# Generalized Metropolis acceptance criterion for hybrid non-equilibrium molecular dynamics—Monte Carlo simulations

## Abstract

A family of hybrid simulation methods that combines the advantages of Monte Carlo (MC) with the strengths of classical molecular dynamics (MD) consists in carrying out short non-equilibrium MD (neMD) trajectories to generate new configurations that are subsequently accepted or rejected via an MC process. In the simplest case where a deterministic dynamic propagator is used to generate the neMD trajectories, the familiar Metropolis acceptance criterion based on the change in the total energy ΔE, min[1, exp( − βΔE)], guarantees that the hybrid algorithm will yield the equilibrium Boltzmann distribution. However, the functional form of the acceptance probability is more complex when the non-equilibrium switching process is generated via a non-deterministic stochastic dissipative propagator coupled to a heat bath. Here, we clarify the conditions under which the Metropolis criterion remains valid to rigorously yield a proper equilibrium Boltzmann distribution within hybrid neMD-MC algorithm.

- Authors:

- Department of Chemistry, University of Chicago, Chicago, Illinois 60637 (United States)
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, Illinois 60637 (United States)

- Publication Date:

- OSTI Identifier:
- 22415817

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 2; 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; ALGORITHMS; COMPUTERIZED SIMULATION; EQUILIBRIUM; MOLECULAR DYNAMICS METHOD; MONTE CARLO METHOD; PROBABILITY; PROPAGATOR; STOCHASTIC PROCESSES

### Citation Formats

```
Chen, Yunjie, and Roux, Benoît, E-mail: roux@uchicago.edu.
```*Generalized Metropolis acceptance criterion for hybrid non-equilibrium molecular dynamics—Monte Carlo simulations*. United States: N. p., 2015.
Web. doi:10.1063/1.4904889.

```
Chen, Yunjie, & Roux, Benoît, E-mail: roux@uchicago.edu.
```*Generalized Metropolis acceptance criterion for hybrid non-equilibrium molecular dynamics—Monte Carlo simulations*. United States. doi:10.1063/1.4904889.

```
Chen, Yunjie, and Roux, Benoît, E-mail: roux@uchicago.edu. Wed .
"Generalized Metropolis acceptance criterion for hybrid non-equilibrium molecular dynamics—Monte Carlo simulations". United States.
doi:10.1063/1.4904889.
```

```
@article{osti_22415817,
```

title = {Generalized Metropolis acceptance criterion for hybrid non-equilibrium molecular dynamics—Monte Carlo simulations},

author = {Chen, Yunjie and Roux, Benoît, E-mail: roux@uchicago.edu},

abstractNote = {A family of hybrid simulation methods that combines the advantages of Monte Carlo (MC) with the strengths of classical molecular dynamics (MD) consists in carrying out short non-equilibrium MD (neMD) trajectories to generate new configurations that are subsequently accepted or rejected via an MC process. In the simplest case where a deterministic dynamic propagator is used to generate the neMD trajectories, the familiar Metropolis acceptance criterion based on the change in the total energy ΔE, min[1, exp( − βΔE)], guarantees that the hybrid algorithm will yield the equilibrium Boltzmann distribution. However, the functional form of the acceptance probability is more complex when the non-equilibrium switching process is generated via a non-deterministic stochastic dissipative propagator coupled to a heat bath. Here, we clarify the conditions under which the Metropolis criterion remains valid to rigorously yield a proper equilibrium Boltzmann distribution within hybrid neMD-MC algorithm.},

doi = {10.1063/1.4904889},

journal = {Journal of Chemical Physics},

number = 2,

volume = 142,

place = {United States},

year = {Wed Jan 14 00:00:00 EST 2015},

month = {Wed Jan 14 00:00:00 EST 2015}

}