# Exact milestoning

## Abstract

A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MDmore »

- Authors:

- Department of Chemistry, Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712 (United States)
- (United States)

- Publication Date:

- OSTI Identifier:
- 22416200

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 9; 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; ACCURACY; ALGORITHMS; APPROXIMATIONS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; FOKKER-PLANCK EQUATION; MATHEMATICAL SOLUTIONS; METASTABLE STATES; MOLECULAR DYNAMICS METHOD; STATISTICAL MECHANICS; THERMODYNAMIC PROPERTIES; TRAJECTORIES; TRAPPING

### Citation Formats

```
Bello-Rivas, Juan M., Elber, Ron, and Department of Chemistry, University of Texas at Austin, Austin, Texas 78712.
```*Exact milestoning*. United States: N. p., 2015.
Web. doi:10.1063/1.4913399.

```
Bello-Rivas, Juan M., Elber, Ron, & Department of Chemistry, University of Texas at Austin, Austin, Texas 78712.
```*Exact milestoning*. United States. doi:10.1063/1.4913399.

```
Bello-Rivas, Juan M., Elber, Ron, and Department of Chemistry, University of Texas at Austin, Austin, Texas 78712. Sat .
"Exact milestoning". United States.
doi:10.1063/1.4913399.
```

```
@article{osti_22416200,
```

title = {Exact milestoning},

author = {Bello-Rivas, Juan M. and Elber, Ron and Department of Chemistry, University of Texas at Austin, Austin, Texas 78712},

abstractNote = {A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied.},

doi = {10.1063/1.4913399},

journal = {Journal of Chemical Physics},

number = 9,

volume = 142,

place = {United States},

year = {Sat Mar 07 00:00:00 EST 2015},

month = {Sat Mar 07 00:00:00 EST 2015}

}