Extracting the diffusion tensor from molecular dynamics simulation with Milestoning
Abstract
We propose an algorithm to extract the diffusion tensor from Molecular Dynamics simulations with Milestoning. A KramersMoyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion tensor. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional FokkerPlanck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion tensor. We illustrate the computation on simple models and on an atomically detailed system—the diffusion along the backbone torsions of a solvated alanine dipeptide.
 Authors:
 Department of Chemistry, University of Texas at Austin, Austin, Texas 78712 (United States)
 (United States)
 Publication Date:
 OSTI Identifier:
 22415451
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALANINES; ALGORITHMS; COMPUTERIZED SIMULATION; COORDINATES; DIFFUSION; EXPANSION; FOKKERPLANCK EQUATION; MARKOV PROCESS; MOLECULAR DYNAMICS METHOD; POTENTIALS; TENSORS; TORSION; TRAJECTORIES
Citation Formats
Mugnai, Mauro L., Elber, Ron, and The Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712. Extracting the diffusion tensor from molecular dynamics simulation with Milestoning. United States: N. p., 2015.
Web. doi:10.1063/1.4904882.
Mugnai, Mauro L., Elber, Ron, & The Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712. Extracting the diffusion tensor from molecular dynamics simulation with Milestoning. United States. doi:10.1063/1.4904882.
Mugnai, Mauro L., Elber, Ron, and The Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712. 2015.
"Extracting the diffusion tensor from molecular dynamics simulation with Milestoning". United States.
doi:10.1063/1.4904882.
@article{osti_22415451,
title = {Extracting the diffusion tensor from molecular dynamics simulation with Milestoning},
author = {Mugnai, Mauro L. and Elber, Ron and The Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712},
abstractNote = {We propose an algorithm to extract the diffusion tensor from Molecular Dynamics simulations with Milestoning. A KramersMoyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion tensor. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional FokkerPlanck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion tensor. We illustrate the computation on simple models and on an atomically detailed system—the diffusion along the backbone torsions of a solvated alanine dipeptide.},
doi = {10.1063/1.4904882},
journal = {Journal of Chemical Physics},
number = 1,
volume = 142,
place = {United States},
year = 2015,
month = 1
}

Improved basis sets for the study of polymer dynamics by means of the diffusion theory, and tests on a melt of cis1,4polyisoprene decamers, and a toluene solution of a 71mer syndiotactic trans1,2polypentadiene were presented recently [R. Gaspari and A. Rapallo, J. Chem. Phys. 128, 244109 (2008)]. The proposed hybrid basis approach (HBA) combined two techniques, the long time sorting procedure and the maximum correlation approximation. The HBA takes advantage of the strength of these two techniques, and its basis sets proved to be very effective and computationally convenient in describing both local and global dynamics in cases of flexible syntheticmore »

Moleculardynamics simulation of grainboundary diffusion creep.
Moleculardynamics (MD) simulations are used, for the first time, to study grainboundary diffusion creep of a model polycrystalline silicon microstructure. Our fully dense model microstructures, with a grain size of up to 7.5 nm, were grown by MD simulations of a melt into which small, randomly oriented crystalline seeds were inserted. In order to prevent grain growth and thus to enable steadystate diffusion creep to be observed on a time scale accessible to MD simulations (of typically 10{sup 9}s), our input microstructures were tailored to (i) have a uniform grain shape and a uniform grain size of nm dimensions andmore » 
Selfdiffusion in highangle FCC metal grain boundaries by molecular dynamics simulation.
Recent molecular dynamics simulations of highenergy highangle twist grain boundaries (GBs) in Si revealed a universal liquidlike hightemperature structure which, at lower temperatures, undergoes a reversible structural and dynamical transition from a confined liquid to a solid; lowenergy boundaries, by contrast, were found to remain solid all the way up to the melting point. Here we demonstrate for the case of palladium that fcc metal GBs behave in much the same manner. Remarkably, at high temperatures the few representative highenergy highangle (tilt or twist) boundaries examined here exhibit the same, rather low selfdiffusion activation energy and an isotropic liquidlike diffusionmore » 
Grainboundary diffusion creep in nanocrystalline palladium by moleculardynamics simulation.
Moleculardynamics (MD) simulations of fully threedimensional (3D), model nanocrystalline facecentered cubic metal microstructures are used to study grainboundary (GB) diffusion creep, one mechanism considered to contribute to the deformation of nanocrystalline materials. To overcome the wellknown limitations associated with the relatively short time interval used in our MD simulation (typically <10{sup 8} s), our simulations are performed at elevated temperatures where the distinct effects of GB diffusion are clearly identifiable. In order to prevent grain growth and thus to enable steadystate diffusion creep to be observed, our input microstructures were tailored to (1) have a uniform grain shape and amore » 
Effects of grain growth on grainboundary diffusion creep by moleculardynamics simulation.
Moleculardynamics simulations are used to elucidate the effects of grain growth on grainboundary diffusion creep and grainboundary sliding during hightemperature deformation of a nanocrystalline Pd model microstructure. The initial microstructure consists of a 25grain polycrystal with an average grain size of about 15 nm and a columnar grain shape. Prior to the onset of significant grain growth, the deformation proceeds via the mechanism of Coble creep accompanied by grainboundary sliding. While grain growth is generally known to decrease the creep rate due to the increase of the average grain size, the results obtained in this study reveal an enhanced creepmore »