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Ge P, Zhang Z, Lei H. Data-Driven Learning of the Generalized Langevin Equation with State-Dependent Memory. PHYSICAL REVIEW LETTERS 2024; 133:077301. [PMID: 39213577 DOI: 10.1103/physrevlett.133.077301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2023] [Revised: 02/27/2024] [Accepted: 07/12/2024] [Indexed: 09/04/2024]
Abstract
We present a data-driven method to learn stochastic reduced models of complex systems that retain a state-dependent memory beyond the standard generalized Langevin equation with a homogeneous kernel. The constructed model naturally encodes the heterogeneous energy dissipation by jointly learning a set of state features and the non-Markovian coupling among the features. Numerical results demonstrate the limitation of the standard generalized Langevin equation and the essential role of the broadly overlooked state-dependency nature in predicting molecule kinetics related to conformation relaxation and transition.
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Affiliation(s)
| | | | - Huan Lei
- Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
- Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824, USA
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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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Brünig FN, Netz RR, Kappler J. Barrier-crossing times for different non-Markovian friction in well and barrier: A numerical study. Phys Rev E 2022; 106:044133. [PMID: 36397504 DOI: 10.1103/physreve.106.044133] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 07/21/2022] [Indexed: 06/16/2023]
Abstract
We introduce a generalized Langevin model system for different non-Markovian effects in the well and barrier regions of a potential, and use it to numerically study the barrier-crossing time. In the appropriate limits, our model interpolates between the theoretical barrier-crossing-time predictions by Grote and Hynes (GH), as well as by Pollak et al., which for a single barrier memory time can differ by several orders of magnitude. Our model furthermore allows one to test an analytic rate theory for space-inhomogeneous memory, which disagrees with our numerical results in the long well-memory regime. In this regime, we find that short barrier memory decreases the barrier-crossing time as compared to long barrier memory. This is in contrast with the short well-memory regime, where both our numerical results and the GH theory predict an acceleration of the barrier crossing time with increasing barrier memory time. Both effects, the "Markovian-barrier acceleration" and GH "non-Markovian-barrier acceleration," can be understood from a committor analysis. Our model combines finite relaxation times of orthogonal degrees of freedom with a space-inhomogeneous coupling to such degrees and represents a step towards more realistic modeling of reaction coordinates.
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Affiliation(s)
- Florian N Brünig
- Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany
| | - Roland R Netz
- Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany
| | - Julian Kappler
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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Antoniou D, Schwartz SD. Quantum proton transfer with spatially dependent friction: Phenol-amine in methyl chloride. J Chem Phys 1999. [DOI: 10.1063/1.478667] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Truhlar DG, Garrett BC, Klippenstein SJ. Current Status of Transition-State Theory. ACTA ACUST UNITED AC 1996. [DOI: 10.1021/jp953748q] [Citation(s) in RCA: 1585] [Impact Index Per Article: 56.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Donald G. Truhlar
- Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431
| | - Bruce C. Garrett
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, 902 Battelle Boulevard, MS K1-96, Richland, Washington 99352
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Haynes GR, Voth GA. Reaction‐coordinate‐dependent friction in classical activated barrier crossing dynamics: When it matters and when it doesn’t. J Chem Phys 1995. [DOI: 10.1063/1.469920] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Roy S, Bagchi B. Effects of solvent polarization relaxation on nonadiabatic outersphere electron transfer reactions in ultrafast dipolar solvents. J Chem Phys 1995. [DOI: 10.1063/1.468992] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Haynes GR, Voth GA, Pollak E. A theory for the activated barrier crossing rate constant in systems influenced by space and time dependent friction. J Chem Phys 1994. [DOI: 10.1063/1.468274] [Citation(s) in RCA: 63] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Rate processes in dissipative systems: scaling in the canonical variational transition state theory. Chem Phys 1994. [DOI: 10.1016/0301-0104(94)00027-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Ben‐Nun M, Levine RD. Ion‐molecule recombination and other activationless processes in solution: Foundations of a capture model. J Chem Phys 1994. [DOI: 10.1063/1.466401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Haynes GR, Voth GA. The dependence of the potential of mean force on the solvent friction: Consequences for condensed phase activated rate theories. J Chem Phys 1993. [DOI: 10.1063/1.465677] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ferrando R, Spadacini R, Tommei GE. Kramers problem in periodic potentials: Jump rate and jump lengths. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:2437-2451. [PMID: 9960877 DOI: 10.1103/physreve.48.2437] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Pollak E, Berezhkovskii AM. Fokker–Planck equation for nonlinear stochastic dynamics in the presence of space and time dependent friction. J Chem Phys 1993. [DOI: 10.1063/1.465379] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Haynes GR, Voth GA, Pollak E. A theory for the thermally activated rate constant in systems with spatially dependent friction. Chem Phys Lett 1993. [DOI: 10.1016/0009-2614(93)89005-3] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Straus JB, Gomez Llorente JM, Voth GA. Manifestations of spatially dependent friction in classical activated rate processes. J Chem Phys 1993. [DOI: 10.1063/1.465044] [Citation(s) in RCA: 49] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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