1
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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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2
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Videla PE, Batista VS. Matsubara dynamics approximation for generalized multi-time correlation functions. J Chem Phys 2023; 158:2889027. [PMID: 37154285 DOI: 10.1063/5.0146654] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 04/21/2023] [Indexed: 05/10/2023] Open
Abstract
We introduce a semi-classical approximation for calculating generalized multi-time correlation functions based on Matsubara dynamics, a classical dynamics approach that conserves the quantum Boltzmann distribution. This method is exact for the zero time and harmonic limits and reduces to classical dynamics when only one Matsubara mode is considered (i.e., the centroid). Generalized multi-time correlation functions can be expressed as canonical phase-space integrals, involving classically evolved observables coupled through Poisson brackets in a smooth Matsubara space. Numerical tests on a simple potential show that the Matsubara approximation exhibits better agreement with exact results than classical dynamics, providing a bridge between the purely quantum and classical descriptions of multi-time correlation functions. Despite the phase problem that prevents practical applications of Matsubara dynamics, the reported work provides a benchmark theory for the future development of quantum-Boltzmann-preserving semi-classical approximations for studies of chemical dynamics in condensed phase systems.
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Affiliation(s)
- Pablo E Videla
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520-8107, USA
| | - Victor S Batista
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520-8107, USA
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3
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Jung KA, Videla PE, Batista VS. Ring-polymer, centroid, and mean-field approximations to multi-time Matsubara dynamics. J Chem Phys 2020; 153:124112. [PMID: 33003707 DOI: 10.1063/5.0021843] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Based on a recently developed generalization of Matsubara dynamics to the multi-time realm, we present a formal derivation of multi-time generalizations of ring-polymer molecular dynamics, thermostatted ring-polymer molecular dynamics (TRPMD), centroid molecular dynamics (CMD), and mean-field Matsubara dynamics. Additionally, we analyze the short-time accuracy of each methodology. We find that for multi-time correlation functions of linear operators, (T)RPMD is accurate up to order t3, while CMD is only correct up to t, indicating a degradation in the accuracy of these methodologies with respect to the single-time counterparts. The present work provides a firm justification for the use of path-integral-based approximations for the calculation of multi-time correlation functions.
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Affiliation(s)
- Kenneth A Jung
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Pablo E Videla
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Victor S Batista
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
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4
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Lu X, Wang X, Fu B, Zhang D. Theoretical Investigations of Rate Coefficients of H + H2O2 → OH + H2O on a Full-Dimensional Potential Energy Surface. J Phys Chem A 2019; 123:3969-3976. [DOI: 10.1021/acs.jpca.9b02526] [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)
- Xiaoxiao Lu
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Zhongshan Road 457, Dalian 116023, China
- Department of Chemical Physics, University of Science and Technology of China, Jinzhai Road 96, Hefei 230026, China
| | - Xingan Wang
- Department of Chemical Physics, University of Science and Technology of China, Jinzhai Road 96, Hefei 230026, China
| | - Bina Fu
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Zhongshan Road 457, Dalian 116023, China
| | - Donghui Zhang
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Zhongshan Road 457, Dalian 116023, China
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5
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Lu X, Meng Q, Wang X, Fu B, Zhang DH. Rate coefficients of the H + H2O2→ H2+ HO2reaction on an accurate fundamental invariant-neural network potential energy surface. J Chem Phys 2018; 149:174303. [PMID: 30409010 DOI: 10.1063/1.5063613] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Xiaoxiao Lu
- Department of Chemical Physics, University of Science and Technology of China, Jinzhai Road 96, Hefei 230026, China
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Zhongshan Road 457, Dalian 116023, China
| | - Qingyong Meng
- Department of Applied Chemistry, Northwestern Polytechnical University, Youyi West Road 127, Xi’an 710072, China
| | - Xingan Wang
- Department of Chemical Physics, University of Science and Technology of China, Jinzhai Road 96, Hefei 230026, China
| | - Bina Fu
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Zhongshan Road 457, Dalian 116023, China
| | - Dong H. Zhang
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Zhongshan Road 457, Dalian 116023, China
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6
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Bhowmick S, Bossion D, Scribano Y, Suleimanov YV. The low temperature D + + H 2→ HD + H + reaction rate coefficient: a ring polymer molecular dynamics and quasi-classical trajectory study. Phys Chem Chem Phys 2018; 20:26752-26763. [PMID: 30324962 DOI: 10.1039/c8cp05398g] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The reaction between D+ and H2 plays an important role in astrochemistry at low temperatures and also serves as a prototype for a simple ion-molecule reaction. Its ground X[combining tilde]1A' state has a very small thermodynamic barrier (up to 1.8 × 10-2 eV) and the reaction proceeds through the formation of an intermediate complex lying within the potential well with a depth of at least 0.2 eV, thus representing a challenge for dynamical studies. In the present work, we analyze the title reaction within the temperature range of 20-100 K by means of ring polymer molecular dynamics (RPMD) and quasi-classical trajectory (QCT) methods over the full-dimensional global potential energy surface developed by Aguado et al. [A. Aguado, O. Roncero, C. Tablero, C. Sanz and M. Paniagua, J. Chem. Phys., 2000, 112, 1240]. The computed thermal RPMD and QCT rate coefficients are found to be almost independent of temperature and fall within the range of 1.34-2.01 × 10-9 cm3 s-1. They are also in very good agreement with previous time-independent quantum mechanical and statistical quantum method calculations. Furthermore, we observe that the choice of asymptotic separation distance between the reactants can markedly alter the rate coefficient in the low temperature regime (20-50 K). Therefore it is of utmost importance to correctly assign the value of this parameter for dynamical studies, particularly at very low temperatures of astrochemical importance. We finally conclude that the experimental rate measurements for the title reaction are highly desirable in future.
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Affiliation(s)
- Somnath Bhowmick
- Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Konstantinou Kavafi Street, Nicosia 2121, Cyprus.
| | - Duncan Bossion
- Laboratoire Univers et Particules de Montpellier, UMR-CNRS 5299, Université de Montpellier, Place Eugène Bataillon, 34095 Montpellier, France
| | - Yohann Scribano
- Laboratoire Univers et Particules de Montpellier, UMR-CNRS 5299, Université de Montpellier, Place Eugène Bataillon, 34095 Montpellier, France
| | - Yury V Suleimanov
- Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Konstantinou Kavafi Street, Nicosia 2121, Cyprus.
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7
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Fang W, Richardson JO, Chen J, Li XZ, Michaelides A. Simultaneous Deep Tunneling and Classical Hopping for Hydrogen Diffusion on Metals. PHYSICAL REVIEW LETTERS 2017; 119:126001. [PMID: 29341641 DOI: 10.1103/physrevlett.119.126001] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2017] [Indexed: 06/07/2023]
Abstract
Hydrogen diffusion on metals exhibits rich quantum behavior, which is not yet fully understood. Using simulations, we show that many hydrogen diffusion barriers can be categorized into those with parabolic tops and those with broad tops. With parabolic-top barriers, hydrogen diffusion evolves gradually from classical hopping, to shallow tunneling, to deep tunneling as the temperature (T) decreases, and noticeable quantum effects persist at moderate T. In contrast, with broad-top barriers quantum effects become important only at low T and the classical-to-quantum transition is sharp, at which classical hopping and deep tunneling both occur. This coexistence indicates that more than one mechanism contributes to the quantum reaction rate. The conventional definition of the classical-to-quantum crossover T is invalid for the broad tops, and we give a new definition. Extending this, we propose a model to predict the transition T for broad-top diffusion, providing a general guide for theory and experiment.
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Affiliation(s)
- Wei Fang
- Thomas Young Centre, London Centre for Nanotechnology and Department of Chemistry, University College London, London WC1E 6BT, United Kingdom
| | | | - Ji Chen
- Thomas Young Centre, London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Xin-Zheng Li
- School of Physics and the Collaborative Innovation Center of Quantum Matters, Peking University, Beijing 100871, People's Republic of China
| | - Angelos Michaelides
- Thomas Young Centre, London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
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8
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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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9
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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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10
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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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11
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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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12
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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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13
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Hickson KM, Loison JC, Guo H, Suleimanov YV. Ring-Polymer Molecular Dynamics for the Prediction of Low-Temperature Rates: An Investigation of the C((1)D) + H2 Reaction. J Phys Chem Lett 2015; 6:4194-4199. [PMID: 26538033 DOI: 10.1021/acs.jpclett.5b02060] [Citation(s) in RCA: 57] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Quantum mechanical calculations are important tools for predicting the rates of elementary reactions, particularly for those involving hydrogen and at low temperatures where quantum effects become increasingly important. These approaches are computationally expensive, however, particularly when applied to complex polyatomic systems or processes characterized by deep potential wells. While several approximate techniques exist, many of these have issues with reliability. The ring-polymer molecular dynamics method was recently proposed as an accurate and efficient alternative. Here, we test this technique at low temperatures (300-50 K) by analyzing the behavior of the barrierless C((1)D) + H2 reaction over the two lowest singlet potential energy surfaces. To validate the theory, rate coefficients were measured using a supersonic flow reactor down to 50 K. The experimental and theoretical rates are in excellent agreement, supporting the future application of this method for determining the kinetics and dynamics of a wide range of low-temperature reactions.
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Affiliation(s)
- Kevin M Hickson
- Institut des Sciences Moléculaires, Université de Bordeaux , F-33400 Talence, France
- CNRS, Institut des Sciences Moléculaires , F-33400 Talence, France
| | - Jean-Christophe Loison
- Institut des Sciences Moléculaires, Université de Bordeaux , F-33400 Talence, France
- CNRS, Institut des Sciences Moléculaires , F-33400 Talence, France
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico , Albuquerque, New Mexico 87131, United States
| | - 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 , 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
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14
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Arseneau DJ, Fleming DG, Li Y, Li J, Suleimanov YV, Guo H. Rate Coefficient for the 4Heμ + CH4 Reaction at 500 K: Comparison between Theory and Experiment. J Phys Chem B 2015; 120:1641-8. [DOI: 10.1021/acs.jpcb.5b08368] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Donald J. Arseneau
- TRIUMF
and Department of Chemistry, University of British Columbia, Vancouver, BC V6T 2Z1, Canada
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