ACS Publications. Most Trusted. Most Cited. Most Read
My Activity
CONTENT TYPES

Figure 1Loading Img

Invariant Manifolds and Rate Constants in Driven Chemical Reactions

  • Matthias Feldmaier
    Matthias Feldmaier
    Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
  • Philippe Schraft
    Philippe Schraft
    Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
  • Robin Bardakcioglu
    Robin Bardakcioglu
    Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
  • Johannes Reiff
    Johannes Reiff
    Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
  • Melissa Lober
    Melissa Lober
    Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
  • Martin Tschöpe
    Martin Tschöpe
    Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
  • Andrej Junginger
    Andrej Junginger
    Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
  • Jörg Main
    Jörg Main
    Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
    More by Jörg Main
  • Thomas Bartsch
    Thomas Bartsch
    Centre for Nonlinear Mathematics and Applications, Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
  • , and 
  • Rigoberto Hernandez*
    Rigoberto Hernandez
    Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, United States
    *E-mail: [email protected]
Cite this: J. Phys. Chem. B 2019, 123, 9, 2070–2086
Publication Date (Web):February 7, 2019
https://doi.org/10.1021/acs.jpcb.8b10541
Copyright © 2019 American Chemical Society

    Article Views

    700

    Altmetric

    -

    Citations

    LEARN ABOUT THESE METRICS
    Other access options

    Abstract

    Abstract Image

    Reaction rates of chemical reactions under nonequilibrium conditions can be determined through the construction of the normally hyperbolic invariant manifold (NHIM) [and moving dividing surface (DS)] associated with the transition state trajectory. Here, we extend our recent methods by constructing points on the NHIM accurately even for multidimensional cases. We also advance the implementation of machine learning approaches to construct smooth versions of the NHIM from a known high-accuracy set of its points. That is, we expand on our earlier use of neural nets and introduce the use of Gaussian process regression for the determination of the NHIM. Finally, we compare and contrast all of these methods for a challenging two-dimensional model barrier case so as to illustrate their accuracy and general applicability.

    Read this article

    To access this article, please review the available access options below.

    Get instant access

    Purchase Access

    Read this article for 48 hours. Check out below using your ACS ID or as a guest.

    Recommended

    Access through Your Institution

    You may have access to this article through your institution.

    Your institution does not have access to this content. You can change your affiliated institution below.

    Cited By

    This article is cited by 23 publications.

    1. Francisco Gonzalez Montoya. The Classical Action as a Tool to Visualise the Phase Space of Hamiltonian Systems. Dynamics 2023, 3 (4) , 678-694. https://doi.org/10.3390/dynamics3040036
    2. Michael Maihöfer, Johannes Reiff, Jörg Main, Rigoberto Hernandez. Transition state theory characterizes thin film macrospin dynamics driven by an oscillatory magnetic field: Inertial effects. Communications in Nonlinear Science and Numerical Simulation 2022, 115 , 106764. https://doi.org/10.1016/j.cnsns.2022.106764
    3. Víctor J. García-Garrido, Stephen Wiggins. Lagrangian descriptors and the action integral of classical mechanics. Physica D: Nonlinear Phenomena 2022, 434 , 133206. https://doi.org/10.1016/j.physd.2022.133206
    4. Johannes Mögerle, Robin Schuldt, Johannes Reiff, Jörg Main, Rigoberto Hernandez. Transition state dynamics of a driven magnetic free layer. Communications in Nonlinear Science and Numerical Simulation 2022, 105 , 106054. https://doi.org/10.1016/j.cnsns.2021.106054
    5. Johannes Reiff, Jonas Zatsch, Jörg Main, Rigoberto Hernandez. On the stability of satellites at unstable libration points of sun–planet–moon systems. Communications in Nonlinear Science and Numerical Simulation 2022, 104 , 106053. https://doi.org/10.1016/j.cnsns.2021.106053
    6. Johannes Reiff, Robin Bardakcioglu, Matthias Feldmaier, Jörg Main, Rigoberto Hernandez. Controlling reaction dynamics in chemical model systems through external driving. Physica D: Nonlinear Phenomena 2021, 427 , 133013. https://doi.org/10.1016/j.physd.2021.133013
    7. Francisco Gonzalez Montoya, Víctor J. García-Garrido, Broncio Aguilar-Sanjuan, Stephen Wiggins. Transport and roaming on the double van der Waals potential energy surface. Communications in Nonlinear Science and Numerical Simulation 2021, 102 , 105917. https://doi.org/10.1016/j.cnsns.2021.105917
    8. Jun Zhong, Shane D Ross. Transition criteria and phase space structures in a three degree of freedom system with dissipation. Journal of Physics A: Mathematical and Theoretical 2021, 54 (36) , 365701. https://doi.org/10.1088/1751-8121/ac16c7
    9. Dániel Jánosi, Tamás Tél. Chaos in conservative discrete-time systems subjected to parameter drift. Chaos: An Interdisciplinary Journal of Nonlinear Science 2021, 31 (3) https://doi.org/10.1063/5.0031660
    10. Johannes Reiff, Matthias Feldmaier, Jörg Main, Rigoberto Hernandez. Dynamics and decay rates of a time-dependent two-saddle system. Physical Review E 2021, 103 (2) https://doi.org/10.1103/PhysRevE.103.022121
    11. I. Santamaría-Holek, A. Pérez-Madrid. Eyring equation and fluctuation–dissipation far away from equilibrium. The Journal of Chemical Physics 2020, 153 (24) https://doi.org/10.1063/5.0032634
    12. Francisco Gonzalez Montoya, Stephen Wiggins. Phase space structure and escape time dynamics in a Van der Waals model for exothermic reactions. Physical Review E 2020, 102 (6) https://doi.org/10.1103/PhysRevE.102.062203
    13. Robin Bardakcioglu, Johannes Reiff, Matthias Feldmaier, Jörg Main, Rigoberto Hernandez. Thermal decay rates of an activated complex in a driven model chemical reaction. Physical Review E 2020, 102 (6) https://doi.org/10.1103/PhysRevE.102.062204
    14. Víctor J. García-Garrido, Makrina Agaoglou, Stephen Wiggins. Exploring isomerization dynamics on a potential energy surface with an index-2 saddle using lagrangian descriptors. Communications in Nonlinear Science and Numerical Simulation 2020, 89 , 105331. https://doi.org/10.1016/j.cnsns.2020.105331
    15. Manuel Kuchelmeister, Johannes Reiff, Jörg Main, Rigoberto Hernandez. Dynamics and Bifurcations on the Normally Hyperbolic Invariant Manifold of a Periodically Driven System with Rank-1 Saddle. Regular and Chaotic Dynamics 2020, 25 (5) , 496-507. https://doi.org/10.1134/S1560354720050068
    16. Matthias Feldmaier, Johannes Reiff, Rosa M. Benito, Florentino Borondo, Jörg Main, Rigoberto Hernandez. Influence of external driving on decays in the geometry of the LiCN isomerization. The Journal of Chemical Physics 2020, 153 (8) https://doi.org/10.1063/5.0015509
    17. Shibabrat Naik, Stephen Wiggins. Detecting reactive islands in a system-bath model of isomerization. Physical Chemistry Chemical Physics 2020, 22 (32) , 17890-17912. https://doi.org/10.1039/D0CP01362E
    18. M. Katsanikas, Víctor J. García-Garrido, S. Wiggins. Detection of Dynamical Matching in a Caldera Hamiltonian System Using Lagrangian Descriptors. International Journal of Bifurcation and Chaos 2020, 30 (09) , 2030026. https://doi.org/10.1142/S0218127420300268
    19. Yutaka Nagahata, F. Borondo, R. M. Benito, Rigoberto Hernandez. Identifying reaction pathways in phase space via asymptotic trajectories. Physical Chemistry Chemical Physics 2020, 22 (18) , 10087-10105. https://doi.org/10.1039/C9CP06610A
    20. Martin Tschöpe, Matthias Feldmaier, Jörg Main, Rigoberto Hernandez. Neural network approach for the dynamics on the normally hyperbolic invariant manifold of periodically driven systems. Physical Review E 2020, 101 (2) https://doi.org/10.1103/PhysRevE.101.022219
    21. Matthias Feldmaier, Robin Bardakcioglu, Johannes Reiff, Jörg Main, Rigoberto Hernandez. Phase-space resolved rates in driven multidimensional chemical reactions. The Journal of Chemical Physics 2019, 151 (24) https://doi.org/10.1063/1.5127539
    22. Shibabrat Naik, Víctor J. García-Garrido, Stephen Wiggins. Finding NHIM: Identifying high dimensional phase space structures in reaction dynamics using Lagrangian descriptors. Communications in Nonlinear Science and Numerical Simulation 2019, 79 , 104907. https://doi.org/10.1016/j.cnsns.2019.104907
    23. Shibabrat Naik, Stephen Wiggins. Finding normally hyperbolic invariant manifolds in two and three degrees of freedom with Hénon-Heiles-type potential. Physical Review E 2019, 100 (2) https://doi.org/10.1103/PhysRevE.100.022204

    Pair your accounts.

    Export articles to Mendeley

    Get article recommendations from ACS based on references in your Mendeley library.

    Pair your accounts.

    Export articles to Mendeley

    Get article recommendations from ACS based on references in your Mendeley library.

    You’ve supercharged your research process with ACS and Mendeley!

    STEP 1:
    Click to create an ACS ID

    Please note: If you switch to a different device, you may be asked to login again with only your ACS ID.

    Please note: If you switch to a different device, you may be asked to login again with only your ACS ID.

    Please note: If you switch to a different device, you may be asked to login again with only your ACS ID.

    MENDELEY PAIRING EXPIRED
    Your Mendeley pairing has expired. Please reconnect