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Pollak E, Upadhyayula S, Liu J. Coherent state representation of thermal correlation functions with applications to rate theory. J Chem Phys 2022; 156:244101. [DOI: 10.1063/5.0088163] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
A coherent state phase space representation of operators, based on the Husimi distribution, is used to derive an exact expression for the symmetrized version of thermal correlation functions. In addition to the time and temperature independent phase space representation of the two operators whose correlation function is of interest, the integrand includes a non-negative distribution function where only one imaginary time and one real time propagation are needed to compute it. The methodology is exemplified for the flux side correlation function used in rate theory. The coherent state representation necessitates the use of a smeared Gaussian flux operator whose coherent state phase space representation is identical to the classical flux expression. The resulting coherent state expression for the flux side correlation function has a number of advantages as compared to previous formulations. Since only one time propagation is needed, it is much easier to converge it with a semiclassical initial value representation. There is no need for forward–backward approximations, and in principle, the computation may be implemented on the fly. It also provides a route for analytic semiclassical approximations for the thermal rate, as exemplified by a computation of the transmission factor through symmetric and asymmetric Eckart barriers using a thawed Gaussian approximation for both imaginary and real time propagations. As a by-product, this example shows that one may obtain “good” tunneling rates using only above barrier classical trajectories even in the deep tunneling regime.
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Affiliation(s)
- Eli Pollak
- Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel
| | - Sameernandan Upadhyayula
- Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel
| | - Jian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
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2
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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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3
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Kleimeier NF, Kaiser RI. Interstellar Enolization-Acetaldehyde (CH 3 CHO) and Vinyl Alcohol (H 2 CCH(OH)) as a Case Study. Chemphyschem 2021; 22:1229-1236. [PMID: 33913232 DOI: 10.1002/cphc.202100111] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Revised: 04/16/2021] [Indexed: 11/11/2022]
Abstract
Owing to the unique conditions in cold molecular clouds, enols-the thermodynamically less stable tautomers of aldehydes and ketones-do not undergo tautomerization to their more stable tautomers in the gas phase because they cannot overcome tautomerization barriers at the low temperatures. Laboratory studies of interstellar analog ices have demonstrated the formation of several keto-enol tautomer pairs in astrochemically relevant ice mixtures over the last years. However, so far only one of them, acetaldehyde-vinyl alcohol, has been detected in deep space. Due to their reactivity with electrophiles, enols can play a crucial role in our understanding of the molecular complexity in the interstellar medium and in comets and meteorites. To study the enolization of aldehydes in interstellar ices by interaction with galactic cosmic rays (GCRs), we irradiated acetaldehyde ices with energetic electrons as proxies of secondary electrons generated in the track of GCRs while penetrating interstellar ices. The results indicate that GCRs can induce enolization of acetaldehyde and that intra- as well as intermolecular processes are relevant. Therefore, enols should be ubiquitous in the interstellar medium and could be searched for using radio telescopes such as ALMA. Once enols are detected and abundances are established, they can serve as tracers for the non-equilibrium chemistry in interstellar ices thus eventually constraining fundamental reaction mechanisms deep inside interstellar ices.
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Affiliation(s)
- N Fabian Kleimeier
- Department of Chemistry and W. M. Keck Research Laboratory in Astrochemistry, University of Hawai'i at Manoa, 2545 McCarthy Mall, Honolulu, HI, 96822, USA
| | - Ralf I Kaiser
- Department of Chemistry and W. M. Keck Research Laboratory in Astrochemistry, University of Hawai'i at Manoa, 2545 McCarthy Mall, Honolulu, HI, 96822, USA
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4
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Gao LG, Fleming DG, Truhlar DG, Xu X. Large Anharmonic Effects on Tunneling and Kinetics: Reaction of Propane with Muonium. J Phys Chem Lett 2021; 12:4154-4159. [PMID: 33890795 DOI: 10.1021/acs.jpclett.1c01229] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Calculations of kinetic isotope effects (KIEs) provide challenging tests of quantal mass effects on reaction rates, and muonium KIEs are the most challenging. Here, we show that it can be very important to include reaction-coordinate-dependent vibrational anharmonicity along the whole reaction path to calculate tunneling probabilities and KIEs. For the reaction of propane with Mu, this decreases both the height and width of the vibrationally adiabatic potential barrier, with both effects increasing the rate constants. Our results agree well with the experimental observations.
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Affiliation(s)
- Lu Gem Gao
- Center for Combustion Energy, Department of Energy and Power Engineering, and Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Donald G Fleming
- TRIUMF and Department of Chemistry, University of British Columbia, 4004 Wesbrook Mall, Vancouver, BC V6T 1Z4, Canada
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Xuefei Xu
- Center for Combustion Energy, Department of Energy and Power Engineering, and Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Tsinghua University, Beijing 100084, China
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5
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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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6
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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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7
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Álvarez-Barcia S, Russ MS, Meisner J, Kästner J. Atom tunnelling in the reaction NH 3+ + H 2 → NH 4+ + H and its astrochemical relevance. Faraday Discuss 2018; 195:69-80. [PMID: 27711847 PMCID: PMC5317219 DOI: 10.1039/c6fd00096g] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The title reaction is involved in the formation of ammonia in the interstellar medium. We have calculated thermal rates including atom tunnelling using different rate theories. Canonical variational theory with microcanonically optimised multidimensional tunnelling was used for bimolecular rates, modelling the gas-phase reaction and also a surface-catalysed reaction of the Eley-Rideal type. Instanton theory provided unimolecular rates, which model the Langmuir-Hinshelwood type surface reaction. The potential energy was calculated on the CCSD(T)-F12 level of theory on the fly. We report thermal rates and H/D kinetic isotope effects. The latter have implications for observed H/D fractionation in molecular clouds. Tunnelling causes rate constants to be sufficient for the reaction to play a role in interstellar chemistry even at cryogenic temperature. We also discuss intricacies and limitations of the different tunnelling approximations to treat this reaction, including its pre-reactive minimum.
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Affiliation(s)
- Sonia Álvarez-Barcia
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany.
| | - Marie-Sophie Russ
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany.
| | - 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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8
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9
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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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10
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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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11
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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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12
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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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13
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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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14
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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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15
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Mori Y. Reaction pathway and H/D kinetic isotope effects of the triple proton transfer in a 7-hydroxyquinoline-methanol complex in the ground state: A computational approach. J PHYS ORG CHEM 2017. [DOI: 10.1002/poc.3747] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Yukie Mori
- Department of Chemistry, Faculty of Science; Ochanomizu University; Tokyo Japan
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16
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Parandaman A, Rajakumar B. Addition and abstraction kinetics of H atom with propylene and isobutylene between 200 and 2500 K: A DFT study. Chem Phys 2017. [DOI: 10.1016/j.chemphys.2017.05.008] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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17
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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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18
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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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20
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Song L, Kästner J. Formation of the prebiotic molecule NH 2CHO on astronomical amorphous solid water surfaces: accurate tunneling rate calculations. Phys Chem Chem Phys 2016; 18:29278-29285. [PMID: 27731439 PMCID: PMC5317214 DOI: 10.1039/c6cp05727f] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2016] [Accepted: 10/03/2016] [Indexed: 11/21/2022]
Abstract
Investigating how formamide forms in the interstellar medium is a hot topic in astrochemistry, which can contribute to our understanding of the origin of life on Earth. We have constructed a QM/MM model to simulate the hydrogenation of isocyanic acid on amorphous solid water surfaces to form formamide. The binding energy of HNCO on the ASW surface varies significantly between different binding sites, we found values between ∼0 and 100 kJ mol-1. The barrier for the hydrogenation reaction is almost independent of the binding energy, though. We calculated tunneling rate constants of H + HNCO → NH2CO at temperatures down to 103 K combining QM/MM with instanton theory. Tunneling dominates the reaction at such low temperatures. The tunneling reaction is hardly accelerated by the amorphous solid water surface compared to the gas phase for this system, even though the activation energy of the surface reaction is lower than the one of the gas-phase reaction. Both the height and width of the barrier affect the tunneling rate in practice. Strong kinetic isotope effects were observed by comparing to rate constants of D + HNCO → NHDCO. At 103 K we found a KIE of 231 on the surface and 146 in the gas phase. Furthermore, we investigated the gas-phase reaction NH2 + H2CO → NH2CHO + H and found it unlikely to occur at cryogenic temperatures. The data of our tunneling rate constants are expected to significantly influence astrochemical models.
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Affiliation(s)
- Lei Song
- 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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21
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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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22
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Meisner J, Kästner J. Reaction rates and kinetic isotope effects of H2 + OH → H2O + H. J Chem Phys 2016; 144:174303. [DOI: 10.1063/1.4948319] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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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23
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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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24
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Meisner J, Kästner J. Atom Tunneling in Chemistry. Angew Chem Int Ed Engl 2016; 55:5400-13. [DOI: 10.1002/anie.201511028] [Citation(s) in RCA: 140] [Impact Index Per Article: 17.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2015] [Revised: 01/08/2016] [Indexed: 01/01/2023]
Affiliation(s)
- Jan Meisner
- Institut für Theoretische Chemie Universität Stuttgart Pfaffenwaldring 55 70569 Stuttgart Germany
| | - Johannes Kästner
- Institut für Theoretische Chemie Universität Stuttgart Pfaffenwaldring 55 70569 Stuttgart Germany
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25
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Affiliation(s)
- Jan Meisner
- Institut für Theoretische Chemie Universität Stuttgart Pfaffenwaldring 55 70569 Stuttgart Deutschland
| | - Johannes Kästner
- Institut für Theoretische Chemie Universität Stuttgart Pfaffenwaldring 55 70569 Stuttgart Deutschland
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26
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Nakamura H, Nanbu S, Teranishi Y, Ohta A. Development of semiclassical molecular dynamics simulation method. Phys Chem Chem Phys 2016; 18:11972-85. [DOI: 10.1039/c5cp07655b] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Various quantum mechanical effects such as nonadiabatic transitions, quantum mechanical tunneling and coherence play crucial roles in a variety of chemical and biological systems.
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Affiliation(s)
- Hiroki Nakamura
- Institute of Molecular Science
- National Chiao Tung University
- Hsinchu
- 30010 Taiwan
| | - Shinkoh Nanbu
- Department of Materials and Life Science
- Sophia University
- Tokyo 102-8554
- Japan
| | | | - Ayumi Ohta
- Department of Materials and Life Science
- Sophia University
- Tokyo 102-8554
- Japan
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27
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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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28
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Abstract
Primary and secondary (18)O equilibrium isotope effects on the acidities of a variety of Brønsted and Lewis acids centered on carbon, boron, nitrogen, and phosphorus were computed by density-functional theory. For many of these acids, the secondary isotope effect was found to be larger than the primary isotope effect. This is a counterintuitive result, because the H atom that is lost is closer to the (18)O atom that is responsible for the primary isotope effect. The relative magnitudes of the isotope effects can be associated with the vibrational frequency and zero-point energy of the X═O vibrations, which are greater than those of the X-O vibrations. However, the difference between these contributions is small, and the major responsibility for the larger secondary isotope effect comes from the moment-of-inertia factor, which depends on the position of the (18)O atom relative to the principal axes of rotation.
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Affiliation(s)
- Charles L Perrin
- Department of Chemistry, University of California-San Diego, La Jolla, California 92093-0358, United States
| | - Kathryn D Burke
- Department of Chemistry, University of California-San Diego, La Jolla, California 92093-0358, United States
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