## Generalized ensemble method applied to study systems with strong first order transitions

## Abstract

At strong first-order phase transitions, the entropy versus energy or, at constant pressure, enthalpy, exhibits convex behavior, and the statistical temperature curve correspondingly exhibits an S-loop or back-bending. In the canonical and isothermal-isobaric ensembles, with temperature as the control variable, the probability density functions become bimodal with peaks localized outside of the S-loop region. Inside, states are unstable, and as a result simulation of equilibrium phase coexistence becomes impossible. To overcome this problem, a method was proposed by Kim, Keyes and Straub, where optimally designed generalized ensemble sampling was combined with replica exchange, and denoted generalized replica exchange method (gREM). This new technique uses parametrized effective sampling weights that lead to a unimodal energy distribution, transforming unstable states into stable ones. In the present study, the gREM, originally developed as a Monte Carlo algorithm, was implemented to work with molecular dynamics in an isobaric ensemble and coded into LAMMPS, a highly optimized open source molecular simulation package. Lastly, the method is illustrated in a study of the very strong solid/liquid transition in water.

- Authors:

- Boston Univ., Boston, MA (United States)
- Broad Institute of Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Harvard Univ., Cambridge, MA (United States)

- Publication Date:

- Research Org.:
- Boston Univ., MA (United States)

- Sponsoring Org.:
- USDOE

- Contributing Org.:
- Boston University Center for Computational Science

- OSTI Identifier:
- 1247484

- Grant/Contract Number:
- SC0008810

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Physics. Conference Series

- Additional Journal Information:
- Journal Volume: 640; Journal Issue: 2; Conference: XXVI IUPAP Conference on Computational Physics (CCP2014) , Boston, MA (United States), 11-14 Aug 2014; Journal ID: ISSN 1742-6588

- Publisher:
- IOP Publishing

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING; phase transitions; computer simulation; algorithm design; water; freezing; melting

### Citation Formats

```
Malolepsza, E., Kim, J., and Keyes, T. Generalized ensemble method applied to study systems with strong first order transitions. United States: N. p., 2015.
Web. doi:10.1088/1742-6596/640/1/012003.
```

```
Malolepsza, E., Kim, J., & Keyes, T. Generalized ensemble method applied to study systems with strong first order transitions. United States. doi:10.1088/1742-6596/640/1/012003.
```

```
Malolepsza, E., Kim, J., and Keyes, T. Mon .
"Generalized ensemble method applied to study systems with strong first order transitions". United States. doi:10.1088/1742-6596/640/1/012003. https://www.osti.gov/servlets/purl/1247484.
```

```
@article{osti_1247484,
```

title = {Generalized ensemble method applied to study systems with strong first order transitions},

author = {Malolepsza, E. and Kim, J. and Keyes, T.},

abstractNote = {At strong first-order phase transitions, the entropy versus energy or, at constant pressure, enthalpy, exhibits convex behavior, and the statistical temperature curve correspondingly exhibits an S-loop or back-bending. In the canonical and isothermal-isobaric ensembles, with temperature as the control variable, the probability density functions become bimodal with peaks localized outside of the S-loop region. Inside, states are unstable, and as a result simulation of equilibrium phase coexistence becomes impossible. To overcome this problem, a method was proposed by Kim, Keyes and Straub, where optimally designed generalized ensemble sampling was combined with replica exchange, and denoted generalized replica exchange method (gREM). This new technique uses parametrized effective sampling weights that lead to a unimodal energy distribution, transforming unstable states into stable ones. In the present study, the gREM, originally developed as a Monte Carlo algorithm, was implemented to work with molecular dynamics in an isobaric ensemble and coded into LAMMPS, a highly optimized open source molecular simulation package. Lastly, the method is illustrated in a study of the very strong solid/liquid transition in water.},

doi = {10.1088/1742-6596/640/1/012003},

journal = {Journal of Physics. Conference Series},

number = 2,

volume = 640,

place = {United States},

year = {2015},

month = {9}

}