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# Extension of the Einstein molecule method for solid free energy calculation to non-periodic and semi-periodic systems

## Abstract

Free energy calculations on solid phases are important for understanding the phase behavior of various systems. For periodic crystalline solids, the Einstein molecule approach can be used to determine the free energy difference between the solid of interest and an ideal crystal for which the free energy can be found analytically. In this work, we show how this method is extensible to systems which are nonperiodic or periodic in some dimensions but not in others. This allows for the calculation of exact absolute free energies of finite-sized crystals having specific shapes and surface geometries. We illustrate this using the fcc Lennard-Jones solid and also illustrate how surface contributions to free energies can easily be extracted from simulations of this solid in semi-infinite slab geometries. We have created a software package which interfaces with the LAMMPS molecular dynamics code to perform these calculations.

- Authors:

- Lehigh Univ., Bethlehem, PA (United States)

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States); Lehigh Univ., Bethlehem, PA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE

- OSTI Identifier:
- 1577597

- Alternate Identifier(s):
- OSTI ID: 1546111

- Grant/Contract Number:
- [AC02-05CH11231; SC0013979]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- [ Journal Volume: 151; Journal Issue: 5]; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

### Citation Formats

```
Pretti, Evan, and Mittal, Jeetain. Extension of the Einstein molecule method for solid free energy calculation to non-periodic and semi-periodic systems. United States: N. p., 2019.
Web. doi:10.1063/1.5100960.
```

```
Pretti, Evan, & Mittal, Jeetain. Extension of the Einstein molecule method for solid free energy calculation to non-periodic and semi-periodic systems. United States. doi:10.1063/1.5100960.
```

```
Pretti, Evan, and Mittal, Jeetain. Fri .
"Extension of the Einstein molecule method for solid free energy calculation to non-periodic and semi-periodic systems". United States. doi:10.1063/1.5100960.
```

```
@article{osti_1577597,
```

title = {Extension of the Einstein molecule method for solid free energy calculation to non-periodic and semi-periodic systems},

author = {Pretti, Evan and Mittal, Jeetain},

abstractNote = {Free energy calculations on solid phases are important for understanding the phase behavior of various systems. For periodic crystalline solids, the Einstein molecule approach can be used to determine the free energy difference between the solid of interest and an ideal crystal for which the free energy can be found analytically. In this work, we show how this method is extensible to systems which are nonperiodic or periodic in some dimensions but not in others. This allows for the calculation of exact absolute free energies of finite-sized crystals having specific shapes and surface geometries. We illustrate this using the fcc Lennard-Jones solid and also illustrate how surface contributions to free energies can easily be extracted from simulations of this solid in semi-infinite slab geometries. We have created a software package which interfaces with the LAMMPS molecular dynamics code to perform these calculations.},

doi = {10.1063/1.5100960},

journal = {Journal of Chemical Physics},

number = [5],

volume = [151],

place = {United States},

year = {2019},

month = {8}

}

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