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 Lab. (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:https://doi.org/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:https://doi.org/10.1063/1.5100960. https://www.osti.gov/servlets/purl/1577597.
@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}
}
Web of Science
Works referenced in this record:
Note: Free energy calculations for atomic solids through the Einstein crystal/molecule methodology using GROMACS and LAMMPS
journal, October 2012
- Aragones, J. L.; Valeriani, C.; Vega, C.
- The Journal of Chemical Physics, Vol. 137, Issue 14
Two-Dimensional Clusters of Colloidal Spheres: Ground States, Excited States, and Structural Rearrangements
journal, June 2015
- Perry, Rebecca W.; Holmes-Cerfon, Miranda C.; Brenner, Michael P.
- Physical Review Letters, Vol. 114, Issue 22
Free energy of small face centred cubic clusters of atoms
journal, January 1973
- Burton, J. J.
- Journal of the Chemical Society, Faraday Transactions 2, Vol. 69
Determination of phase diagrams via computer simulation: methodology and applications to water, electrolytes and proteins
journal, March 2008
- Vega, C.; Sanz, E.; Abascal, J. L. F.
- Journal of Physics: Condensed Matter, Vol. 20, Issue 15
Crystal nucleation of hard spheres using molecular dynamics, umbrella sampling, and forward flux sampling: A comparison of simulation techniques
journal, December 2010
- Filion, L.; Hermes, M.; Ni, R.
- The Journal of Chemical Physics, Vol. 133, Issue 24
Energy landscapes of planar colloidal clusters
journal, January 2014
- Morgan, John W. R.; Wales, David J.
- Nanoscale, Vol. 6, Issue 18
Evaluating surface tension using grand-canonical transition-matrix Monte Carlo simulation and finite-size scaling
journal, January 2003
- Errington, Jeffrey R.
- Physical Review E, Vol. 67, Issue 1
Melting Transition and Communal Entropy for Hard Spheres
journal, October 1968
- Hoover, William G.; Ree, Francis H.
- The Journal of Chemical Physics, Vol. 49, Issue 8
Driving diffusionless transformations in colloidal crystals using DNA handshaking
journal, January 2012
- Casey, Marie T.; Scarlett, Raynaldo T.; Benjamin Rogers, W.
- Nature Communications, Vol. 3, Issue 1
Comparative Study of the Effect of Tail Corrections on Surface Tension Determined by Molecular Simulation
journal, June 2007
- Shen, Vincent K.; Mountain, Raymond D.; Errington, Jeffrey R.
- The Journal of Physical Chemistry B, Vol. 111, Issue 22
Fast Parallel Algorithms for Short-Range Molecular Dynamics
journal, March 1995
- Plimpton, Steve
- Journal of Computational Physics, Vol. 117, Issue 1
On the convergence of multi-scale free energy simulations
journal, November 2017
- König, Gerhard; Brooks, Bernard R.; Thiel, Walter
- Molecular Simulation, Vol. 44, Issue 13-14
Finite-size corrections to the free energies of crystalline solids
journal, March 2000
- Polson, J. M.; Trizac, E.; Pronk, S.
- The Journal of Chemical Physics, Vol. 112, Issue 12
Revisiting the Frenkel-Ladd method to compute the free energy of solids: The Einstein molecule approach
journal, October 2007
- Vega, Carlos; Noya, Eva G.
- The Journal of Chemical Physics, Vol. 127, Issue 15
Long Range Corrections in Inhomogeneous Simulations
journal, March 2006
- Janeček, Jiří
- The Journal of Physical Chemistry B, Vol. 110, Issue 12
Accuracy of free-energy perturbation calculations in molecular simulation. I. Modeling
journal, May 2001
- Lu, Nandou; Kofke, David A.
- The Journal of Chemical Physics, Vol. 114, Issue 17
Computer simulations of liquid/vapor interface in Lennard-Jones fluids: Some questions and answers
journal, November 1999
- Trokhymchuk, Andrij; Alejandre, José
- The Journal of Chemical Physics, Vol. 111, Issue 18
Entropy Stabilizes Floppy Crystals of Mobile DNA-Coated Colloids
journal, January 2018
- Hu, Hao; Ruiz, Pablo Sampedro; Ni, Ran
- Physical Review Letters, Vol. 120, Issue 4
Comparison of the potential energies for various packings of microcrystallites
journal, July 1971
- Dave, J. V.; Abraham, Farid F.
- Surface Science, Vol. 26, Issue 2
New Monte Carlo method to compute the free energy of arbitrary solids. Application to the fcc and hcp phases of hard spheres
journal, October 1984
- Frenkel, Daan; Ladd, Anthony J. C.
- The Journal of Chemical Physics, Vol. 81, Issue 7
Thermodynamics of Microcrystallites and Its Relation to Nucleation Theory
journal, August 1971
- Abraham, Farid F.; Dave, J. V.
- The Journal of Chemical Physics, Vol. 55, Issue 4
A cell theory for solid solutions: Application to hard sphere mixtures
journal, December 1993
- Cottin, X.; Monson, P. A.
- The Journal of Chemical Physics, Vol. 99, Issue 11
Numerical calculation of the rate of crystal nucleation in a Lennard‐Jones system at moderate undercooling
journal, June 1996
- Rein ten Wolde, Pieter; Ruiz‐Montero, Maria J.; Frenkel, Daan
- The Journal of Chemical Physics, Vol. 104, Issue 24
Number Dependence of Small‐Crystal Thermodynamic Properties. I
journal, September 1972
- Hoover, William G.; Hindmarsh, Alan C.; Holian, Brad Lee
- The Journal of Chemical Physics, Vol. 57, Issue 5
Monte Carlo calculation of the surface tension for two- and three-dimensional lattice-gas models
journal, March 1982
- Binder, K.
- Physical Review A, Vol. 25, Issue 3
Computation of the free energy of solids
journal, June 2007
- Almarza, N. G.
- The Journal of Chemical Physics, Vol. 126, Issue 21
On a Generalized Einstein Theory for the Thermodynamics of Planar Surfaces and Microcrystallites
journal, November 1971
- Abraham, Farid F.; Dave, J. V.
- The Journal of Chemical Physics, Vol. 55, Issue 10
Planar density-functional approach to the solid-fluid interface of simple liquids
journal, February 1993
- Marr, D. W.; Gast, A. P.
- Physical Review E, Vol. 47, Issue 2