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Xie P, E W. Coarse-Graining Conformational Dynamics with Multidimensional Generalized Langevin Equation: How, When, and Why. J Chem Theory Comput 2024. [PMID: 39258946 DOI: 10.1021/acs.jctc.4c00729] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/12/2024]
Abstract
A data-driven ab initio generalized Langevin equation (AIGLE) approach is developed to learn and simulate high-dimensional, heterogeneous, coarse-grained (CG) conformational dynamics. Constrained by the fluctuation-dissipation theorem, the approach can build CG models in dynamical consistency (DC) with all-atom molecular dynamics. We also propose practical criteria for AIGLE to enforce long-term DC. Case studies of a toy polymer, with 20 CG sites, and the alanine dipeptide, with two dihedral angles, elucidate why one should adopt AIGLE or its Markovian limit for modeling CG conformational dynamics in practice.
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Affiliation(s)
- Pinchen Xie
- Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, United States
- Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Weinan E
- AI for Science Institute, Beijing 100080, China
- Center for Machine Learning Research and School of Mathematical Sciences, Peking University, Beijing 100084, China
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Xie P, Car R, E W. Ab initio generalized Langevin equation. Proc Natl Acad Sci U S A 2024; 121:e2308668121. [PMID: 38551836 PMCID: PMC10998567 DOI: 10.1073/pnas.2308668121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Accepted: 02/22/2024] [Indexed: 04/08/2024] Open
Abstract
We introduce a machine learning-based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables (CVs) in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori-Zwanzig formalism, under the constraint of the fluctuation-dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multiscale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of CVs by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency.
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Affiliation(s)
- Pinchen Xie
- Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ08544
| | - Roberto Car
- Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ08544
- Department of Chemistry and Princeton Materials Institute, Princeton University, Princeton, NJ08544
- Department of Physics, Princeton University, Princeton, NJ08544
| | - Weinan E
- AI for Science Institute, Beijing100080, China
- Center for Machine Learning Research and School of Mathematical Sciences, Peking University, Beijing100084, China
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Klippenstein V, Tripathy M, Jung G, Schmid F, van der Vegt NFA. Introducing Memory in Coarse-Grained Molecular Simulations. J Phys Chem B 2021; 125:4931-4954. [PMID: 33982567 PMCID: PMC8154603 DOI: 10.1021/acs.jpcb.1c01120] [Citation(s) in RCA: 40] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
Preserving the correct dynamics at the coarse-grained (CG) level is a pressing problem in the development of systematic CG models in soft matter simulation. Starting from the seminal idea of simple time-scale mapping, there have been many efforts over the years toward establishing a meticulous connection between the CG and fine-grained (FG) dynamics based on fundamental statistical mechanics approaches. One of the most successful attempts in this context has been the development of CG models based on the Mori-Zwanzig (MZ) theory, where the resulting equation of motion has the form of a generalized Langevin equation (GLE) and closely preserves the underlying FG dynamics. In this Review, we describe some of the recent studies in this regard. We focus on the construction and simulation of dynamically consistent systematic CG models based on the GLE, both in the simple Markovian limit and the non-Markovian case. Some recent studies of physical effects of memory are also discussed. The Review is aimed at summarizing recent developments in the field while highlighting the major challenges and possible future directions.
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Affiliation(s)
- Viktor Klippenstein
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, 64287 Darmstadt, Germany
| | - Madhusmita Tripathy
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, 64287 Darmstadt, Germany
| | - Gerhard Jung
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21 A, A-6020 Innsbruck, Austria
| | - Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55128 Mainz, Germany
| | - Nico F A van der Vegt
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, 64287 Darmstadt, Germany
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Shim Y, Kim HJ. Vibrational energy relaxation of a diatomic molecule in a room-temperature ionic liquid. J Chem Phys 2006; 125:24507. [PMID: 16848592 DOI: 10.1063/1.2206579] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Vibrational energy relaxation (VER) dynamics of a diatomic solute in ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate (EMI(+)PF(6) (-)) are studied via equilibrium and nonequilibrium molecular dynamics simulations. The time scale for VER is found to decrease markedly with the increasing solute dipole moment, consonant with many previous studies in polar solvents. A detailed analysis of nonequilibrium results shows that for a dipolar solute, dissipation of an excess solute vibrational energy occurs almost exclusively via the Lennard-Jones interactions between the solute and solvent, while an oscillatory energy exchange between the two is mainly controlled by their electrostatic interactions. Regardless of the anharmonicity of the solute vibrational potential, VER becomes accelerated as the initial vibrational energy increases. This is attributed primarily to the enhancement in variations of the solvent force on the solute bond, induced by large-amplitude solute vibrations. One interesting finding is that if a time variable scaled with the initial excitation energy is employed, dissipation dynamics of the excess vibrational energy of the dipolar solute tend to show a universal behavior irrespective of its initial vibrational state. Comparison with water and acetonitrile shows that overall characteristics of VER in EMI(+)PF(6) (-) are similar to those in acetonitrile, while relaxation in water is much faster than the two. It is also found that the Landau-Teller theory predictions for VER time scale obtained via equilibrium simulations of the solvent force autocorrelation function are in reasonable agreement with the nonequilibrium results.
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Affiliation(s)
- Youngseon Shim
- Department of Chemistry, Carnegie Mellon University, Pittsburgh, PA 15213, USA
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Akkermans RLC, Briels WJ. Coarse-grained dynamics of one chain in a polymer melt. J Chem Phys 2000. [DOI: 10.1063/1.1308513] [Citation(s) in RCA: 97] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kühne T, Küster R, Vöhringer P. Femtosecond photodissociation of triiodide in solution: Excitation energy dependence and transition state dynamics. Chem Phys 1998. [DOI: 10.1016/s0301-0104(97)00354-6] [Citation(s) in RCA: 46] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Gnanakaran S, Hochstrasser RM. Vibrational relaxation of HgI in ethanol: Equilibrium molecular dynamics simulations. J Chem Phys 1996. [DOI: 10.1063/1.472218] [Citation(s) in RCA: 71] [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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Pullen S, Walker LA, Sension RJ. Femtosecond studies of the iodine–mesitylene charge‐transfer complex. J Chem Phys 1995. [DOI: 10.1063/1.470205] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mishra B, Berne BJ. Hydrodynamic calculation of the frequency dependent friction on the bond of a diatomic molecule. J Chem Phys 1995. [DOI: 10.1063/1.469826] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Talkner P, Pollak E. Relationship between variational transition state theory and the Rayleigh quotient method for activated rate processes. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 50:2646-2653. [PMID: 9962303 DOI: 10.1103/physreve.50.2646] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Russell D, Harris C. Vibrational relaxation in simple fluids: a comparison of experimental results to the predictions of isolated binary collision theory. Chem Phys 1994. [DOI: 10.1016/0301-0104(94)00059-x] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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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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Gao J, Weiner JH. Screened intermolecular forces and covalent bond forces in polymer melts. J Chem Phys 1993. [DOI: 10.1063/1.464530] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Banin U, Ruhman S. Ultrafast photodissociation of I3. Coherent photochemistry in solution. J Chem Phys 1993. [DOI: 10.1063/1.465066] [Citation(s) in RCA: 163] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Rey R, Guàrdia E, Padró JA. Generalized Langevin dynamics simulation of activated processes in solution: Ion pair interconversion in water. J Chem Phys 1992. [DOI: 10.1063/1.463398] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Xu X, Yu S, Lingle R, Zhu H, Hopkins JB. Ultrafast transient Raman investigation of geminate recombination and vibrational energy relaxation in iodine: The role of energy relaxation pathways to solvent vibrations. J Chem Phys 1991. [DOI: 10.1063/1.460949] [Citation(s) in RCA: 54] [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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Zhang JZ, Harris CB. Generalized Brownian dynamics. III. Vibrational relaxation of heteronuclear diatomics in rare gases. J Chem Phys 1991. [DOI: 10.1063/1.460494] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Straub JE, Berne BJ, Roux B. Spatial dependence of time‐dependent friction for pair diffusion in a simple fluid. J Chem Phys 1990. [DOI: 10.1063/1.458950] [Citation(s) in RCA: 55] [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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Berne BJ, Tuckerman ME, Straub JE, Bug ALR. Dynamic friction on rigid and flexible bonds. J Chem Phys 1990. [DOI: 10.1063/1.458647] [Citation(s) in RCA: 106] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Torii H, Tasumi M. Effects of collision‐induced perturbation of atomic motions on the vibrational relaxation of polyatomic molecules. J Chem Phys 1990. [DOI: 10.1063/1.459169] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Smith DE, Harris CB. Generalized Brownian dynamics. I. Numerical integration of the generalized Langevin equation through autoregressive modeling of the memory function. J Chem Phys 1990. [DOI: 10.1063/1.458140] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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