1
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Bridge O, Lazzaroni P, Martinazzo R, Rossi M, Althorpe SC, Litman Y. Quantum rates in dissipative systems with spatially varying friction. J Chem Phys 2024; 161:024110. [PMID: 38984959 DOI: 10.1063/5.0216823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2024] [Accepted: 06/20/2024] [Indexed: 07/11/2024] Open
Abstract
We investigate whether making the friction spatially dependent on the reaction coordinate introduces quantum effects into the thermal reaction rates for dissipative reactions. Quantum rates are calculated using the numerically exact multi-configuration time-dependent Hartree method, as well as the approximate ring-polymer molecular dynamics (RPMD), ring-polymer instanton methods, and classical molecular dynamics. By conducting simulations across a wide range of temperatures and friction strengths, we can identify the various regimes that govern the reactive dynamics. At high temperatures, in addition to the spatial-diffusion and energy-diffusion regimes predicted by Kramer's rate theory, a (coherent) tunneling-dominated regime is identified at low friction. At low temperatures, incoherent tunneling dominates most of Kramer's curve, except at very low friction, when coherent tunneling becomes dominant. Unlike in classical mechanics, the bath's influence changes the equilibrium time-independent properties of the system, leading to a complex interplay between spatially dependent friction and nuclear quantum effects even at high temperatures. More specifically, a realistic friction profile can lead to an increase (or decrease) of the quantum (classical) rates with friction within the spatial-diffusion regime, showing that classical and quantum rates display qualitatively different behaviors. Except at very low frictions, we find that RPMD captures most of the quantum effects in the thermal reaction rates.
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Affiliation(s)
- Oliver Bridge
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Paolo Lazzaroni
- MPI for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Rocco Martinazzo
- Department of Chemistry, Università degli Studi di Milano, Via Golgi 19, 20133 Milano, Italy
| | - Mariana Rossi
- MPI for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Stuart C Althorpe
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Yair Litman
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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2
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Pollak E. A personal perspective of the present status and future challenges facing thermal reaction rate theory. J Chem Phys 2024; 160:150902. [PMID: 38639316 DOI: 10.1063/5.0199557] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2024] [Accepted: 03/06/2024] [Indexed: 04/20/2024] Open
Abstract
Reaction rate theory has been at the center of physical chemistry for well over one hundred years. The evolution of the theory is not only of historical interest. Reliable and accurate computation of reaction rates remains a challenge to this very day, especially in view of the development of quantum chemistry methods, which predict the relevant force fields. It is still not possible to compute the numerically exact rate on the fly when the system has more than at most a few dozen anharmonic degrees of freedom, so one must consider various approximate methods, not only from the practical point of view of constructing numerical algorithms but also on conceptual and formal levels. In this Perspective, I present some of the recent analytical results concerning leading order terms in an ℏ2m series expansion of the exact rate and their implications on various approximate theories. A second aspect has to do with the crossover temperature between tunneling and thermal activation. Using a uniform semiclassical transmission probability rather than the "primitive" semiclassical theory leads to the conclusion that there is no divergence problem associated with a "crossover temperature." If one defines a semiclassical crossover temperature as the point at which the tunneling energy of the instanton equals the barrier height, then it is a factor of two higher than its previous estimate based on the "primitive" semiclassical approximation. In the low temperature tunneling regime, the uniform semiclassical theory as well as the "primitive" semiclassical theory were based on the classical Euclidean action of a periodic orbit on the inverted potential. The uniform semiclassical theory wrongly predicts that the "half-point," which is the energy at which the transmission probability equals 1/2, for any barrier potential, is always the barrier energy. We describe here how augmenting the Euclidean action with constant terms of order ℏ2 can significantly improve the accuracy of the semiclassical theory and correct this deficiency. This also leads to a deep connection with and improvement of vibrational perturbation theory. The uniform semiclassical theory also enables an extension of the quantum version of Kramers' turnover theory to temperatures below the "crossover temperature." The implications of these recent advances on various approximate methods used to date are discussed at length, leading to the conclusion that reaction rate theory will continue to challenge us both on conceptual and practical levels for years to come.
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Affiliation(s)
- Eli Pollak
- Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel
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3
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Cook L, Runeson JE, Richardson JO, Hele TJH. Which Algorithm Best Propagates the Meyer-Miller-Stock-Thoss Mapping Hamiltonian for Non-Adiabatic Dynamics? J Chem Theory Comput 2023; 19:6109-6125. [PMID: 37704193 PMCID: PMC10536990 DOI: 10.1021/acs.jctc.3c00709] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2023] [Indexed: 09/15/2023]
Abstract
A common strategy to simulate mixed quantum-classical dynamics is by propagating classical trajectories with mapping variables, often using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian or the related spin-mapping approach. When mapping the quantum subsystem, the coupled dynamics reduce to a set of equations of motion to integrate. Several numerical algorithms have been proposed, but a thorough performance comparison appears to be lacking. Here, we compare three time-propagation algorithms for the MMST Hamiltonian: the Momentum Integral (MInt) (J. Chem. Phys., 2018, 148, 102326), the Split-Liouvillian (SL) (Chem. Phys., 2017, 482, 124-134), and the algorithm in J. Chem. Phys., 2012, 136, 084101 that we refer to as the Degenerate Eigenvalue (DE) algorithm due to the approximation required during derivation. We analyze the accuracy of individual trajectories, correlation functions, energy conservation, symplecticity, Liouville's theorem, and the computational cost. We find that the MInt algorithm is the only rigorously symplectic algorithm. However, comparable accuracy at a lower computational cost can be obtained with the SL algorithm. The approximation implicitly made within the DE algorithm conserves energy poorly, even for small timesteps, and thus leads to slightly different results. These results should guide future mapping-variable simulations.
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Affiliation(s)
- Lauren
E. Cook
- Department
of Chemistry, University College London, Christopher Ingold Building, London WC1H 0AJ, U.K.
| | - Johan E. Runeson
- Department
of Chemistry and Applied Biosciences, ETH
Zürich, Zürich 8093, Switzerland
| | - Jeremy O. Richardson
- Department
of Chemistry and Applied Biosciences, ETH
Zürich, Zürich 8093, Switzerland
| | - Timothy J. H. Hele
- Department
of Chemistry, University College London, Christopher Ingold Building, London WC1H 0AJ, U.K.
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4
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Anderson MC, Schile AJ, Limmer DT. Nonadiabatic transition paths from quantum jump trajectories. J Chem Phys 2022; 157:164105. [DOI: 10.1063/5.0102891] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a means of studying rare reactive pathways in open quantum systems using transition path theory and ensembles of quantum jump trajectories. This approach allows for the elucidation of reactive paths for dissipative, nonadiabatic dynamics when the system is embedded in a Markovian environment. We detail the dominant pathways and rates of thermally activated processes and the relaxation pathways and photoyields following vertical excitation in a minimal model of a conical intersection. We find that the geometry of the conical intersection affects the electronic character of the transition state as defined through a generalization of a committor function for a thermal barrier crossing event. Similarly, the geometry changes the mechanism of relaxation following a vertical excitation. Relaxation in models resulting from small diabatic coupling proceeds through pathways dominated by pure dephasing, while those with large diabatic coupling proceed through pathways limited by dissipation. The perspective introduced here for the nonadiabatic dynamics of open quantum systems generalizes classical notions of reactive paths to fundamentally quantum mechanical processes.
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Affiliation(s)
- Michelle C. Anderson
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Addison J. Schile
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - David T. Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Kavli Energy NanoSciences Institute, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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5
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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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7
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8
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Novikov IS, Suleimanov YV, Shapeev AV. Automated calculation of thermal rate coefficients using ring polymer molecular dynamics and machine-learning interatomic potentials with active learning. Phys Chem Chem Phys 2018; 20:29503-29512. [DOI: 10.1039/c8cp06037a] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We propose a methodology for the fully automated calculation of thermal rate coefficients of gas phase chemical reactions, which is based on combining ring polymer molecular dynamics (RPMD) and machine-learning interatomic potentials actively learning on-the-fly.
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Affiliation(s)
- I. S. Novikov
- Skolkovo Institute of Science and Technology
- Skolkovo Innovation Center
- Moscow 143026
- Russia
| | - Y. V. Suleimanov
- Computation-based Science and Technology Research Center
- Cyprus Institute
- Nicosia 2121
- Cyprus
- Department of Chemical Engineering
| | - A. V. Shapeev
- Skolkovo Institute of Science and Technology
- Skolkovo Innovation Center
- Moscow 143026
- Russia
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9
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Affiliation(s)
- Timothy J. H. Hele
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, USA
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10
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Abstract
This paper summarizes the contributions to the Faraday Discussion on reaction rate theory. The topics range from contemporary usage of transition state theory, including rare event sampling, to instantons and non-adiabatic dynamics.
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Affiliation(s)
- David Chandler
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - David E Manolopoulos
- Department of Chemistry, University of Oxford, Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, UK
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11
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Bai M, Lu D, Li Y, Li J. Ring-polymer molecular dynamical calculations for the F + HCl → HF + Cl reaction on the ground 1 2A' potential energy surface. Phys Chem Chem Phys 2016; 18:32031-32041. [PMID: 27407007 DOI: 10.1039/c6cp03306g] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2023]
Abstract
The reaction kinetics of the heavy-light-heavy abstraction reaction F + HCl → HF + Cl on the ground electronic state potential energy surface (PES) is investigated theoretically by a recently developed ring polymer molecular dynamics (RPMD) approach. First, a new PES is developed by the permutation invariant polynomial neural network (PIP-NN) approach based on 30 620 points sampled over a large configuration space from the latest and most accurate Deskevich-Hayes-Takahashi-Skodje-Nesbitt (DHTSN) PES (J. Chem. Phys., 2006, 124, 224303). Excellent fitting performance was achieved with only 521 parameters. The PIP-NN PES is 11 times faster than the DHTSN PES. Besides, the first analytical derivatives with respect to the coordinates of the atoms have been obtained for the PIP-NN PES. The RPMD rate coefficients on the PIP-NN PES are calculated and compared with available theoretical and experimental results. It is found that the experimental rate coefficients are significantly larger than the theoretical results on the DHTSN PES, due to its overestimated reaction barrier. We conclude that a reliable PES for this important heavy-light-heavy reaction is highly desirable.
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Affiliation(s)
- Mengna Bai
- School of Chemistry and Chemical Engineering, Chongqing University, Chongqing 401331, China.
| | - Dandan Lu
- School of Chemistry and Chemical Engineering, Chongqing University, Chongqing 401331, China.
| | - Yongle Li
- Department of Physics, International Center of Quantum and Molecular Structure, and Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University, Shanghai 200444, China.
| | - Jun Li
- School of Chemistry and Chemical Engineering, Chongqing University, Chongqing 401331, China.
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12
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Suleimanov YV, Aoiz FJ, Guo H. Chemical Reaction Rate Coefficients from Ring Polymer Molecular Dynamics: Theory and Practical Applications. J Phys Chem A 2016; 120:8488-8502. [DOI: 10.1021/acs.jpca.6b07140] [Citation(s) in RCA: 92] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Yury V. Suleimanov
- Computation-based Science
and Technology Research Center, Cyprus Institute, 20 Kavafi Street, Nicosia 2121, Cyprus
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - F. Javier Aoiz
- Departamento de Química
Física I, Facultad de CC. Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Hua Guo
- Department of Chemistry and
Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
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13
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Lu CY, Perez D, Voter AF. Accelerating ring-polymer molecular dynamics with parallel-replica dynamics. J Chem Phys 2016; 144:244109. [DOI: 10.1063/1.4954311] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Affiliation(s)
- Chun-Yaung Lu
- Department of Energy Resources Engineering, Stanford University, Stanford, CA 94305, USA
| | - Danny Perez
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| | - Arthur F. Voter
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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14
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Hele TJH, Althorpe SC. An alternative derivation of ring-polymer molecular dynamics transition-state theory. J Chem Phys 2016; 144:174107. [DOI: 10.1063/1.4947589] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [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
| | - Stuart C. Althorpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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15
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Hele TJH. On the relation between thermostatted ring-polymer molecular dynamics and exact quantum dynamics. Mol Phys 2016. [DOI: 10.1080/00268976.2015.1136003] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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16
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Hele TJH, Ananth N. Deriving the exact nonadiabatic quantum propagator in the mapping variable representation. Faraday Discuss 2016; 195:269-289. [DOI: 10.1039/c6fd00106h] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and discrete electronic states. The resulting Liouvillian is a Moyal series that, when suitably approximated, can allow for the use of classical dynamics to efficiently model large systems. We demonstrate that different truncations of the exact Liouvillian lead to existing approximate semiclassical and mixed quantum–classical methods and we derive an associated error term for each method. Furthermore, by combining the imaginary-time path-integral representation of the Boltzmann operator with the exact Liouvillian, we obtain an analytic expression for thermal quantum real-time correlation functions. These results provide a rigorous theoretical foundation for the development of accurate and efficient classical-like dynamics to compute observables such as electron transfer reaction rates in complex quantized systems.
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Affiliation(s)
| | - Nandini Ananth
- Department of Chemistry and Chemical Biology
- Cornell University
- Ithaca
- USA
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17
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Cendagorta JR, Powers A, Hele TJH, Marsalek O, Bačić Z, Tuckerman ME. Competing quantum effects in the free energy profiles and diffusion rates of hydrogen and deuterium molecules through clathrate hydrates. Phys Chem Chem Phys 2016; 18:32169-32177. [DOI: 10.1039/c6cp05968f] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Depending on the temperature, competing quantum effects are found to accelerate or decelerate the diffusion rate of hydrogen compared to deuterium in clathrates.
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Affiliation(s)
| | - Anna Powers
- Department of Chemistry
- New York University
- New York
- USA
| | | | | | - Zlatko Bačić
- Department of Chemistry
- New York University
- New York
- USA
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai
| | - Mark E. Tuckerman
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai
- Shanghai
- China
- Department of Chemistry and Courant Institute of Mathematical Sciences
- New York University
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18
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Richardson JO, Bauer R, Thoss M. Semiclassical Green’s functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit. J Chem Phys 2015; 143:134115. [DOI: 10.1063/1.4932361] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [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
| | - Rainer Bauer
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstraße 7/B2, 91058 Erlangen, Germany
| | - Michael Thoss
- 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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19
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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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20
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Hele TJH, Willatt MJ, Muolo A, Althorpe SC. Communication: Relation of centroid molecular dynamics and ring-polymer molecular dynamics to exact quantum dynamics. J Chem Phys 2015; 142:191101. [DOI: 10.1063/1.4921234] [Citation(s) in RCA: 77] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Affiliation(s)
- Timothy J. H. Hele
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Michael J. Willatt
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Andrea Muolo
- 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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21
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Hele TJH, Willatt MJ, Muolo A, Althorpe SC. Boltzmann-conserving classical dynamics in quantum time-correlation functions: “Matsubara dynamics”. J Chem Phys 2015; 142:134103. [DOI: 10.1063/1.4916311] [Citation(s) in RCA: 71] [Impact Index Per Article: 7.9] [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
| | - Michael J. Willatt
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Andrea Muolo
- 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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Pérez de Tudela R, Suleimanov YV, Richardson JO, Sáez Rábanos V, Green WH, Aoiz FJ. Stress Test for Quantum Dynamics Approximations: Deep Tunneling in the Muonium Exchange Reaction D + HMu → DMu + H. J Phys Chem Lett 2014; 5:4219-4224. [PMID: 26278957 DOI: 10.1021/jz502216g] [Citation(s) in RCA: 57] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Quantum effects play a crucial role in chemical reactions involving light atoms at low temperatures, especially when a light particle is exchanged between two heavier partners. Different theoretical methodologies have been developed in the last decades attempting to describe zero-point energy and tunneling effects without abandoning a classical or semiclassical framework. In this work, we have chosen the D + HMu → DMu + H reaction as a stress test system for three well-established methods: two representative versions of transition state theory (TST), canonical variational theory and semiclassical instanton, and ring polymer molecular dynamics (RPMD). These calculations will be compared with accurate quantum mechanical results. Despite its apparent simplicity, the exchange of the extremely light muonium atom (0.114 u) becomes a most challenging reaction for conventional methods. The main result of this work is that RPMD provides an overall better performance than TST-based methods for such a demanding reaction. RPMD might well turn out to be a useful tool beyond TST applicability.
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Affiliation(s)
- Ricardo Pérez de Tudela
- †Departamento de Quı́mica Fı́sica I, Facultad de CC. Quı́micas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Yury V Suleimanov
- ‡Computation-based Science and Technology Research Center, Cyprus Institute, 20 Kavafi Str., Nicosia 2121, Cyprus
- ∥Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Jeremy O Richardson
- ¶Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany
| | - Vicente Sáez Rábanos
- §Departamento de Quı́mica y Bioquı́mica, ETS Ingenieros de Montes, Universidad Politécnica, 28040 Madrid, Spain
| | - William H Green
- ∥Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - F J Aoiz
- †Departamento de Quı́mica Fı́sica I, Facultad de CC. Quı́micas, Universidad Complutense de Madrid, 28040 Madrid, Spain
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23
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Zhang Y, Stecher T, Cvitaš MT, Althorpe SC. Which Is Better at Predicting Quantum-Tunneling Rates: Quantum Transition-State Theory or Free-Energy Instanton Theory? J Phys Chem Lett 2014; 5:3976-3980. [PMID: 26276480 DOI: 10.1021/jz501889v] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Quantum transition-state theory (QTST) and free-energy instanton theory (FEIT) are two closely related methods for estimating the quantum rate coefficient from the free-energy at the reaction barrier. In calculations on one-dimensional models, FEIT typically gives closer agreement than QTST with the exact quantum results at all temperatures below the crossover to deep tunneling, suggesting that FEIT is a better approximation than QTST in this regime. Here we show that this simple trend does not hold for systems of greater dimensionality. We report tests on several collinear and three-dimensional reactions, in which QTST outperforms FEIT over a range of temperatures below crossover, which can extend down to half the crossover temperature (below which FEIT outperforms QTST). This suggests that QTST-based methods such as ring-polymer molecular dynamics (RPMD) may often give closer agreement with the exact quantum results than FEIT.
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Affiliation(s)
- Yanchuan Zhang
- †Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Thomas Stecher
- †Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Marko T Cvitaš
- ‡Ruđer Bošković Institute, Department of Physical Chemistry, Bijenička Cesta 54, 10000 Zagreb, Croatia
| | - Stuart C Althorpe
- †Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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24
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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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25
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Rossi M, Ceriotti M, Manolopoulos DE. How to remove the spurious resonances from ring polymer molecular dynamics. J Chem Phys 2014; 140:234116. [DOI: 10.1063/1.4883861] [Citation(s) in RCA: 133] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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26
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Jang S, Sinitskiy AV, Voth GA. Can the ring polymer molecular dynamics method be interpreted as real time quantum dynamics? J Chem Phys 2014. [DOI: 10.1063/1.4870717] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Menzeleev AR, Bell F, Miller TF. Kinetically constrained ring-polymer molecular dynamics for non-adiabatic chemical reactions. J Chem Phys 2014; 140:064103. [DOI: 10.1063/1.4863919] [Citation(s) in RCA: 85] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Zhang Y, Rommel JB, Cvitaš MT, Althorpe SC. Shallow-tunnelling correction factor for use with Wigner–Eyring transition-state theory. Phys Chem Chem Phys 2014; 16:24292-300. [DOI: 10.1039/c4cp03235g] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We obtain a shallow-tunnelling correction factor for use with Wigner–Eyring transition-state theory (TST).
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Affiliation(s)
- Yanchuan Zhang
- Department of Chemistry
- University of Cambridge
- Cambridge CB2 1EW, UK
| | - Judith B. Rommel
- Department of Chemistry
- University of Cambridge
- Cambridge CB2 1EW, UK
| | - Marko T. Cvitaš
- Ruđer Bošković Institute
- Department of Physical Chemistry
- 10000 Zagreb, Croatia
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de Tudela RP, Suleimanov YV, Menéndez M, Castillo JF, Aoiz FJ. A ring polymer molecular dynamics study of the Cl + O3 reaction. Phys Chem Chem Phys 2014; 16:2920-7. [DOI: 10.1039/c3cp54405b] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
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