1
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Jin J, Voth GA. Understanding dynamics in coarse-grained models. IV. Connection of fine-grained and coarse-grained dynamics with the Stokes-Einstein and Stokes-Einstein-Debye relations. J Chem Phys 2024; 161:034114. [PMID: 39012809 DOI: 10.1063/5.0212973] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2024] [Accepted: 06/28/2024] [Indexed: 07/18/2024] Open
Abstract
Applying an excess entropy scaling formalism to the coarse-grained (CG) dynamics of liquids, we discovered that missing rotational motions during the CG process are responsible for artificially accelerated CG dynamics. In the context of the dynamic representability between the fine-grained (FG) and CG dynamics, this work introduces the well-known Stokes-Einstein and Stokes-Einstein-Debye relations to unravel the rotational dynamics underlying FG trajectories, thereby allowing for an indirect evaluation of the effective rotations based only on the translational information at the reduced CG resolution. Since the representability issue in CG modeling limits a direct evaluation of the shear stress appearing in the Stokes-Einstein and Stokes-Einstein-Debye relations, we introduce a translational relaxation time as a proxy to employ these relations, and we demonstrate that these relations hold for the ambient conditions studied in our series of work. Additional theoretical links to our previous work are also established. First, we demonstrate that the effective hard sphere radius determined by the classical perturbation theory can approximate the complex hydrodynamic radius value reasonably well. Furthermore, we present a simple derivation of an excess entropy scaling relationship for viscosity by estimating the elliptical integral of molecules. In turn, since the translational and rotational motions at the FG level are correlated to each other, we conclude that the "entropy-free" CG diffusion only depends on the shape of the reference molecule. Our results and analyses impart an alternative way of recovering the FG diffusion from the CG description by coupling the translational and rotational motions at the hydrodynamic level.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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2
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Klippenstein V, Wolf N, van der Vegt NFA. A Gauss-Newton method for iterative optimization of memory kernels for generalized Langevin thermostats in coarse-grained molecular dynamics simulations. J Chem Phys 2024; 160:204115. [PMID: 38804493 DOI: 10.1063/5.0203832] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2024] [Accepted: 05/08/2024] [Indexed: 05/29/2024] Open
Abstract
In molecular dynamics simulations, dynamically consistent coarse-grained (CG) models commonly use stochastic thermostats to model friction and fluctuations that are lost in a CG description. While Markovian, i.e., time-local, formulations of such thermostats allow for an accurate representation of diffusivities/long-time dynamics, a correct description of the dynamics on all time scales generally requires non-Markovian, i.e., non-time-local, thermostats. These thermostats typically take the form of a Generalized Langevin Equation (GLE) determined by a memory kernel. In this work, we use a Markovian embedded formulation of a position-independent GLE thermostat acting independently on each CG degree of freedom. Extracting the memory kernel of this CG model from atomistic reference data requires several approximations. Therefore, this task is best understood as an inverse problem. While our recently proposed approximate Newton scheme allows for the iterative optimization of memory kernels (IOMK), Markovian embedding remained potentially error-prone and computationally expensive. In this work, we present an IOMK-Gauss-Newton scheme (IOMK-GN) based on IOMK that allows for the direct parameterization of a Markovian embedded model.
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Affiliation(s)
- Viktor Klippenstein
- Department of Chemistry, Technical University of Darmstadt, 64287 Darmstadt, Germany
| | - Niklas Wolf
- Department of Chemistry, Technical University of Darmstadt, 64287 Darmstadt, Germany
| | - Nico F A van der Vegt
- Department of Chemistry, Technical University of Darmstadt, 64287 Darmstadt, Germany
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3
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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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4
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Zhang XZ, Shi R, Lu ZY, Qian HJ. Chemically Specific Systematic Coarse-Grained Polymer Model with Both Consistently Structural and Dynamical Properties. JACS AU 2024; 4:1018-1030. [PMID: 38559727 PMCID: PMC10976574 DOI: 10.1021/jacsau.3c00756] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/30/2023] [Revised: 02/23/2024] [Accepted: 02/28/2024] [Indexed: 04/04/2024]
Abstract
The coarse-grained (CG) model serves as a powerful tool for the simulation of polymer systems; its reliability depends on the accurate representation of both structural and dynamical properties. However, strong correlations between structural and dynamical properties on different scales and also a strong memory effect, enforced by chain connectivity between monomers in polymer systems, render developing a chemically specific systematic CG model a formidable task. In this study, we report a systematic CG approach that combines the iterative Boltzmann inversion (IBI) method and the generalized Langevin equation (GLE) dynamics. Structural properties are ensured by using conservative CG potentials derived from the IBI method. To retrieve the correct dynamical properties in the system, we demonstrate that using a combination of a Rouse-type delta function and a time-dependent short-time kernel in the GLE simulation is practically efficient. The former can be used to adjust the long-time diffusion dynamics, and the latter can be reconstructed from an iterative procedure according to the velocity autocorrelation function (ACF) from all-atomistic (AA) simulations. Taking the polystyrene as an example, we show that not only structural properties of radial distribution function, intramolecular bond, and angle distributions can be reproduced but also dynamical properties of mean-square displacement, velocity ACF, and force ACF resulted from our CG model have quantitative agreement with the reference AA model. In addition, reasonable agreements are observed in other collective properties between our GLE-CG model and the AA simulations as well.
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Affiliation(s)
| | | | - Zhong-Yuan Lu
- State Key Laboratory of Supramolecular
Structure and Materials, Institute of Theoretical Chemistry, College
of Chemistry, Jilin University, Changchun 130021, China
| | - Hu-Jun Qian
- State Key Laboratory of Supramolecular
Structure and Materials, Institute of Theoretical Chemistry, College
of Chemistry, Jilin University, Changchun 130021, China
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5
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Nie Y, Zheng Z, Li C, Zhan H, Kou L, Gu Y, Lü C. Resolving the dynamic properties of entangled linear polymers in non-equilibrium coarse grain simulation with a priori scaling factors. NANOSCALE 2024. [PMID: 38494916 DOI: 10.1039/d3nr06185j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/19/2024]
Abstract
The molecular weight of polymers can influence the material properties, but the molecular weight at the experiment level sometimes can be a huge burden for property prediction with full-atomic simulations. The traditional bottom-up coarse grain (CG) simulation can reduce the computation cost. However, the dynamic properties predicted by the CG simulation can deviate from the full-atomic simulation result. Usually, in CG simulations, the diffusion is faster and the viscosity and modulus are much lower. The fast dynamics in CG are usually solved by a posteriori scaling on time, temperature, or potential modifications, which usually have poor transferability to other non-fitted physical properties because of a lack of fundamental physics. In this work, a priori scaling factors were calculated by the loss of degrees of freedom and implemented in the iterative Boltzmann inversion. According to the simulation results on 3 different CG levels at different temperatures and loading rates, such a priori scaling factors can help in reproducing some dynamic properties of polycaprolactone in CG simulation more accurately, such as heat capacity, Young's modulus, and viscosity, while maintaining the accuracy in the structural distribution prediction. The transferability of entropy-enthalpy compensation and a dissipative particle dynamics thermostat is also presented for comparison. The proposed method reveals the huge potential for developing customized CG thermostats and offers a simple way to rebuild multiphysics CG models for polymers with good transferability.
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Affiliation(s)
- Yihan Nie
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
| | - Zhuoqun Zheng
- School of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
| | - Chengkai Li
- School of Materials Science and Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China
| | - Haifei Zhan
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology (QUT), Brisbane QLD 4001, Australia
- Center for Materials Science, Queensland University of Technology (QUT), Brisbane QLD 4001, Australia
| | - Liangzhi Kou
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology (QUT), Brisbane QLD 4001, Australia
- Center for Materials Science, Queensland University of Technology (QUT), Brisbane QLD 4001, Australia
| | - Yuantong Gu
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology (QUT), Brisbane QLD 4001, Australia
- Center for Materials Science, Queensland University of Technology (QUT), Brisbane QLD 4001, Australia
| | - Chaofeng Lü
- Faculty of Mechanical Engineering & Mechanics, Ningbo University, Ningbo 315211, China
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
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6
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Jin J, Lee EK, Voth GA. Understanding dynamics in coarse-grained models. III. Roles of rotational motion and translation-rotation coupling in coarse-grained dynamics. J Chem Phys 2023; 159:164102. [PMID: 37870140 DOI: 10.1063/5.0167158] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Accepted: 09/29/2023] [Indexed: 10/24/2023] Open
Abstract
This paper series aims to establish a complete correspondence between fine-grained (FG) and coarse-grained (CG) dynamics by way of excess entropy scaling (introduced in Paper I). While Paper II successfully captured translational motions in CG systems using a hard sphere mapping, the absence of rotational motions in single-site CG models introduces differences between FG and CG dynamics. In this third paper, our objective is to faithfully recover atomistic diffusion coefficients from CG dynamics by incorporating rotational dynamics. By extracting FG rotational diffusion, we unravel, for the first time reported to our knowledge, a universality in excess entropy scaling between the rotational and translational diffusion. Once the missing rotational dynamics are integrated into the CG translational dynamics, an effective translation-rotation coupling becomes essential. We propose two different approaches for estimating this coupling parameter: the rough hard sphere theory with acentric factor (temperature-independent) or the rough Lennard-Jones model with CG attractions (temperature-dependent). Altogether, we demonstrate that FG diffusion coefficients can be recovered from CG diffusion coefficients by (1) incorporating "entropy-free" rotational diffusion with translation-rotation coupling and (2) recapturing the missing entropy. Our findings shed light on the fundamental relationship between FG and CG dynamics in molecular fluids.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Eok Kyun Lee
- Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, South Korea
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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7
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Lyu L, Lei H. Construction of Coarse-Grained Molecular Dynamics with Many-Body Non-Markovian Memory. PHYSICAL REVIEW LETTERS 2023; 131:177301. [PMID: 37955502 DOI: 10.1103/physrevlett.131.177301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2023] [Accepted: 09/19/2023] [Indexed: 11/14/2023]
Abstract
We introduce a machine-learning-based coarse-grained molecular dynamics model that faithfully retains the many-body nature of the intermolecular dissipative interactions. Unlike the common empirical coarse-grained models, the present model is constructed based on the Mori-Zwanzig formalism and naturally inherits the heterogeneous state-dependent memory term rather than matching the mean-field metrics such as the velocity autocorrelation function. Numerical results show that preserving the many-body nature of the memory term is crucial for predicting the collective transport and diffusion processes, where empirical forms generally show limitations.
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Affiliation(s)
- Liyao Lyu
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - 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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8
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Farahvash A, Agrawal M, Peterson AA, Willard AP. Modeling Surface Vibrations and Their Role in Molecular Adsorption: A Generalized Langevin Approach. J Chem Theory Comput 2023; 19:6452-6460. [PMID: 37682532 DOI: 10.1021/acs.jctc.3c00473] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/09/2023]
Abstract
The atomic vibrations of a solid surface can play a significant role in the reactions of surface-bound molecules, as well as their adsorption and desorption. Relevant phonon modes can involve the collective motion of atoms over a wide array of length scales. In this paper, we demonstrate how the generalized Langevin equation can be utilized to describe these collective motions weighted by their coupling to individual sites. Our approach builds upon the generalized Langevin oscillator (GLO) model originally developed by Tully. We extend the GLO by deriving parameters from atomistic simulation data. We apply this approach to study the memory kernel of a model platinum surface and demonstrate that the memory kernel has a bimodal form due to coupling to both low-energy acoustic modes and high-energy modes near the Debye frequency. The same bimodal form was observed across a wide variety of solids of different elemental compositions, surface structures, and solvation states. By studying how these dominant modes depend on the simulation size, we argue that the acoustic modes are frozen in the limit of macroscopic lattices. By simulating periodically replicated slabs of various sizes, we quantify the influence of phonon confinement effects in the memory kernel and their concomitant effect on simulated sticking coefficients.
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Affiliation(s)
- Ardavan Farahvash
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Mayank Agrawal
- School of Engineering, Brown University, Providence, Rhode Island 02912, United States
| | - Andrew A Peterson
- School of Engineering, Brown University, Providence, Rhode Island 02912, United States
| | - Adam P Willard
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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9
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Johnson LC, Phelan FR. Comparison of Friction Parametrization from Dynamics and Material Properties for a Coarse-Grained Polymer Melt. J Phys Chem B 2023; 127:7054-7069. [PMID: 37523783 PMCID: PMC10472480 DOI: 10.1021/acs.jpcb.3c03273] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/02/2023]
Abstract
In this work, we extend an approach to coarse-grained (CG) modeling for polymer melts in which the conservative potential is parametrized using the iterative Boltzmann inversion (IBI) method and the accelerated dynamics inherent to IBI are corrected using the dissipative Langevin thermostat with a single tunable friction parameter (J. Chem. Phys. 2021, 154, 084114). Diffusive measures from picoseconds to nanoseconds are used to determine the Langevin friction factor to apply to the CG model to recover all-atom (AA) dynamics; the resulting friction factors are then compared for consistency. Here, we additionally parametrize the CG dynamics using a material property, the zero-shear viscosity, which we measure using the Green-Kubo (GK) method. Two materials are studied, squalane as a function of temperature and the same polystyrene oligomers previously studied as a function of chain length. For squalane, the friction derived from the long-time diffusive measures and the viscosity all strongly increase with decreasing temperature, showing an Arrhenius-like dependence, and remain consistent with each other over the entire temperature range. In contrast, the friction required for the picosecond diffusive measurement, the Debye-Waller factor, is somewhat lower than the friction from long-time measures and relatively insensitive to temperature. A time-dependent friction would be required to exactly reproduce the AA measurements during the caging transition connecting these two extremes over the entire timespan at this level of coarse-graining. For the polystyrene oligomers for which we previously characterized the diffusive friction, the viscosity-parametrized frictions are consistent with the diffusive measures for the smallest chain length. However, for the longer chains, we find different trends based on measurement method with friction derived from rotational diffusion remaining nearly constant, friction derived from translational diffusion showing a modestly increasing trend, and viscosity-derived friction showing a modest decreasing trend. This seems to indicate that there is some sensitivity of the friction measurement method for systems with increased relaxation times and that in particular, the unsteady dynamics of the individual parametrization schemes plays a role in this. Increased difficulty in applying the GK method with increasing relaxation time of the longer chain systems is also discussed. Overall, we find that when the material is in a high-temperature melt state and the viscosity measurement is reliable, the friction parametrization from the diffusive friction measures is consistent and the lower cost diffusive parametrization is a reliable means for modeling viscosity. Our data give insight into the time-dependent friction one might compute using a non-Markovian approach to enable the recovery of AA dynamics over a wider range of time scales than can be computed using a single friction.
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Affiliation(s)
- Lilian C Johnson
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Frederick R Phelan
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
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10
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Klippenstein V, van der Vegt NFA. Bottom-Up Informed and Iteratively Optimized Coarse-Grained Non-Markovian Water Models with Accurate Dynamics. J Chem Theory Comput 2023; 19:1099-1110. [PMID: 36745567 PMCID: PMC9979609 DOI: 10.1021/acs.jctc.2c00871] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
Molecular dynamics (MD) simulations based on coarse-grained (CG) particle models of molecular liquids generally predict accelerated dynamics and misrepresent the time scales for molecular vibrations and diffusive motions. The parametrization of Generalized Langevin Equation (GLE) thermostats based on the microscopic dynamics of the fine-grained model provides a promising route to address this issue, in conjunction with the conservative interactions of the CG model obtained with standard coarse graining methods, such as iterative Boltzmann inversion, force matching, or relative entropy minimization. We report the application of a recently introduced bottom-up dynamic coarse graining method, based on the Mori-Zwanzig formalism, which provides accurate estimates of isotropic GLE memory kernels for several CG models of liquid water. We demonstrate that, with an additional iterative optimization of the memory kernels (IOMK) for the CG water models based on a practical iterative optimization technique, the velocity autocorrelation function of liquid water can be represented very accurately within a few iterations. By considering the distinct Van Hove function, we demonstrate that, with the presented methods, an accurate representation of structural relaxation can be achieved. We consider several distinct CG potentials to study how the choice of the CG potential affects the performance of bottom-up informed and iteratively optimized models.
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11
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Jin J, Schweizer KS, Voth GA. Understanding dynamics in coarse-grained models. II. Coarse-grained diffusion modeled using hard sphere theory. J Chem Phys 2023; 158:034104. [PMID: 36681632 DOI: 10.1063/5.0116300] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
The first paper of this series [J. Chem. Phys. 158, 034103 (2023)] demonstrated that excess entropy scaling holds for both fine-grained and corresponding coarse-grained (CG) systems. Despite its universality, a more exact determination of the scaling relationship was not possible due to the semi-empirical nature. In this second paper, an analytical excess entropy scaling relation is derived for bottom-up CG systems. At the single-site CG resolution, effective hard sphere systems are constructed that yield near-identical dynamical properties as the target CG systems by taking advantage of how hard sphere dynamics and excess entropy can be analytically expressed in terms of the liquid packing fraction. Inspired by classical equilibrium perturbation theories and recent advances in constructing hard sphere models for predicting activated dynamics of supercooled liquids, we propose a new approach for understanding the diffusion of molecular liquids in the normal regime using hard sphere reference fluids. The proposed "fluctuation matching" is designed to have the same amplitude of long wavelength density fluctuations (dimensionless compressibility) as the CG system. Utilizing the Enskog theory to derive an expression for hard sphere diffusion coefficients, a bridge between the CG dynamics and excess entropy is then established. The CG diffusion coefficient can be roughly estimated using various equations of the state, and an accurate prediction of accelerated CG dynamics at different temperatures is also possible in advance of running any CG simulation. By introducing another layer of coarsening, these findings provide a more rigorous method to assess excess entropy scaling and understand the accelerated CG dynamics of molecular fluids.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - Kenneth S Schweizer
- Department of Material Science, Department of Chemistry, Department of Chemical and Biomolecular Engineering, and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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12
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Jin J, Schweizer KS, Voth GA. Understanding dynamics in coarse-grained models. I. Universal excess entropy scaling relationship. J Chem Phys 2023; 158:034103. [PMID: 36681649 DOI: 10.1063/5.0116299] [Citation(s) in RCA: 15] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural properties, assessing dynamic properties in CG modeling is often unfeasible due to the accelerated dynamics of the CG models, which allows for more efficient structural sampling. Therefore, the ultimate goal of the present series of articles is to establish a better correspondence between the FG and CG dynamics. To assess and compare dynamical properties in the FG and the corresponding CG models, we utilize the excess entropy scaling relationship. For Paper I of this series, we provide evidence that the FG and the corresponding CG counterpart follow the same universal scaling relationship. By carefully reviewing and examining the literature, we develop a new theory to calculate excess entropies for the FG and CG systems while accounting for entropy representability. We demonstrate that the excess entropy scaling idea can be readily applied to liquid water and methanol systems at both the FG and CG resolutions. For both liquids, we reveal that the scaling exponents remain unchanged from the coarse-graining process, indicating that the scaling behavior is universal for the same underlying molecular systems. Combining this finding with the concept of mapping entropy in CG models, we show that the missing entropy plays an important role in accelerating the CG dynamics.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - Kenneth S Schweizer
- Department of Material Science, Department of Chemistry, Department of Chemical and Biomolecular Engineering, and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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13
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Schmid F. Understanding and Modeling Polymers: The Challenge of Multiple Scales. ACS POLYMERS AU 2022. [DOI: 10.1021/acspolymersau.2c00049] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55128Mainz, Germany
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14
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Jin J, Pak AJ, Durumeric AEP, Loose TD, Voth GA. Bottom-up Coarse-Graining: Principles and Perspectives. J Chem Theory Comput 2022; 18:5759-5791. [PMID: 36070494 PMCID: PMC9558379 DOI: 10.1021/acs.jctc.2c00643] [Citation(s) in RCA: 72] [Impact Index Per Article: 36.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Indexed: 01/14/2023]
Abstract
Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry,
Chicago Center for Theoretical Chemistry, Institute for Biophysical
Dynamics, and James Franck Institute, The
University of Chicago, Chicago, Illinois 60637, United States
| | - Alexander J. Pak
- Department of Chemistry,
Chicago Center for Theoretical Chemistry, Institute for Biophysical
Dynamics, and James Franck Institute, The
University of Chicago, Chicago, Illinois 60637, United States
| | - Aleksander E. P. Durumeric
- Department of Chemistry,
Chicago Center for Theoretical Chemistry, Institute for Biophysical
Dynamics, and James Franck Institute, The
University of Chicago, Chicago, Illinois 60637, United States
| | - Timothy D. Loose
- Department of Chemistry,
Chicago Center for Theoretical Chemistry, Institute for Biophysical
Dynamics, and James Franck Institute, The
University of Chicago, Chicago, Illinois 60637, United States
| | - Gregory A. Voth
- Department of Chemistry,
Chicago Center for Theoretical Chemistry, Institute for Biophysical
Dynamics, and James Franck Institute, The
University of Chicago, Chicago, Illinois 60637, United States
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15
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Klippenstein V, van der Vegt N. Cross-Correlation Corrected Friction in Generalized Langevin Models: Application to the continuous Asakura-Oosawa Model. J Chem Phys 2022; 157:044103. [DOI: 10.1063/5.0093056] [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
In a previous study we proposed a method to parameterize isotropic, configuration independent, non-Markovian generalized Langevin thermostats to achieve dynamic consistency in coarse-grained models. In the current study, by applying the same strategy, we develop coarse-grained implicit solvent models for the continuous Asakura-Oosawa model, which under certain conditions allows to develop very accurate coarse-grained potentials. By developing coarse-grained models for different reference systems with varying parameters, we test the broader applicability of the proposed procedure and demonstrate the relevance of accurate coarse-grained potentials in bottom-up derived dissipative models. We study how different system parameters affect the dynamic representability of the coarse-grained models. In particular we find that the quality of the coarse-grained potential is crucial to correctly model the backscattering effect due to collisions on the coarse-grained scale. In the dynamics of colloid suspensions the hydrodynamic interactions affect the long-time scale dynamics by solvent mediated momentum transfer. These interactions are not explicitly modeled in the presented coarse-grained models, which poses some limitations to the proposed coarse-graining scheme. The Asakura-Oosawa model allows a tuning of system parameters, to gain an improved understanding of these limitations. We also propose three new iterative optimization schemes to fine tune the generalized Langevin thermostat to exactly match the reference velocity-autocorrelation function.
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Affiliation(s)
| | - Nico van der Vegt
- Chemistry, Technische Universität Darmstadt Fachbereich Chemie, Germany
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16
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Vroylandt H, Monmarché P. Position-dependent memory kernel in generalized Langevin equations: Theory and numerical estimation. J Chem Phys 2022; 156:244105. [DOI: 10.1063/5.0094566] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
Generalized Langevin equations with non-linear forces and position-dependent linear friction memory kernels, such as commonly used to describe the effective dynamics of coarse-grained variables in molecular dynamics, are rigorously derived within the Mori–Zwanzig formalism. A fluctuation–dissipation theorem relating the properties of the noise to the memory kernel is shown. The derivation also yields Volterra-type equations for the kernel, which can be used for a numerical parametrization of the model from all-atom simulations.
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Affiliation(s)
- Hadrien Vroylandt
- Sorbonne Université, Institut des Sciences du Calcul et des Données, ISCD, F-75005 Paris, France
| | - Pierre Monmarché
- Sorbonne Université, Laboratoire Jacques-Louis Lions, LJLL, F-75005 Paris, France
- Sorbonne Université, Laboratoire de Chimie Théorique, LCT, F-75005 Paris, France
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17
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Bao JD, Li Y, Marchesoni F. Consistent Hamiltonian models for space-momentum diffusion. Phys Rev E 2022; 105:L052105. [PMID: 35706220 DOI: 10.1103/physreve.105.l052105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2021] [Accepted: 05/15/2022] [Indexed: 06/15/2023]
Abstract
We develop a unified Hamiltonian approach to the diffusion of a particle coupled to a dissipative environment, an archetypal model widely invoked to interpret condensed phase phenomena, such as polymerization and cold-atom diffusion in optical lattices. By appropriate choices of the coupling functions, we reformulate phenomenological diffusion models by adding otherwise ignored space-momentum terms. We thus numerically predict a variety of diffusion regimes, from diffusion saturation to superballistic diffusion. With reference to ultracold atoms in optical lattices, we also show that time correlated external noises prevent superdiffusion from exceeding Richardson's law. Some of these results are unexpected and call for experimental validation.
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Affiliation(s)
- Jing-Dong Bao
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Yunyun Li
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Fabio Marchesoni
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
- Dipartimento di Fisica, Università di Camerino, I-62032 Camerino, Italy
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18
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Abstract
The analysis of complex systems with many degrees of freedom generally involves the definition of low-dimensional collective variables more amenable to physical understanding. Their dynamics can be modeled by generalized Langevin equations, whose coefficients have to be estimated from simulations of the initial high-dimensional system. These equations feature a memory kernel describing the mutual influence of the low-dimensional variables and their environment. We introduce and implement an approach where the generalized Langevin equation is designed to maximize the statistical likelihood of the observed data. This provides an efficient way to generate reduced models to study dynamical properties of complex processes such as chemical reactions in solution, conformational changes in biomolecules, or phase transitions in condensed matter systems. We introduce a method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from chemical reactions in solution to conformational changes in biomolecules or phase transitions in condensed matter systems. The standard Markovian approximation often breaks down due to the lack of a proper separation of time scales, and memory effects must be taken into account. Using a parametrization based on hidden auxiliary variables, we obtain a generalized Langevin equation by maximizing the statistical likelihood of the observed trajectories. Both the memory kernel and random noise are correctly recovered by this procedure. This data-driven approach provides a reduced dynamical model for multidimensional collective variables, enabling the accurate sampling of their long-time dynamical properties at a computational cost drastically reduced with respect to all-atom numerical simulations. The present strategy, based on the reproduction of the dynamics of trajectories rather than the memory kernel or the velocity-autocorrelation function, conveniently provides other observables beyond these two, including, e.g., stationary currents in nonequilibrium situations or the distribution of first passage times between metastable states.
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19
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Santo KP, Neimark AV. Dissipative particle dynamics simulations in colloid and Interface science: a review. Adv Colloid Interface Sci 2021; 298:102545. [PMID: 34757286 DOI: 10.1016/j.cis.2021.102545] [Citation(s) in RCA: 35] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2021] [Revised: 10/07/2021] [Accepted: 10/08/2021] [Indexed: 12/31/2022]
Abstract
Dissipative particle dynamics (DPD) is one of the most efficient mesoscale coarse-grained methodologies for modeling soft matter systems. Here, we comprehensively review the progress in theoretical formulations, parametrization strategies, and applications of DPD over the last two decades. DPD bridges the gap between the microscopic atomistic and macroscopic continuum length and time scales. Numerous efforts have been performed to improve the computational efficiency and to develop advanced versions and modifications of the original DPD framework. The progress in the parametrization techniques that can reproduce the engineering properties of experimental systems attracted a lot of interest from the industrial community longing to use DPD to characterize, help design and optimize the practical products. While there are still areas for improvements, DPD has been efficiently applied to numerous colloidal and interfacial phenomena involving phase separations, self-assembly, and transport in polymeric, surfactant, nanoparticle, and biomolecules systems.
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Affiliation(s)
- Kolattukudy P Santo
- Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, United States
| | - Alexander V Neimark
- Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, United States.
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20
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Dhamankar S, Webb MA. Chemically specific coarse‐graining of polymers: Methods and prospects. JOURNAL OF POLYMER SCIENCE 2021. [DOI: 10.1002/pol.20210555] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Satyen Dhamankar
- Department of Chemical and Biological Engineering Princeton University Princeton New Jersey USA
| | - Michael A. Webb
- Department of Chemical and Biological Engineering Princeton University Princeton New Jersey USA
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21
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Wang S, Ma Z, Pan W. Data-driven coarse-grained modeling of non-equilibrium systems. SOFT MATTER 2021; 17:6404-6412. [PMID: 34132317 DOI: 10.1039/d1sm00413a] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Modeling a high-dimensional Hamiltonian system in reduced dimensions with respect to coarse-grained (CG) variables can greatly reduce computational cost and enable efficient bottom-up prediction of main features of the system for many applications. However, it usually experiences significantly altered dynamics due to loss of degrees of freedom upon coarse-graining. To establish CG models that can faithfully preserve dynamics, previous efforts mainly focused on equilibrium systems. In contrast, various soft matter systems are known to be out of equilibrium. Therefore, the present work concerns non-equilibrium systems and enables accurate and efficient CG modeling that preserves non-equilibrium dynamics and is generally applicable to any non-equilibrium process and any observable of interest. To this end, the dynamic equation of a CG variable is built in the form of the non-stationary generalized Langevin equation (nsGLE), where the two-time memory kernel is determined from the data of the auto-correlation function of the observable of interest. By embedding the nsGLE in an extended dynamics framework, the nsGLE can be solved efficiently to predict the non-equilibrium dynamics of the CG variable. To prove and exploit the equivalence of the nsGLE and extended dynamics, the memory kernel is parameterized in a two-time exponential expansion. A data-driven hybrid optimization process is proposed for the parameterization, which integrates the differential-evolution method with the Levenberg-Marquardt algorithm to efficiently tackle a non-convex and high-dimensional optimization problem.
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Affiliation(s)
- Shu Wang
- Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA.
| | - Zhan Ma
- Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA.
| | - Wenxiao Pan
- Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA.
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22
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Ma Z, Wang S, Kim M, Liu K, Chen CL, Pan W. Transfer learning of memory kernels for transferable coarse-graining of polymer dynamics. SOFT MATTER 2021; 17:5864-5877. [PMID: 34096961 DOI: 10.1039/d1sm00364j] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The present work concerns the transferability of coarse-grained (CG) modeling in reproducing the dynamic properties of the reference atomistic systems across a range of parameters. In particular, we focus on implicit-solvent CG modeling of polymer solutions. The CG model is based on the generalized Langevin equation, where the memory kernel plays the critical role in determining the dynamics in all time scales. Thus, we propose methods for transfer learning of memory kernels. The key ingredient of our methods is Gaussian process regression. By integration with the model order reduction via proper orthogonal decomposition and the active learning technique, the transfer learning can be practically efficient and requires minimum training data. Through two example polymer solution systems, we demonstrate the accuracy and efficiency of the proposed transfer learning methods in the construction of transferable memory kernels. The transferability allows for out-of-sample predictions, even in the extrapolated domain of parameters. Built on the transferable memory kernels, the CG models can reproduce the dynamic properties of polymers in all time scales at different thermodynamic conditions (such as temperature and solvent viscosity) and for different systems with varying concentrations and lengths of polymers.
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Affiliation(s)
- Zhan Ma
- Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA.
| | - Shu Wang
- Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA.
| | - Minhee Kim
- Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA
| | - Kaibo Liu
- Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA
| | - Chun-Long Chen
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, WA 99352, USA
| | - Wenxiao Pan
- Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA.
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23
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Klippenstein V, van der Vegt NFA. Cross-correlation corrected friction in (generalized) Langevin models. J Chem Phys 2021; 154:191102. [PMID: 34240903 DOI: 10.1063/5.0049324] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a route for parameterizing isotropic (generalized) Langevin [(G)LE] thermostats with the aim to correct the dynamics of coarse-grained (CG) models with pairwise conservative interactions. The approach is based on the Mori-Zwanzig formalism and derives the memory kernels from Q-projected time correlation functions. Bottom-up informed (GLE and LE) thermostats for a CG star-polymer melt are investigated, and it is demonstrated that the inclusion of memory in the CG simulation leads to predictions of polymer diffusion in quantitative agreement with fine-grained simulations. Interestingly, memory effects are observed in the diffusive regime. We demonstrate that previously neglected cross-correlations between the "irrelevant" and the CG degree of freedom are important and lie at the origin of shortcomings in previous CG simulations.
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Affiliation(s)
- Viktor Klippenstein
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, 64287 Darmstadt, 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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24
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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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25
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Bockius N, Shea J, Jung G, Schmid F, Hanke M. Model reduction techniques for the computation of extended Markov parameterizations for generalized Langevin equations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:214003. [PMID: 33592585 DOI: 10.1088/1361-648x/abe6df] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2021] [Accepted: 02/16/2021] [Indexed: 06/12/2023]
Abstract
The generalized Langevin equation is a model for the motion of coarse-grained particles where dissipative forces are represented by a memory term. The numerical realization of such a model requires the implementation of a stochastic delay-differential equation and the estimation of a corresponding memory kernel. Here we develop a new approach for computing a data-driven Markov model for the motion of the particles, given equidistant samples of their velocity autocorrelation function. Our method bypasses the determination of the underlying memory kernel by representing it via up to about twenty auxiliary variables. The algorithm is based on a sophisticated variant of the Prony method for exponential interpolation and employs the positive real lemma from model reduction theory to extract the associated Markov model. We demonstrate the potential of this approach for the test case of anomalous diffusion, where data are given analytically, and then apply our method to velocity autocorrelation data of molecular dynamics simulations of a colloid in a Lennard-Jones fluid. In both cases, the velocity autocorrelation function and the memory kernel can be reproduced very accurately. Moreover, we show that the algorithm can also handle input data with large statistical noise. We anticipate that it will be a very useful tool in future studies that involve dynamic coarse-graining of complex soft matter systems.
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Affiliation(s)
- N Bockius
- Institut für Mathematik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
| | - J Shea
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
| | - G Jung
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - F Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
| | - M Hanke
- Institut für Mathematik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
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26
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Li B, Daoulas K, Schmid F. Dynamic coarse-graining of polymer systems using mobility functions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:194004. [PMID: 33690176 DOI: 10.1088/1361-648x/abed1b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2021] [Accepted: 03/09/2021] [Indexed: 06/12/2023]
Abstract
We propose a dynamic coarse-graining (CG) scheme for mapping heterogeneous polymer fluids onto extremely CG models in a dynamically consistent manner. The idea is to use as target function for the mapping a wave-vector dependent mobility function derived from the single-chain dynamic structure factor, which is calculated in the microscopic reference system. In previous work, we have shown that dynamic density functional calculations based on this mobility function can accurately reproduce the order/disorder kinetics in polymer melts, thus it is a suitable starting point for dynamic mapping. To enable the mapping over a range of relevant wave vectors, we propose to modify the CG dynamics by introducing internal friction parameters that slow down the CG monomer dynamics on local scales, without affecting the static equilibrium structure of the system. We illustrate and discuss the method using the example of infinitely long linear Rouse polymers mapped onto ultrashort CG chains. We show that our method can be used to construct dynamically consistent CG models for homopolymers with CG chain lengthN= 4, whereas for copolymers, longer CG chain lengths are necessary.
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Affiliation(s)
- Bing Li
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
| | - Kostas Daoulas
- Max-Planck Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany
| | - Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
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27
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Han Y, Jin J, Voth GA. Constructing many-body dissipative particle dynamics models of fluids from bottom-up coarse-graining. J Chem Phys 2021; 154:084122. [PMID: 33639745 DOI: 10.1063/5.0035184] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
Since their emergence in the 1990s, mesoscopic models of fluids have been widely used to study complex organization and transport phenomena beyond the molecular scale. Even though these models are designed based on results from physics at the meso- and macroscale, such as fluid mechanics and statistical field theory, the underlying microscopic foundation of these models is not as well defined. This paper aims to build such a systematic connection using bottom-up coarse-graining methods. From the recently developed dynamic coarse-graining scheme, we introduce a statistical inference framework of explicit many-body conservative interaction that quantitatively recapitulates the mesoscopic structure of the underlying fluid. To further consider the dissipative and fluctuation forces, we design a novel algorithm that parameterizes these forces. By utilizing this algorithm, we derive pairwise decomposable friction kernels under both non-Markovian and Markovian limits where both short- and long-time features of the coarse-grained dynamics are reproduced. Finally, through these new developments, the many-body dissipative particle dynamics type of equations of motion are successfully derived. The methodologies developed in this work thus open a new avenue for the construction of direct bottom-up mesoscopic models that naturally bridge the meso- and macroscopic physics.
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Affiliation(s)
- Yining Han
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
| | - Jaehyeok Jin
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
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28
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Wang S, Ma Z, Pan W. Data-driven coarse-grained modeling of polymers in solution with structural and dynamic properties conserved. SOFT MATTER 2020; 16:8330-8344. [PMID: 32785383 DOI: 10.1039/d0sm01019g] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We present data-driven coarse-grained (CG) modeling for polymers in solution, which conserves the dynamic as well as structural properties of the underlying atomistic system. The CG modeling is built upon the framework of the generalized Langevin equation (GLE). The key is to determine each term in the GLE by directly linking it to atomistic data. In particular, we propose a two-stage Gaussian process-based Bayesian optimization method to infer the non-Markovian memory kernel from the data of the velocity autocorrelation function (VACF). Considering that the long-time behaviors of the VACF and memory kernel for polymer solutions can exhibit hydrodynamic scaling (algebraic decay with time), we further develop an active learning method to determine the emergence of hydrodynamic scaling, which can accelerate the inference process of the memory kernel. The proposed methods do not rely on how the mean force or CG potential in the GLE is constructed. Thus, we also compare two methods for constructing the CG potential: a deep learning method and the iterative Boltzmann inversion method. With the memory kernel and CG potential determined, the GLE is mapped onto an extended Markovian process to circumvent the expensive cost of directly solving the GLE. The accuracy and computational efficiency of the proposed CG modeling are assessed in a model star-polymer solution system at three representative concentrations. By comparing with the reference atomistic simulation results, we demonstrate that the proposed CG modeling can robustly and accurately reproduce the dynamic and structural properties of polymers in solution.
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Affiliation(s)
- Shu Wang
- Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA.
| | - Zhan Ma
- Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA.
| | - Wenxiao Pan
- Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA.
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29
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Mantha S, Qi S, Schmid F. Bottom-up Construction of Dynamic Density Functional Theories for Inhomogeneous Polymer Systems from Microscopic Simulations. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c00130] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Sriteja Mantha
- Institut für Physik, Johannes Gutenberg Universität Mainz, Staudingerweg 9, 55128 Mainz, Germany
| | - Shuanhu Qi
- Key Laboratory of Bio-inspired Smart Interfacial Science and Technology of Ministry of Education, School of Chemistry, Beihang University, Beijing 100191, China
| | - Friederike Schmid
- Institut für Physik, Johannes Gutenberg Universität Mainz, Staudingerweg 9, 55128 Mainz, Germany
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30
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Müller M. Process-directed self-assembly of copolymers: Results of and challenges for simulation studies. Prog Polym Sci 2020. [DOI: 10.1016/j.progpolymsci.2019.101198] [Citation(s) in RCA: 38] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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31
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Meyer H, Pelagejcev P, Schilling T. Non-Markovian out-of-equilibrium dynamics: A general numerical procedure to construct time-dependent memory kernels for coarse-grained observables. ACTA ACUST UNITED AC 2020. [DOI: 10.1209/0295-5075/128/40001] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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32
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Avalos JB, Lísal M, Larentzos JP, Mackie AD, Brennan JK. Generalised dissipative particle dynamics with energy conservation: density- and temperature-dependent potentials. Phys Chem Chem Phys 2019; 21:24891-24911. [PMID: 31690923 DOI: 10.1039/c9cp04404c] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a generalised, energy-conserving dissipative particle dynamics (DPDE) method appropriate for the non-isothermal simulation of particle interaction force fields that are both density- and temperature-dependent. A detailed derivation is formulated in a bottom-up manner by considering the thermodynamics of small systems with the appropriate consideration of the fluctuations. Connected to the local volume is a local density and corresponding local pressure, which is determined from an equation-of-state based force field that depends also on a particle temperature. Compared to the original DPDE method, the formulation of the generalised DPDE method requires a change in the independent variable from the particle internal energy to the particle entropy. As part of the re-formulation, the terms dressed particle entropy and the corresponding dressed particle temperature are introduced, which depict the many-body contributions in the local volume. The generalised DPDE method has similarities to the energy form of the smoothed dissipative particle dynamics method, yet fundamental differences exist, which are described in the manuscript. The basic dynamic equations are presented along with practical considerations for implementing the generalised DPDE method, including a numerical integration scheme based on the Shardlow-like splitting algorithm. Demonstrations and validation tests are performed using analytical equation-of-states for the van der Waals and Lennard-Jones fluids. Particle probability distributions are analysed, where excellent agreement with theoretical estimates is demonstrated. As further validation of the generalised DPDE method, both equilibrium and non-equilibrium simulation scenarios are considered, including adiabatic flash heating response and vapour-liquid phase separation.
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Affiliation(s)
- Josep Bonet Avalos
- Department d'Enginyeria Qumica, ETSEQ, Universitat Rovira i Virgili, Tarragona, Spain
| | - Martin Lísal
- Department of Molecular and Mesoscopic Modelling, Institute of Chemical Process Fundamentals of the CAS, Prague, Czech Republic and Department of Physics, Faculty of Science, J. E. Purkinje University, Úst n. Lab., Czech Republic
| | - James P Larentzos
- Weapons and Materials Research Directorate, U.S. Army Combat Capabilities Development Command Army Research Laboratory, Aberdeen Proving Ground, MD, USA.
| | - Allan D Mackie
- Department d'Enginyeria Qumica, ETSEQ, Universitat Rovira i Virgili, Tarragona, Spain
| | - John K Brennan
- Weapons and Materials Research Directorate, U.S. Army Combat Capabilities Development Command Army Research Laboratory, Aberdeen Proving Ground, MD, USA.
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33
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Wang S, Li Z, Pan W. Implicit-solvent coarse-grained modeling for polymer solutions via Mori-Zwanzig formalism. SOFT MATTER 2019; 15:7567-7582. [PMID: 31436282 DOI: 10.1039/c9sm01211g] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We present a bottom-up coarse-graining (CG) method to establish implicit-solvent CG modeling for polymers in solution, which conserves the dynamic properties of the reference microscopic system. In particular, tens to hundreds of bonded polymer atoms (or Lennard-Jones beads) are coarse-grained as one CG particle, and the solvent degrees of freedom are eliminated. The dynamics of the CG system is governed by the generalized Langevin equation (GLE) derived via the Mori-Zwanzig formalism, by which the CG variables can be directly and rigorously linked to the microscopic dynamics generated by molecular dynamics (MD) simulations. The solvent-mediated dynamics of polymers is modeled by the non-Markovian stochastic dynamics in GLE, where the memory kernel can be computed from the MD trajectories. To circumvent the difficulty in direct evaluation of the memory term and generation of colored noise, we exploit the equivalence between the non-Markovian dynamics and Markovian dynamics in an extended space. To this end, the CG system is supplemented with auxiliary variables that are coupled linearly to the momentum and among themselves, subject to uncorrelated Gaussian white noise. A high-order time-integration scheme is used to solve the extended dynamics to further accelerate the CG simulations. To assess, validate, and demonstrate the established implicit-solvent CG modeling, we have applied it to study four different types of polymers in solution. The dynamic properties of polymers characterized by the velocity autocorrelation function, diffusion coefficient, and mean square displacement as functions of time are evaluated in both CG and MD simulations. Results show that the extended dynamics with auxiliary variables can construct arbitrarily high-order CG models to reproduce dynamic properties of the reference microscopic system and to characterize long-time dynamics of polymers in solution.
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Affiliation(s)
- Shu Wang
- Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA.
| | - Zhen Li
- Department of Mechanical Engineering, Clemson University, Clemson, SC 29634, USA
| | - Wenxiao Pan
- Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA.
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Recent Progress towards Chemically-Specific Coarse-Grained Simulation Models with Consistent Dynamical Properties. COMPUTATION 2019. [DOI: 10.3390/computation7030042] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
Coarse-grained (CG) models can provide computationally efficient and conceptually simple characterizations of soft matter systems. While generic models probe the underlying physics governing an entire family of free-energy landscapes, bottom-up CG models are systematically constructed from a higher-resolution model to retain a high level of chemical specificity. The removal of degrees of freedom from the system modifies the relationship between the relative time scales of distinct dynamical processes through both a loss of friction and a “smoothing” of the free-energy landscape. While these effects typically result in faster dynamics, decreasing the computational expense of the model, they also obscure the connection to the true dynamics of the system. The lack of consistent dynamics is a serious limitation for CG models, which not only prevents quantitatively accurate predictions of dynamical observables but can also lead to qualitatively incorrect descriptions of the characteristic dynamical processes. With many methods available for optimizing the structural and thermodynamic properties of chemically-specific CG models, recent years have seen a stark increase in investigations addressing the accurate description of dynamical properties generated from CG simulations. In this review, we present an overview of these efforts, ranging from bottom-up parameterizations of generalized Langevin equations to refinements of the CG force field based on a Markov state modeling framework. We aim to make connections between seemingly disparate approaches, while laying out some of the major challenges as well as potential directions for future efforts.
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35
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Te Vrugt M, Wittkowski R. Mori-Zwanzig projection operator formalism for far-from-equilibrium systems with time-dependent Hamiltonians. Phys Rev E 2019; 99:062118. [PMID: 31330634 DOI: 10.1103/physreve.99.062118] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2019] [Indexed: 11/07/2022]
Abstract
The Mori-Zwanzig projection operator formalism is a powerful method for the derivation of mesoscopic and macroscopic theories based on known microscopic equations of motion. It has applications in a large number of areas including fluid mechanics, solid-state theory, spin relaxation theory, and particle physics. In its present form, however, the formalism cannot be directly applied to systems with time-dependent Hamiltonians. Such systems are relevant in many scenarios such as driven soft matter or nuclear magnetic resonance. In this article we derive a generalization of the present Mori-Zwanzig formalism that is able to treat also time-dependent Hamiltonians. The extended formalism can be applied to classical and quantum systems, close to and far from thermodynamic equilibrium, and even in the case of explicitly-time-dependent observables. Moreover, we develop a variety of approximation techniques that enhance the practical applicability of our formalism. Generalizations and approximations are developed for both equations of motion and correlation functions. Our formalism is demonstrated for the important case of spin relaxation in a time-dependent external magnetic field. The Bloch equations are derived together with microscopic expressions for the relaxation times.
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Affiliation(s)
- Michael Te Vrugt
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany.,Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany.,Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany.,Center for Nonlinear Science, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
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36
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Lee HS, Ahn SH, Darve EF. The multi-dimensional generalized Langevin equation for conformational motion of proteins. J Chem Phys 2019; 150:174113. [PMID: 31067888 DOI: 10.1063/1.5055573] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Using the generalized Langevin equation (GLE) is a promising approach to build coarse-grained (CG) models of molecular systems since the GLE model often leads to more accurate thermodynamic and kinetic predictions than Brownian dynamics or Langevin models by including a more sophisticated friction with memory. The GLE approach has been used for CG coordinates such as the center of mass of a group of atoms with pairwise decomposition and for a single CG coordinate. We present a GLE approach when CG coordinates are multiple generalized coordinates, defined, in general, as nonlinear functions of microscopic atomic coordinates. The CG model for multiple generalized coordinates is described by the multidimensional GLE from the Mori-Zwanzig formalism, which includes an exact memory matrix. We first present a method to compute the memory matrix in a multidimensional GLE using trajectories of a full system. Then, in order to reduce the computational cost of computing the multidimensional friction with memory, we introduce a method that maps the GLE to an extended Markovian system. In addition, we study the effect of using a nonconstant mass matrix in the CG model. In particular, we include mass-dependent terms in the mean force. We used the proposed CG model to describe the conformational motion of a solvated alanine dipeptide system, with two dihedral angles as the CG coordinates. We showed that the CG model can accurately reproduce two important kinetic quantities: the velocity autocorrelation function and the distribution of first passage times.
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Affiliation(s)
- Hee Sun Lee
- Mechanical Engineering Department, Stanford University, Stanford, California 94305, USA
| | - Surl-Hee Ahn
- Chemistry Department, Stanford University, Stanford, California 94305, USA
| | - Eric F Darve
- Mechanical Engineering Department, Stanford University, Stanford, California 94305, USA
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37
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Deichmann G, van der Vegt NFA. Conditional Reversible Work Coarse-Grained Models with Explicit Electrostatics—An Application to Butylmethylimidazolium Ionic Liquids. J Chem Theory Comput 2019; 15:1187-1198. [DOI: 10.1021/acs.jctc.8b00881] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Gregor Deichmann
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
| | - Nico F. A. van der Vegt
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
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Deichmann G, van der Vegt NFA. Bottom-up approach to represent dynamic properties in coarse-grained molecular simulations. J Chem Phys 2019; 149:244114. [PMID: 30599732 DOI: 10.1063/1.5064369] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Several molecular coarse-graining methods have been proposed in recent years to derive chemical- and state-point transferable force fields. While these force fields describe structural and thermodynamic properties in good agreement with fine-grained models and experiments, dynamic properties are usually overestimated. Herein, we examine if the long-time dynamic properties of molecular coarse-grained (CG) systems can be correctly represented by employing a dissipative particle dynamics (DPD) thermostat, which is "bottom-up informed" by means of a variant of the Markovian Mori-Zwanzig (MZ) DPD coarse-graining method. We report single-site and multiple-site CG models for a monomer, dimer, and 24mer based on 2,2-dimethyl propane as a chemical repeat unit and report data obtained from MZ-DPD simulations of liquids, polymer solutions, and polymer melts. We find that despite incomplete time scale separation of the molecular CG model, MZ-DPD achieves quantitative accuracy in predicting diffusive dynamics in single-component liquids and polymer solutions (24mers in a dimer solvent). We also find that MZ-DPD simulations of molecular penetrant diffusion in polymer networks do not reach quantitative agreement with the fine-grained model. Modeling diffusion governed by the activated barrier crossing of small molecular penetrants in these dense systems requires an accurate description of energy barriers, presumably combined with the treatment of memory effects. The use of a MZ-DPD thermostat extends the scope and applicability of molecular CG models for multicomponent systems where a correct description of the relative diffusion rates of the different components is important.
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Affiliation(s)
- Gregor Deichmann
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
| | - Nico F A van der Vegt
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
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Lebold KM, Noid WG. Systematic study of temperature and density variations in effective potentials for coarse-grained models of molecular liquids. J Chem Phys 2019; 150:014104. [DOI: 10.1063/1.5050509] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Affiliation(s)
- Kathryn M. Lebold
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
| | - W. G. Noid
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
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Di Pasquale N, Hudson T, Icardi M. Systematic derivation of hybrid coarse-grained models. Phys Rev E 2019; 99:013303. [PMID: 30780282 DOI: 10.1103/physreve.99.013303] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2018] [Indexed: 06/09/2023]
Abstract
Molecular dynamics represents a key enabling technology for applications ranging from biology to the development of new materials. However, many real-world applications remain inaccessible to fully resolved simulations due to their unsustainable computational costs and must therefore rely on semiempirical coarse-grained models. Significant efforts have been devoted in the last decade towards improving the predictivity of these coarse-grained models and providing a rigorous justification of their use, through a combination of theoretical studies and data-driven approaches. One of the most promising research efforts is the (re)discovery of the Mori-Zwanzig projection as a generic, yet systematic, theoretical tool for deriving coarse-grained models. Despite its clean mathematical formulation and generality, there are still many open questions about its applicability and assumptions. In this work, we propose a detailed derivation of a hybrid multiscale system, generalizing and further investigating the approach developed in Español [Europhys. Lett. 88, 40008 (2009)10.1209/0295-5075/88/40008]. Issues such as the general coexistence of atoms (fully resolved degrees of freedom) and beads (larger coarse-grained units), the role of the fine-to-coarse mapping chosen, and the approximation of effective potentials are discussed. The theoretical discussion is supported by numerical simulations of a monodimensional nonlinear periodic benchmark system with an open-source parallel Julia code, easily extensible to arbitrary potential models and fine-to-coarse mapping functions. The results presented highlight the importance of introducing, in the macroscopic model, nonconstant fluctuating and dissipative terms, given by the Mori-Zwanzig approach, to correctly reproduce the reference fine-grained results, without requiring ad hoc calibration of interaction potentials and thermostats.
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Affiliation(s)
- Nicodemo Di Pasquale
- Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom
| | - Thomas Hudson
- Warwick Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Matteo Icardi
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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Jung G, Hanke M, Schmid F. Generalized Langevin dynamics: construction and numerical integration of non-Markovian particle-based models. SOFT MATTER 2018; 14:9368-9382. [PMID: 30427043 DOI: 10.1039/c8sm01817k] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We propose a generalized Langevin dynamics (GLD) technique to construct non-Markovian particle-based coarse-grained models from fine-grained reference simulations and to efficiently integrate them. The proposed GLD model has the form of a discretized generalized Langevin equation with distance-dependent two-particle contributions to the self- and pair-memory kernels. The memory kernels are iteratively reconstructed from the dynamical correlation functions of an underlying fine-grained system. We develop a simulation algorithm for this class of non-Markovian models that scales linearly with the number of coarse-grained particles. Our GLD method is suitable for coarse-grained studies of systems with incomplete time scale separation, as is often encountered, e.g., in soft matter systems. We apply the method to a suspension of nanocolloids with frequency-dependent hydrodynamic interactions. We show that the results from GLD simulations perfectly reproduce the dynamics of the underlying fine-grained system. The effective speedup of these simulations amounts to a factor of about 104. Additionally, the transferability of the coarse-grained model with respect to changes of the nanocolloid density is investigated. The results indicate that the model is transferable to systems with nanocolloid densities that differ by up to one order of magnitude from the density of the reference system.
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Affiliation(s)
- Gerhard Jung
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55128 Mainz, Germany.
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42
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Han Y, Dama JF, Voth GA. Mesoscopic coarse-grained representations of fluids rigorously derived from atomistic models. J Chem Phys 2018; 149:044104. [DOI: 10.1063/1.5039738] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Affiliation(s)
- Yining Han
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
| | - James F. Dama
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
| | - Gregory A. Voth
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
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43
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Mukherjee B, Peter C, Kremer K. Single molecule translocation in smectics illustrates the challenge for time-mapping in simulations on multiple scales. J Chem Phys 2018; 147:114501. [PMID: 28938812 DOI: 10.1063/1.5001482] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
Understanding the connections between the characteristic dynamical time scales associated with a coarse-grained (CG) and a detailed representation is central to the applicability of the coarse-graining methods to understand molecular processes. The process of coarse graining leads to an accelerated dynamics, owing to the smoothening of the underlying free-energy landscapes. Often a single time-mapping factor is used to relate the time scales associated with the two representations. We critically examine this idea using a model system ideally suited for this purpose. Single molecular transport properties are studied via molecular dynamics simulations of the CG and atomistic representations of a liquid crystalline, azobenzene containing mesogen, simulated in the smectic and the isotropic phases. The out-of-plane dynamics in the smectic phase occurs via molecular hops from one smectic layer to the next. Hopping can occur via two mechanisms, with and without significant reorientation. The out-of-plane transport can be understood as a superposition of two (one associated with each mode of transport) independent continuous time random walks for which a single time-mapping factor would be rather inadequate. A comparison of the free-energy surfaces, relevant to the out-of-plane transport, qualitatively supports the above observations. Thus, this work underlines the need for building CG models that exhibit both structural and dynamical consistency to the underlying atomistic model.
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Affiliation(s)
| | - Christine Peter
- Department of Chemistry, University of Konstanz, 78547 Konstanz, Germany
| | - Kurt Kremer
- Max-Planck-Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany
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Lafond PG, Izvekov S. Multiscale Coarse-Graining with Effective Polarizabilities: A Fully Bottom-Up Approach. J Chem Theory Comput 2018; 14:1873-1886. [DOI: 10.1021/acs.jctc.7b00917] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Patrick G. Lafond
- Weapons and Materials Research Directorate, U.S. Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, United States
| | - Sergei Izvekov
- Weapons and Materials Research Directorate, U.S. Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, United States
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Yoshimoto Y, Li Z, Kinefuchi I, Karniadakis GE. Construction of non-Markovian coarse-grained models employing the Mori–Zwanzig formalism and iterative Boltzmann inversion. J Chem Phys 2017; 147:244110. [DOI: 10.1063/1.5009041] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yuta Yoshimoto
- Department of Mechanical Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Zhen Li
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
| | - Ikuya Kinefuchi
- Department of Mechanical Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - George Em Karniadakis
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
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46
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Meyer H, Voigtmann T, Schilling T. On the non-stationary generalized Langevin equation. J Chem Phys 2017; 147:214110. [DOI: 10.1063/1.5006980] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Hugues Meyer
- Physikalisches Institut, Albert-Ludwigs-Universität, 79104 Freiburg, Germany
- Research Unit in Engineering Science, Université du Luxembourg, L-4364 Esch-sur-Alzette, Luxembourg
| | - Thomas Voigtmann
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany
- Department of Physics, Heinrich Heine University, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Tanja Schilling
- Physikalisches Institut, Albert-Ludwigs-Universität, 79104 Freiburg, Germany
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47
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Lu L, Li H, Bian X, Li X, Karniadakis GE. Mesoscopic Adaptive Resolution Scheme toward Understanding of Interactions between Sickle Cell Fibers. Biophys J 2017; 113:48-59. [PMID: 28700924 DOI: 10.1016/j.bpj.2017.05.050] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2016] [Revised: 05/25/2017] [Accepted: 05/30/2017] [Indexed: 12/17/2022] Open
Abstract
Understanding of intracellular polymerization of sickle hemoglobin (HbS) and subsequent interaction with the membrane of a red blood cell (RBC) is important to predict the altered morphologies and mechanical properties of sickle RBCs in sickle cell anemia. However, modeling the integrated processes of HbS nucleation, polymerization, HbS fiber interaction, and subsequent distortion of RBCs is challenging as they occur at multispatial scales, ranging from nanometers to micrometers. To make progress toward simulating the integrated processes, we propose a hybrid HbS fiber model, which couples fine-grained and coarse-grained HbS fiber models through a mesoscopic adaptive resolution scheme (MARS). To this end, we apply a microscopic model to capture the dynamic process of polymerization of HbS fibers, while maintaining the mechanical properties of polymerized HbS fibers by the mesoscopic model, thus providing a means of bridging the subcellular and cellular phenomena in sickle cell disease. At the subcellular level, this model can simulate HbS polymerization with preexisting HbS nuclei. At the cellular level, if combined with RBC models, the generated HbS fibers could be applied to study the morphologies and membrane stiffening of sickle RBCs. One important feature of the MARS is that it can be easily employed in other particle-based multiscale simulations where a dynamic coarse-graining and force-blending method is required. As demonstrations, we first apply the hybrid HbS fiber model to simulate the interactions of two growing fibers and find that their final configurations depend on the orientation and interaction distance between two fibers, in good agreement with experimental observations. We also model the formation of fiber bundles and domains so that we explore the mechanism that causes fiber branching.
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Affiliation(s)
- Lu Lu
- Division of Applied Mathematics, Brown University, Providence, Rhode Island
| | - He Li
- Division of Applied Mathematics, Brown University, Providence, Rhode Island
| | - Xin Bian
- Division of Applied Mathematics, Brown University, Providence, Rhode Island
| | - Xuejin Li
- Division of Applied Mathematics, Brown University, Providence, Rhode Island
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Abstract
In recent years, it has become increasingly popular to construct coarse-grained models with non-Markovian dynamics to account for an incomplete separation of time scales. One challenge of a systematic coarse-graining procedure is the extraction of the dynamical properties, namely, the memory kernel, from equilibrium all-atom simulations. In this article, we propose an iterative method for memory reconstruction from dynamical correlation functions. Compared to previously proposed noniterative techniques, it ensures by construction that the target correlation functions of the original fine-grained systems are reproduced accurately by the coarse-grained system, regardless of time step and discretization effects. Furthermore, we also propose a new numerical integrator for generalized Langevin equations that is significantly more accurate than the more commonly used generalization of the velocity Verlet integrator. We demonstrate the performance of the above-described methods using the example of backflow-induced memory in the Brownian diffusion of a single colloid. For this system, we are able to reconstruct realistic coarse-grained dynamics with time steps about 200 times larger than those used in the original molecular dynamics simulations.
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Affiliation(s)
- Gerhard Jung
- Institut für Physik, ‡Graduate School of Excellence Materials Science in Mainz, §Institut für Mathematik, Johannes Gutenberg-Universität Mainz , Staudingerweg 9, 55128 Mainz, Germany
| | - Martin Hanke
- Institut für Physik, ‡Graduate School of Excellence Materials Science in Mainz, §Institut für Mathematik, Johannes Gutenberg-Universität Mainz , Staudingerweg 9, 55128 Mainz, Germany
| | - Friederike Schmid
- Institut für Physik, ‡Graduate School of Excellence Materials Science in Mainz, §Institut für Mathematik, Johannes Gutenberg-Universität Mainz , Staudingerweg 9, 55128 Mainz, Germany
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