be useful for understanding future experiments on the diffusion and clustering of hydrogen-bonded adsorbates. The experimental observation that water dimers diffuse more rapidly than monomers across materials’ surfaces is yet to be clarified. Here the authors show by ab initio calculations classical and quantum mechanical mechanisms for faster water dimer diffusion on a broad range of metal and non-metal surfaces.
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24
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Heller ER, Richardson JO. Instanton formulation of Fermi’s golden rule in the Marcus inverted regime. J Chem Phys 2020; 152:034106. [DOI: 10.1063/1.5137823] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Eric R. Heller
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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25
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Sakaushi K, Kumeda T, Hammes-Schiffer S, Melander MM, Sugino O. Advances and challenges for experiment and theory for multi-electron multi-proton transfer at electrified solid–liquid interfaces. Phys Chem Chem Phys 2020; 22:19401-19442. [DOI: 10.1039/d0cp02741c] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
Understanding microscopic mechanism of multi-electron multi-proton transfer reactions at complexed systems is important for advancing electrochemistry-oriented science in the 21st century.
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Affiliation(s)
- Ken Sakaushi
- Center for Green Research on Energy and Environmental Materials
- National Institute for Materials Science
- Ibaraki 305-0044
- Japan
| | - Tomoaki Kumeda
- Center for Green Research on Energy and Environmental Materials
- National Institute for Materials Science
- Ibaraki 305-0044
- Japan
| | | | - Marko M. Melander
- Nanoscience Center
- Department of Chemistry
- University of Jyväskylä
- Jyväskylä
- Finland
| | - Osamu Sugino
- The Institute of Solid State Physics
- the University of Tokyo
- Chiba 277-8581
- Japan
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26
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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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27
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Sanches-Neto FO, Coutinho ND, Palazzetti F, Carvalho-Silva VH. Temperature dependence of rate constants for the H(D) + CH4 reaction in gas and aqueous phase: deformed Transition-State Theory study including quantum tunneling and diffusion effects. Struct Chem 2019. [DOI: 10.1007/s11224-019-01437-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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28
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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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29
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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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30
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Winter P, Richardson JO. Divide-and-Conquer Method for Instanton Rate Theory. J Chem Theory Comput 2019; 15:2816-2825. [DOI: 10.1021/acs.jctc.8b01267] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Pierre Winter
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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31
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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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32
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Affiliation(s)
- Wei Fang
- School of Physics and Collaborative Innovation Centre of Quantum Matter, Peking University, Beijing, People's Republic of China
- Thomas Young Centre, London Centre for Nanotechnology, and Department of Physics and Astronomy, University College London, London, UK
- Laboratory of Physical Chemistry, ETH Zurich, Zurich, Switzerland
| | - Ji Chen
- Department of Electronic Structure Theory, Max Plank Institute for Solid State Research, Stuttgart, Germany
| | - Yexin Feng
- School of Physics and Electronics, Hunan University, Changsha, People's Republic of China
| | - Xin-Zheng Li
- School of Physics and Collaborative Innovation Centre of Quantum Matter, Peking University, Beijing, People's Republic of China
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Peking University, Beijing, People's Republic of China
| | - Angelos Michaelides
- Thomas Young Centre, London Centre for Nanotechnology, and Department of Physics and Astronomy, University College London, London, UK
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33
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Litman Y, Richardson JO, Kumagai T, Rossi M. Elucidating the Nuclear Quantum Dynamics of Intramolecular Double Hydrogen Transfer in Porphycene. J Am Chem Soc 2019; 141:2526-2534. [PMID: 30648386 PMCID: PMC6728096 DOI: 10.1021/jacs.8b12471] [Citation(s) in RCA: 50] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
![]()
We address the double hydrogen transfer
(DHT) dynamics of the porphycene molecule, a complex paradigmatic
system in which the making and breaking of H-bonds in a highly anharmonic
potential energy surface require a quantum mechanical treatment not
only of the electrons but also of the nuclei. We combine density functional
theory calculations, employing hybrid functionals and van der Waals
corrections, with recently proposed and optimized path-integral ring-polymer
methods for the approximation of quantum vibrational spectra and reaction
rates. Our full-dimensional ring-polymer instanton simulations show
that below 100 K the concerted DHT tunneling pathway dominates but
between 100 and 300 K there is a competition between concerted and
stepwise pathways when nuclear quantum effects are included. We obtain
ground-state reaction rates of 2.19 × 1011 s–1 at 150 K and 0.63 × 1011 s–1 at
100 K, in good agreement with experiment. We also reproduce the puzzling
N–H stretching band of porphycene with very good accuracy from
thermostated ring-polymer molecular dynamics simulations. The position
and line shape of this peak, centered at around 2600 cm–1 and spanning 750 cm–1, stem from a combination
of very strong H-bonds, the coupling to low-frequency modes, and the
access to cis-like isomeric conformations, which
cannot be appropriately captured with classical-nuclei dynamics. These
results verify the appropriateness of our general theoretical approach
and provide a framework for a deeper physical understanding of hydrogen
transfer dynamics in complex systems.
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Affiliation(s)
- Yair Litman
- Theory Department , Fritz Haber Institute of the Max Planck Society , Faradayweg 4-6 , 14195 Berlin , Germany
| | | | - Takashi Kumagai
- Physical Chemistry Department , Fritz Haber Institute of the Max Planck Society , Faradayweg 4-6 , 14195 Berlin , Germany
| | - Mariana Rossi
- Theory Department , Fritz Haber Institute of the Max Planck Society , Faradayweg 4-6 , 14195 Berlin , Germany
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34
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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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35
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Trenins G, Althorpe SC. Mean-field Matsubara dynamics: Analysis of path-integral curvature effects in rovibrational spectra. J Chem Phys 2018; 149:014102. [DOI: 10.1063/1.5038616] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- George Trenins
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Stuart C. Althorpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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36
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37
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38
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Ásgeirsson V, Arnaldsson A, Jónsson H. Efficient evaluation of atom tunneling combined with electronic structure calculations. J Chem Phys 2018; 148:102334. [DOI: 10.1063/1.5007180] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Vilhjálmur Ásgeirsson
- Science Institute and Faculty of Physical Sciences, University of Iceland VR-III, 107 Reykjavík, Iceland
| | - Andri Arnaldsson
- Science Institute and Faculty of Physical Sciences, University of Iceland VR-III, 107 Reykjavík, Iceland
- Vatnaskil, Sídumúli 28, 108 Reykjavík, Iceland
| | - Hannes Jónsson
- Science Institute and Faculty of Physical Sciences, University of Iceland VR-III, 107 Reykjavík, Iceland
- Center for Nonlinear Studies, Los Alamos, New Mexico 87545, USA
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39
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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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40
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Affiliation(s)
- Jan Meisner
- 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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41
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Cooper AM, Hallmen PP, Kästner J. Potential energy surface interpolation with neural networks for instanton rate calculations. J Chem Phys 2018. [DOI: 10.1063/1.5015950] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- April M. Cooper
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Philipp P. Hallmen
- 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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42
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Lamberts T, Samanta PK, Köhn A, Kästner J. Quantum tunneling during interstellar surface-catalyzed formation of water: the reaction H + H 2O 2 → H 2O + OH. Phys Chem Chem Phys 2018; 18:33021-33030. [PMID: 27886292 PMCID: PMC5317215 DOI: 10.1039/c6cp06457d] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The final step of the water formation network on interstellar grain surfaces starting from the H + O2 route is the reaction between H and H2O2. This reaction is known to have a high activation energy and therefore at low temperatures it can only proceed via tunneling. To date, however, no rate constants are available at temperatures below 200 K. In this work, we use instanton theory to compute rate constants for the title reaction with and without isotopic substitutions down to temperatures of 50 K. The calculations are based on density functional theory, with additional benchmarks for the activation energy using unrestricted single-reference and multireference coupled-cluster single-point energies. Gas-phase bimolecular rate constants are calculated and compared with available experimental data not only for H + H2O2 → H2O + OH, but also for H + H2O2 → H2 + HO2. We find a branching ratio where the title reaction is favored by at least two orders of magnitude at 114 K. In the interstellar medium this reaction predominantly occurs on water surfaces, which increases the probability that the two reactants meet. To mimic this, one, two, or three spectator H2O molecules are added to the system. Eley-Rideal bimolecular and Langmuir-Hinshelwood unimolecular rate constants are presented here. The kinetic isotope effects for the various cases are compared to experimental data as well as to expressions commonly used in astrochemical models. Both the rectangular barrier and the Eckart approximations lead to errors of about an order of magnitude. Finally, fits of the rate constants are provided as input for astrochemical models.
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Affiliation(s)
- Thanja Lamberts
- Institute for Theoretical Chemistry, University of Stuttgart, Stuttgart, Germany.
| | | | - Andreas Köhn
- Institute for Theoretical Chemistry, University of Stuttgart, Stuttgart, Germany.
| | - Johannes Kästner
- Institute for Theoretical Chemistry, University of Stuttgart, Stuttgart, Germany.
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43
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Laude G, Calderini D, Tew DP, Richardson JO. Ab initio instanton rate theory made efficient using Gaussian process regression. Faraday Discuss 2018; 212:237-258. [PMID: 30230495 DOI: 10.1039/c8fd00085a] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
Ab initio instanton rate theory is a computational method for rigorously including tunnelling effects into the calculations of chemical reaction rates based on a potential-energy surface computed on the fly from electronic-structure theory. This approach is necessary to extend conventional transition-state theory into the deep-tunnelling regime, but it is also more computationally expensive as it requires many more ab initio calculations. We propose an approach which uses Gaussian process regression to fit the potential-energy surface locally around the dominant tunnelling pathway. The method can be converged to give the same result as from an on-the-fly ab initio instanton calculation but it requires far fewer electronic-structure calculations. This makes it a practical approach for obtaining accurate rate constants based on high-level electronic-structure methods. We show fast convergence to reproduce benchmark H + CH4 results and evaluate new low-temperature rates of H + C2H6 in full dimensionality at a UCCSD(T)-F12b/cc-pVTZ-F12 level.
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Affiliation(s)
- Gabriel Laude
- Laboratory of Physical Chemistry, ETH Zurich, Switzerland. and On exchange from School of Chemistry, University of Edinburgh, UK
| | | | - David P Tew
- Max-Planck-Institut für Festkörperforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany
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44
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Karandashev K, Xu ZH, Meuwly M, Vaníček J, Richardson JO. Kinetic isotope effects and how to describe them. STRUCTURAL DYNAMICS (MELVILLE, N.Y.) 2017; 4:061501. [PMID: 29282447 PMCID: PMC5729036 DOI: 10.1063/1.4996339] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2017] [Accepted: 08/23/2017] [Indexed: 06/01/2023]
Abstract
We review several methods for computing kinetic isotope effects in chemical reactions including semiclassical and quantum instanton theory. These methods describe both the quantization of vibrational modes as well as tunneling and are applied to the ⋅H + H2 and ⋅H + CH4 reactions. The absolute rate constants computed with the semiclassical instanton method both using on-the-fly electronic structure calculations and fitted potential-energy surfaces are also compared directly with exact quantum dynamics results. The error inherent in the instanton approximation is found to be relatively small and similar in magnitude to that introduced by using fitted surfaces. The kinetic isotope effect computed by the quantum instanton is even more accurate, and although it is computationally more expensive, the efficiency can be improved by path-integral acceleration techniques. We also test a simple approach for designing potential-energy surfaces for the example of proton transfer in malonaldehyde. The tunneling splittings are computed, and although they are found to deviate from experimental results, the ratio of the splitting to that of an isotopically substituted form is in much better agreement. We discuss the strengths and limitations of the potential-energy surface and based on our findings suggest ways in which it can be improved.
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Affiliation(s)
- Konstantin Karandashev
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Zhen-Hao Xu
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Markus Meuwly
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Jiří Vaníček
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Jeremy O Richardson
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, Eidgenössische Technische Hochschule Zürich (ETHZ), CH-8093 Zürich, Switzerland
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45
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Fang W, Richardson JO, Chen J, Li XZ, Michaelides A. Simultaneous Deep Tunneling and Classical Hopping for Hydrogen Diffusion on Metals. PHYSICAL REVIEW LETTERS 2017; 119:126001. [PMID: 29341641 DOI: 10.1103/physrevlett.119.126001] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2017] [Indexed: 06/07/2023]
Abstract
Hydrogen diffusion on metals exhibits rich quantum behavior, which is not yet fully understood. Using simulations, we show that many hydrogen diffusion barriers can be categorized into those with parabolic tops and those with broad tops. With parabolic-top barriers, hydrogen diffusion evolves gradually from classical hopping, to shallow tunneling, to deep tunneling as the temperature (T) decreases, and noticeable quantum effects persist at moderate T. In contrast, with broad-top barriers quantum effects become important only at low T and the classical-to-quantum transition is sharp, at which classical hopping and deep tunneling both occur. This coexistence indicates that more than one mechanism contributes to the quantum reaction rate. The conventional definition of the classical-to-quantum crossover T is invalid for the broad tops, and we give a new definition. Extending this, we propose a model to predict the transition T for broad-top diffusion, providing a general guide for theory and experiment.
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Affiliation(s)
- Wei Fang
- Thomas Young Centre, London Centre for Nanotechnology and Department of Chemistry, University College London, London WC1E 6BT, United Kingdom
| | | | - Ji Chen
- Thomas Young Centre, London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Xin-Zheng Li
- School of Physics and the Collaborative Innovation Center of Quantum Matters, Peking University, Beijing 100871, People's Republic of China
| | - Angelos Michaelides
- Thomas Young Centre, London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
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46
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McConnell S, Kästner J. Instanton rate constant calculations close to and above the crossover temperature. J Comput Chem 2017; 38:2570-2580. [DOI: 10.1002/jcc.24914] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2017] [Revised: 07/24/2017] [Accepted: 07/25/2017] [Indexed: 01/17/2023]
Affiliation(s)
- Sean McConnell
- Institute for Theoretical Chemistry, University of Stuttgart; Pfaffenwaldring 55, Stuttgart 70569 Germany
| | - Johannes Kästner
- Institute for Theoretical Chemistry, University of Stuttgart; Pfaffenwaldring 55, Stuttgart 70569 Germany
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47
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Manthe U. Wavepacket dynamics and the multi-configurational time-dependent Hartree approach. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:253001. [PMID: 28430111 DOI: 10.1088/1361-648x/aa6e96] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.
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Affiliation(s)
- Uwe Manthe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
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48
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Senevirathne B, Andersson S, Dulieu F, Nyman G. Hydrogen atom mobility, kinetic isotope effects and tunneling on interstellar ices (I and ASW). ACTA ACUST UNITED AC 2017. [DOI: 10.1016/j.molap.2017.01.005] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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49
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McConnell SR, Löhle A, Kästner J. Rate constants from instanton theory via a microcanonical approach. J Chem Phys 2017; 146:074105. [DOI: 10.1063/1.4976129] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sean R. McConnell
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - 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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50
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Meisner J, Markmeyer MN, Bohner MU, Kästner J. Comparison of classical reaction paths and tunneling paths studied with the semiclassical instanton theory. Phys Chem Chem Phys 2017; 19:23085-23094. [DOI: 10.1039/c7cp03722h] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Comparison of classical reaction paths and semiclassical instanton paths for a proton transfer reaction mechanism.
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Affiliation(s)
- Jan Meisner
- Institute for Theoretical Chemistry
- University of Stuttgart
- Pfaffenwaldring 55
- Stuttgart
- Germany
| | - Max N. Markmeyer
- Institute for Theoretical Chemistry
- University of Stuttgart
- Pfaffenwaldring 55
- Stuttgart
- Germany
| | - Matthias U. Bohner
- Institute for Theoretical Chemistry
- University of Stuttgart
- Pfaffenwaldring 55
- Stuttgart
- Germany
| | - Johannes Kästner
- Institute for Theoretical Chemistry
- University of Stuttgart
- Pfaffenwaldring 55
- Stuttgart
- Germany
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