Note: Free energy calculations for atomic solids through the Einstein crystal/molecule methodology using GROMACS and LAMMPS

Abstract

In this work the free energy of solid phases is computed for the Lennard-Jones potential and for a model of NaCl. The free energy is evaluated through the Einstein crystal/molecule methodologies using the Molecular Dynamics programs: GROMACS and LAMMPS. The obtained results are compared with the results obtained from Monte Carlo. Good agreement between the different programs and methodologies was found. The procedure to perform the free energy calculations for the solid phase in the Molecular Dynamic programs is described. Since these programs allow to study any continuous intermolecular potential (when given in a tabulated form) this work shows that for isotropic potentials (describing for instance atomic solids or colloidal particles) free energy calculations can be performed on a routinely basis using GROMACS and/or LAMMPS.

Computational methodology for solubility prediction: Application to the sparingly soluble solutes

“…(A1) βA 0 = 3 2Nln βK max π , the analytic expression for an Einstein atomic crystal at state (0) without the constraints on the center of mass and the total momentum, and βA 0 = 3 2 (N − 1) ln βK max π + ln N V − 3 2ln (N), the analytic expression for an Einstein atomic crystal with these constraints plus the general free energy difference between any two solids with and without these constraints. 41 The value of βA 0 − βA 0 N is around 0.1 k B T /molecule for N solid = 240 and K max = 1 046 000 (kJ/mol)/nm 2 , comparable to or smaller than errors of computed excess solvation free energies.…”

“…The method is based upon the original Einstein crystal method 34,38,39 and its recent adaptations. [40][41][42][43][44] In the present work, it has been adapted to be used in MD simulations in LAMMPS without extra codes.…”

“…All the numerical techniques used in this work are standard alchemical free energy methods [31][32][33][34][35] such as free energy perturbation (FEP) and thermodynamic integration (TI) that are commonly used in molecular dynamics (MD) or Monte Carlo (MC) simulations for computing solvation free energies 36,37 as well as absolute solid free energies. [38][39][40][41][42][43][44] The modeling challenge is focused on developing atomistic modeling tools that will make it possible to predict the solubility of simple organic crystals (we use naphthalene as an example) for potential generalization to a broader range of compounds.…”

Structural and dynamic properties of liquid tin from a new modified embedded-atom method force field

“…The last term ∆F 2 is the Helmholtz free energy difference between the "interacting Einstein crystal" and the real crystal. Calculating F solid using LAMMPS has been described in detail by Aragones et al 51 However, we will briefly describe how to calculate each term based on their work.…”

“…We set the harmonic spring constant to be Λ E = 7500 k B T/Å 2 . This value was chosen following the empirical rule given by Aragones et al 51 The authors state that a good choice of Λ E is one that yields a value of ∆F 1 to be about 0.02N k B T higher than U lattice .…”