1
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Qiu G, Schreiner PR. The Intrinsic Barrier Width and Its Role in Chemical Reactivity. ACS CENTRAL SCIENCE 2023; 9:2129-2137. [PMID: 38033803 PMCID: PMC10683502 DOI: 10.1021/acscentsci.3c00926] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Revised: 09/29/2023] [Accepted: 10/12/2023] [Indexed: 12/02/2023]
Abstract
Chemical reactions are in virtually all cases understood and explained on the basis of depicting the molecular potential energy landscape, i.e., the change in atomic positions vs the free-energy change. With such landscapes, the features of the reaction barriers solely determine chemical reactivities. The Marcus dissection of the barrier height (activation energy) on such a potential into the thermodynamically independent (intrinsic) and the thermodynamically dependent (Bell-Evans-Polanyi) contributions successfully models the interplay of reaction rate and driving force. This has led to the well-known and ubiquitously used reactivity paradigm of "kinetic versus thermodynamic control". However, an analogous dissection concept regarding the barrier width is absent. Here we define and outline the concept of intrinsic barrier width and the driving force effect on the barrier width and report experimental as well as theoretical studies to demonstrate their distinct roles. We present the idea of changing the barrier widths of conformational isomerizations of some simple aromatic carboxylic acids as models and use quantum mechanical tunneling (QMT) half-lives as a read-out for these changes because QMT is particularly sensitive to barrier widths. We demonstrate the distinct roles of the intrinsic and the thermodynamic contributions of the barrier width on QMT half-lives. This sheds light on resolving conflicting trends in chemical reactivities where barrier widths are relevant and allows us to draw some important conclusions about the general relevance of barrier widths, their qualitative definition, and the consequences for more complete descriptions of chemical reactions.
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Affiliation(s)
- Guanqi Qiu
- Institute of Organic Chemistry, Justus Liebig University, Heinrich-Buff-Ring 17, 35392 Giessen, Germany
| | - Peter R. Schreiner
- Institute of Organic Chemistry, Justus Liebig University, Heinrich-Buff-Ring 17, 35392 Giessen, Germany
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2
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Chen BW. Equilibrium and kinetic isotope effects in heterogeneous catalysis: A density functional theory perspective. CATAL COMMUN 2023. [DOI: 10.1016/j.catcom.2023.106654] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/29/2023] Open
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3
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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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4
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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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5
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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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6
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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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7
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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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8
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Karandashev K, Vaníček J. Accelerating equilibrium isotope effect calculations. II. Stochastic implementation of direct estimators. J Chem Phys 2019; 151:134116. [PMID: 31594323 DOI: 10.1063/1.5124995] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Path integral calculations of equilibrium isotope effects and isotopic fractionation are expensive due to the presence of path integral discretization errors, statistical errors, and thermodynamic integration errors. Whereas the discretization errors can be reduced by high-order factorization of the path integral and statistical errors by using centroid virial estimators, two recent papers proposed alternative ways to completely remove the thermodynamic integration errors: Cheng and Ceriotti [J. Chem. Phys. 141, 244112 (2015)] employed a variant of free-energy perturbation called "direct estimators," while Karandashev and Vaníček [J. Chem. Phys. 143, 194104 (2017)] combined the thermodynamic integration with a stochastic change of mass and piecewise-linear umbrella biasing potential. Here, we combine the former approach with the stochastic change in mass in order to decrease its statistical errors when applied to larger isotope effects and perform a thorough comparison of different methods by computing isotope effects first on a harmonic model and then on methane and methanium, where we evaluate all isotope effects of the form CH4-xDx/CH4 and CH5-xDx +/CH5 +, respectively. We discuss the reasons for a surprising behavior of the original method of direct estimators, which performed well for a much larger range of isotope effects than what had been expected previously, as well as some implications of our work for the more general problem of free energy difference calculations.
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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
| | - Jiří Vaníček
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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9
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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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10
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Trenins G, Willatt MJ, Althorpe SC. Path-integral dynamics of water using curvilinear centroids. J Chem Phys 2019. [DOI: 10.1063/1.5100587] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [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
| | - Michael J. Willatt
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Stuart C. Althorpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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11
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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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12
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Vasquez L, Rostkowski M, Gelman F, Dybala-Defratyka A. Can Path Integral Molecular Dynamics Make a Good Approximation for Vapor Pressure Isotope Effects Prediction for Organic Solvents? A Comparison to ONIOM QM/MM and QM Cluster Calculation. J Phys Chem B 2018; 122:7353-7364. [PMID: 29961315 DOI: 10.1021/acs.jpcb.8b03444] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
Isotopic fractionation of volatile organic compounds (VOCs), which are under strict measures of control because of their potential harm to the environment and humans, has an important ecological aspect, as the isotopic composition of compounds may depend on the conditions in which such compounds are distributed in Nature. Therefore, detailed knowledge on isotopic fractionation, not only experimental but also based on theoretical models, is crucial to follow conditions and pathways within which these contaminants are spread throughout the ecosystems. In this work, we present carbon and, for the first time, bromine vapor pressure isotope effect (VPIE) on the evaporation process from pure-phase systems-dibromomethane and bromobenzene, the representatives of aliphatic and aromatic brominated VOCs. We combine isotope effects measurements with their theoretical prediction using three computational techniques, namely path integral molecular dynamics, QM cluster, and hybrid ONIOM models. While evaporation of both compounds resulted in normal bromine VPIEs, the difference in the direction of carbon isotopic fractionation is observed for the aliphatic and aromatic compounds, where VPIEs are inverse and normal, respectively. Even though theoretical models tested here turned out to be insufficient for quantitative agreement with the experimental values, cluster electronic structure calculations, as well as two-layer ONIOM computations, provided better reproduction of experimental trends.
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Affiliation(s)
- Luis Vasquez
- Institute of Applied Radiation Chemistry, Faculty of Chemistry , Lodz University of Technology , Żeromskiego 116 , 90-924 Łódź , Poland
| | - Michal Rostkowski
- Institute of Applied Radiation Chemistry, Faculty of Chemistry , Lodz University of Technology , Żeromskiego 116 , 90-924 Łódź , Poland
| | - Faina Gelman
- Geological Survey of Israel , Malkhei Israel Street 30 , 95501 Jerusalem , Israel
| | - Agnieszka Dybala-Defratyka
- Institute of Applied Radiation Chemistry, Faculty of Chemistry , Lodz University of Technology , Żeromskiego 116 , 90-924 Łódź , Poland
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13
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14
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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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15
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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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16
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Buchowiecki M, Prątnicki F. High temperature partition function – a key role of ro-vibrational coupling and inflection points. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1334132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Marcin Buchowiecki
- Institute of Physics, Department of Mathematics and Physics, University of Szczecin, Szczecin, Poland
| | - Filip Prątnicki
- Institute of Physics, Department of Mathematics and Physics, University of Szczecin, Szczecin, Poland
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17
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Abstract
Attosecond ionization experiments have not resolved the question "What is the tunneling time?". Different definitions of tunneling time lead to different results. Second, a zero tunneling time for a material particle suggests that the nonrelativistic theory includes speeds greater than the speed of light. Chemical reactions, occurring via tunneling, should then not be considered in terms of a nonrelativistic quantum theory calling into question quantum dynamics computations on tunneling reactions. To answer these questions, we define a new experimentally measurable paradigm, the tunneling flight time, and show that it vanishes for scattering through an Eckart or a square barrier, irrespective of barrier length or height, generalizing the Hartman effect. We explain why this result does not lead to experimental measurement of speeds greater than the speed of light. We show that this tunneling is an incoherent process by comparing a classical Wigner theory with exact quantum mechanical computations.
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Affiliation(s)
- Jakob Petersen
- Chemical Physics Department, Weizmann Institute of Science , 76100 Rehovoth, Israel
| | - Eli Pollak
- Chemical Physics Department, Weizmann Institute of Science , 76100 Rehovoth, Israel
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18
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Wang W, Zhao Y. The dissociation and recombination rates of CH 4 through the Ni(111) surface: The effect of lattice motion. J Chem Phys 2017; 147:044703. [PMID: 28764359 DOI: 10.1063/1.4995299] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Methane dissociation is a prototypical system for the study of surface reaction dynamics. The dissociation and recombination rates of CH4 through the Ni(111) surface are calculated by using the quantum instanton method with an analytical potential energy surface. The Ni(111) lattice is treated rigidly, classically, and quantum mechanically so as to reveal the effect of lattice motion. The results demonstrate that it is the lateral displacements rather than the upward and downward movements of the surface nickel atoms that affect the rates a lot. Compared with the rigid lattice, the classical relaxation of the lattice can increase the rates by lowering the free energy barriers. For instance, at 300 K, the dissociation and recombination rates with the classical lattice exceed the ones with the rigid lattice by 6 and 10 orders of magnitude, respectively. Compared with the classical lattice, the quantum delocalization rather than the zero-point energy of the Ni atoms further enhances the rates by widening the reaction path. For instance, the dissociation rate with the quantum lattice is about 10 times larger than that with the classical lattice at 300 K. On the rigid lattice, due to the zero-point energy difference between CH4 and CD4, the kinetic isotope effects are larger than 1 for the dissociation process, while they are smaller than 1 for the recombination process. The increasing kinetic isotope effect with decreasing temperature demonstrates that the quantum tunneling effect is remarkable for the dissociation process.
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Affiliation(s)
- Wenji Wang
- College of Chemistry & Pharmacy, Northwest A&F University, Yangling, 712100 Shaanxi Province, People's Republic of China
| | - Yi Zhao
- State Key Laboratory for Physical Chemistry of Solid Surfaces and Fujian Provincial Key Lab of Theoretical and Computational Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China
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19
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Aieta C, Ceotto M. A quantum method for thermal rate constant calculations from stationary phase approximation of the thermal flux-flux correlation function integral. J Chem Phys 2017; 146:214115. [DOI: 10.1063/1.4984099] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Chiara Aieta
- Dipartimento di Chimica, Università degli Studi di Milano, Via C. Golgi 19, 20133 Milano, Italy
| | - Michele Ceotto
- Dipartimento di Chimica, Università degli Studi di Milano, Via C. Golgi 19, 20133 Milano, Italy
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20
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Karandashev K, Vaníček J. Accelerating equilibrium isotope effect calculations. I. Stochastic thermodynamic integration with respect to mass. J Chem Phys 2017. [DOI: 10.1063/1.4981260] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- Konstantin Karandashev
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, 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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21
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Beyer AN, Richardson JO, Knowles PJ, Rommel J, Althorpe SC. Quantum Tunneling Rates of Gas-Phase Reactions from On-the-Fly Instanton Calculations. J Phys Chem Lett 2016; 7:4374-4379. [PMID: 27775889 DOI: 10.1021/acs.jpclett.6b02115] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The instanton method obtains approximate tunneling rates from the minimum-action path (known as the instanton) linking reactants to the products at a given temperature. An efficient way to find the instanton is to search for saddle-points on the ring-polymer potential surface, which is obtained by expressing the quantum Boltzmann operator as a discrete path-integral. Here we report a practical implementation of this ring-polymer form of instanton theory into the Molpro electronic-structure package, which allows the rates to be computed on-the-fly, without the need for a fitted analytic potential-energy surface. As a test case, we compute tunneling rates for the benchmark H + CH4 reaction, showing how the efficiency of the instanton method allows the user systematically to converge the tunneling rate with respect to the level of electronic-structure theory.
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Affiliation(s)
- Adrian N Beyer
- Department of Chemistry, University of Cambridge , Lensfield Road, Cambridge, CB2 1EW, United Kingdom
| | - Jeremy O Richardson
- Department of Chemistry, University of Cambridge , Lensfield Road, Cambridge, CB2 1EW, United Kingdom
- Department of Chemistry, Durham University , South Road, Durham, DH1 3LE, United Kingdom
| | - Peter J Knowles
- School of Chemistry, Cardiff University , Main Building, Park Place, Cardiff, CF10 3AT, United Kingdom
| | - Judith Rommel
- 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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22
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Zhao H, Wang W, Zhao Y. Thermal Rate Constants for the O( 3P) + CH 4 → OH + CH 3 Reaction: The Effects of Quantum Tunneling and Potential Energy Barrier Shape. J Phys Chem A 2016; 120:7589-7597. [PMID: 27640428 DOI: 10.1021/acs.jpca.6b07029] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The rate constants and kinetic isotope effects for the O(3P) + CH4 reaction have been investigated with the quantum instanton method in full dimensionality. The calculated rate constants are in good agreement with the experimental values above 400 K, below which the measured values are scattered. Compared to other theoretical approaches, the quantum instanton method predicts the largest quantum tunneling effect, so it gives the largest rate constants at low temperatures. The calculated kinetic isotope effects are always much larger than 1 and increase with decreasing temperature, due to the zero-point energy and quantum tunneling. Our calculations on different potential energy surfaces demonstrate that the potential energy barrier shape dominates the magnitude of quantum tunneling and has a great effect on the kinetic isotope effect.
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Affiliation(s)
- Huali Zhao
- College of Science, Northwest A&F University , Yangling, 712100 Shaanxi Province, P. R. China
| | - Wenji Wang
- College of Science, Northwest A&F University , Yangling, 712100 Shaanxi Province, P. R. China
| | - Yi Zhao
- State Key Laboratory for Physical Chemistry of Solid Surfaces and Fujian Provincial Key Lab of Theoretical and Computational Chemistry, College of Chemistry and Chemical Engineering, Xiamen University , Xiamen 361005, P. R. China
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23
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Ceriotti M, Fang W, Kusalik PG, McKenzie RH, Michaelides A, Morales MA, Markland TE. Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges. Chem Rev 2016; 116:7529-50. [DOI: 10.1021/acs.chemrev.5b00674] [Citation(s) in RCA: 339] [Impact Index Per Article: 42.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Michele Ceriotti
- Laboratory
of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Wei Fang
- Thomas
Young Centre, London Centre for Nanotechnology and Department of Physics
and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Peter G. Kusalik
- Department
of Chemistry, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Ross H. McKenzie
- School
of Mathematics and Physics, University of Queensland, Brisbane, 4072 Queensland Australia
| | - Angelos Michaelides
- Thomas
Young Centre, London Centre for Nanotechnology and Department of Physics
and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Miguel A. Morales
- Lawrence Livermore National Laboratory, Livermore, California 94550, United States
| | - Thomas E. Markland
- Department
of Chemistry, Stanford University, 333 Campus Drive, Stanford, California 94305, United States
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24
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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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25
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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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26
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Karandashev K, Vaníček J. Accelerating quantum instanton calculations of the kinetic isotope effects. J Chem Phys 2015; 143:194104. [DOI: 10.1063/1.4935701] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Konstantin Karandashev
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne CH-1015, Switzerland
| | - Jiří Vaníček
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne CH-1015, Switzerland
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27
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Nava M, Quhe R, Palazzesi F, Tiwary P, Parrinello M. de Broglie Swapping Metadynamics for Quantum and Classical Sampling. J Chem Theory Comput 2015; 11:5114-9. [DOI: 10.1021/acs.jctc.5b00818] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Marco Nava
- Department
of Chemistry and Applied Biosciences, ETH Zurich, and Facoltà
di Informatica, Istituto di Scienze Computazionali, Università della Svizzera Italiana, Via G. Buffi 13, 6900 Lugano, Ticino, Switzerland
| | - Ruge Quhe
- Department
of Chemistry and Applied Biosciences, ETH Zurich, and Facoltà
di Informatica, Istituto di Scienze Computazionali, Università della Svizzera Italiana, Via G. Buffi 13, 6900 Lugano, Ticino, Switzerland
- State Key Laboratory of Information Photonics and Optical Communications & School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Ferruccio Palazzesi
- Department
of Chemistry and Applied Biosciences, ETH Zurich, and Facoltà
di Informatica, Istituto di Scienze Computazionali, Università della Svizzera Italiana, Via G. Buffi 13, 6900 Lugano, Ticino, Switzerland
| | - Pratyush Tiwary
- Department
of Chemistry and Applied Biosciences, ETH Zurich, and Facoltà
di Informatica, Istituto di Scienze Computazionali, Università della Svizzera Italiana, Via G. Buffi 13, 6900 Lugano, Ticino, Switzerland
- Department
of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Michele Parrinello
- Department
of Chemistry and Applied Biosciences, ETH Zurich, and Facoltà
di Informatica, Istituto di Scienze Computazionali, Università della Svizzera Italiana, Via G. Buffi 13, 6900 Lugano, Ticino, Switzerland
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28
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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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29
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Hele TJH, Suleimanov YV. Should thermostatted ring polymer molecular dynamics be used to calculate thermal reaction rates? J Chem Phys 2015; 143:074107. [DOI: 10.1063/1.4928599] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Timothy J. H. Hele
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Yury V. Suleimanov
- Computation-based Science and Technology Research Center, Cyprus Institute, 20 Kavafi St., Nicosia 2121, Cyprus
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
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30
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Song L, Shi Q. A new approach to calculate charge carrier transport mobility in organic molecular crystals from imaginary time path integral simulations. J Chem Phys 2015; 142:174103. [DOI: 10.1063/1.4919061] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Linze Song
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
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31
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Wang W, Zhao Y. The direct and precursor mediated dissociation rates of H2 on a Ni(111) surface. Phys Chem Chem Phys 2015; 17:5901-12. [PMID: 25630487 DOI: 10.1039/c4cp05624h] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The dissociation and recombination rates of physisorbed H2, and the direct and steady state dissociation (i.e., the precursor mediated dissociation) rates of gas phase H2 on Ni(111), as well as the corresponding kinetic isotope effects, are calculated using the quantum instanton method, together with path integral Monte Carlo and adaptive umbrella sampling techniques. All these rates except the recombination one first decrease and then increase with the increasing temperature, and their minimum values appear at about 250, 300 and 250 K, respectively. These non-monotonic behaviors reveal that the quantum effect of H2 should be very remarkable at low temperatures. The steady state rates are smaller than the direct rates at low temperatures, however, they become larger than the direct ones at high temperatures, these two kinds of rates become equal at about 400 and 300 K on the rigid and quantum lattices, respectively. The quantum motion of the lattice can enhance the direct and steady state rates, and it increases the steady state rate much more than the direct one, for instance, the direct and steady state rates on the quantum lattice are 1.30 and 2.08 times larger than that on the rigid one at 300 K. The calculated kinetic isotope effects are much larger than 1, which reveals that H2 always has a larger rate than that of D2, and the direct process predicts much larger kinetic isotope effects than the steady state process at low temperatures. In addition, the kinetic isotope effects are not affected by the lattice motion.
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Affiliation(s)
- Wenji Wang
- College of Science, Northwest A&F University, Yangling, 712100, Shaanxi Province, P. R. China.
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32
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Richardson JO, Thoss M. Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory. J Chem Phys 2014; 141:074106. [DOI: 10.1063/1.4892865] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Huang J, Buchowiecki M, Nagy T, Vaníček J, Meuwly M. Kinetic isotope effect in malonaldehyde determined from path integral Monte Carlo simulations. Phys Chem Chem Phys 2014; 16:204-11. [DOI: 10.1039/c3cp53698j] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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34
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Wang W, Zhao Y. Dissociation rates of H2on a Ni(100) surface: the role of the physisorbed state. Phys Chem Chem Phys 2014; 16:13318-28. [DOI: 10.1039/c4cp01705f] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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35
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Buchowiecki M, Vaníček J. Monte Carlo evaluation of the equilibrium isotope effects using the Takahashi–Imada factorization of the Feynman path integral. Chem Phys Lett 2013. [DOI: 10.1016/j.cplett.2013.09.070] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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36
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Hele TJH, Althorpe SC. On the uniqueness of t → 0+ quantum transition-state theory. J Chem Phys 2013; 139:084116. [DOI: 10.1063/1.4819077] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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37
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Althorpe SC, Hele TJH. Derivation of a true (t → 0+) quantum transition-state theory. II. Recovery of the exact quantum rate in the absence of recrossing. J Chem Phys 2013; 139:084115. [DOI: 10.1063/1.4819076] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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38
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Wang W, Zhao Y. Quantum instanton calculation of rate constant for CH4 + OH → CH3 + H2O reaction: torsional anharmonicity and kinetic isotope effect. J Chem Phys 2013; 137:214306. [PMID: 23231230 DOI: 10.1063/1.4768874] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Thermal rate constants for the title reaction are calculated by using the quantum instanton approximation within the full dimensional Cartesian coordinates. The results reveal that the quantum effect is remarkable for the reaction at both low and high temperatures, and the obtained rates are in good agreement with experimental measurements at high temperatures. Compared to the harmonic approximation, the torsional anharmonic effect of the internal rotation has a little influence on the rates at low temperatures, however, it enhances the rate by about 20% at 1000 K. In addition, the free energy barriers for the isotopic reactions and the temperature dependence of kinetic isotope effects are also investigated. Generally speaking, for the title reaction, the replacement of OH with OD will reduce the free energy barrier, while substituting D for H (connected to C) will increase the free energy barrier.
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Affiliation(s)
- Wenji Wang
- College of Science, Northwest A&F University, Shaanxi Province, Yangling, 712100, People's Republic of China.
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39
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Hele TJH, Althorpe SC. Derivation of a true (t → 0+) quantum transition-state theory. I. Uniqueness and equivalence to ring-polymer molecular dynamics transition-state-theory. J Chem Phys 2013; 138:084108. [DOI: 10.1063/1.4792697] [Citation(s) in RCA: 92] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
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40
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Suleimanov YV, de Tudela RP, Jambrina PG, Castillo JF, Sáez-Rábanos V, Manolopoulos DE, Aoiz FJ. A ring polymer molecular dynamics study of the isotopologues of the H + H2 reaction. Phys Chem Chem Phys 2013; 15:3655-65. [DOI: 10.1039/c2cp44364c] [Citation(s) in RCA: 60] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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41
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Quantum Instanton Evaluations of the Thermal Rate Constants for
Complex Systems. ADVANCES IN CHEMICAL PHYSICS 2012. [DOI: 10.1155/2012/483504] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Quantum instanton (QI) approximation is recently proposed for the evaluations of the chemical reaction rate constants with use of full dimensional potential energy surfaces. Its strategy is to use the instanton mechanism and to approximate time-dependent quantum dynamics to the imaginary time propagation of the quantities of partition function. It thus incorporates the properties of the instanton idea and the quantum effect of partition function and can be applied to chemical reactions of complex systems. In this paper, we present the QI approach and its applications to several complex systems mainly done by us. The concrete systems include, (1) the reaction of H+CH4→H2+CH3, (2) the reaction of H+SiH4→H2+SiH3, (3) H diffusion on Ni(100) surface; and (4) surface-subsurface transport and interior migration for H/Ni. Available experimental and other theoretical data are also presented for the purpose of comparison.
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42
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Salomon-Ferrer R, Case DA, Walker RC. An overview of the Amber biomolecular simulation package. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2012. [DOI: 10.1002/wcms.1121] [Citation(s) in RCA: 1192] [Impact Index Per Article: 99.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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43
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Head-Gordon M. Publications. Mol Phys 2012. [DOI: 10.1080/00268976.2012.693252] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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44
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BUCHOWIECKI MARCIN. THE RATE CONSTANT OF THE O(3P) + HCl → OH + Cl REACTION WITHIN QUANTUM INSTANTON APPROXIMATION. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2012. [DOI: 10.1142/s0219633612500095] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Temperature dependence of the rate constant of the O (3 P ) + HCl → OH + Cl reaction was calculated for 200–700 K range within the quantum instanton approximation using the 3A″ potential energy surface. Curvature of the Arrhenius plot arising from quantum effects in the hydrogen exchange reaction was observed. Results of the present method were found to significantly improve upon those obtained within the ICVT/μOMT method. The errors pertaining to the present method were estimated.
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Affiliation(s)
- MARCIN BUCHOWIECKI
- Institute of Physics, University of Szczecin, Wielkopolska 15, Szczecin, 70-451, Poland
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45
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Buchowiecki M. Quantum calculations of the temperature dependence of the rate constant and the equilibrium constant for the NH3+H⇌NH2+H2 reaction. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2012.01.075] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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46
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Rommel JB, Kästner J. Adaptive integration grids in instanton theory improve the numerical accuracy at low temperature. J Chem Phys 2011; 134:184107. [DOI: 10.1063/1.3587240] [Citation(s) in RCA: 63] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
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47
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Rommel JB, Goumans TPM, Kästner J. Locating Instantons in Many Degrees of Freedom. J Chem Theory Comput 2011; 7:690-8. [DOI: 10.1021/ct100658y] [Citation(s) in RCA: 99] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Judith B. Rommel
- Computational Biochemistry Group, Institute of Theoretical Chemistry, University of Stuttgart, Stuttgart, Germany
| | - T. P. M. Goumans
- Gorlaeus Laboratories, LIC, Leiden University, Leiden, The Netherlands
| | - Johannes Kästner
- Computational Biochemistry Group, Institute of Theoretical Chemistry, University of Stuttgart, Stuttgart, Germany
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48
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Wang W, Zhao Y. Quantum instanton calculation of rate constants for the C2H6 + H → C2H5 + H2 reaction: anharmonicity and kinetic isotope effects. Phys Chem Chem Phys 2011; 13:19362-70. [DOI: 10.1039/c1cp22255d] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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49
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Buchowiecki M, Vanícek J. Direct evaluation of the temperature dependence of the rate constant based on the quantum instanton approximation. J Chem Phys 2010; 132:194106. [PMID: 20499950 DOI: 10.1063/1.3425617] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A general method for the direct evaluation of the temperature dependence of the quantum-mechanical reaction rate constant in many-dimensional systems is described. The method is based on the quantum instanton approximation for the rate constant, thermodynamic integration with respect to the inverse temperature, and the path integral Monte Carlo evaluation. It can describe deviations from the Arrhenius law due to the coupling of rotations and vibrations, zero-point energy, tunneling, corner-cutting, and other nuclear quantum effects. The method is tested on the Eckart barrier and the full-dimensional H+H(2)-->H(2)+H reaction. In the temperature range from 300 to 1500 K, the error of the present method remains within 13% despite the very large deviations from the Arrhenius law. The direct approach makes the calculations much more efficient, and the efficiency is increased even further (by up to two orders of magnitude in the studied reactions) by using optimal estimators for reactant and transition state thermal energies. Which of the estimators is optimal, however, depends on the system and the strength of constraint in a constrained simulation.
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Affiliation(s)
- Marcin Buchowiecki
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingenierie Chimiques, Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne CH-1015, Switzerland
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50
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Zimmermann T, Vaníček J. Three applications of path integrals: equilibrium and kinetic isotope effects, and the temperature dependence of the rate constant of the [1,5] sigmatropic hydrogen shift in (Z)-1,3-pentadiene. J Mol Model 2010; 16:1779-87. [DOI: 10.1007/s00894-010-0711-y] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2010] [Accepted: 03/21/2010] [Indexed: 11/28/2022]
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