# 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 Kramers-Moyal 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 Fokker-Planck 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; FOKKER-PLANCK 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. Wed .
"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 Kramers-Moyal 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 Fokker-Planck 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 = {Wed Jan 07 00:00:00 EST 2015},

month = {Wed Jan 07 00:00:00 EST 2015}

}