Free-energy calculations using classical molecular simulation: application to the determination of the melting point and chemical potential of a flexible RDX model

Abstract

We present an extension of various free-energy methodologies to determine the chemical potential of the solid and liquid phases of a fully-flexible molecule using classical simulation. The methods are applied to the Smith-Bharadwaj atomistic potential representation of cyclotrimethylene trinitramine (RDX), a well-studied energetic material, to accurately determine the solid and liquid phase Gibbs free energies, and the melting point (Tm). We outline an efficient technique to find the absolute chemical potential and melting point of a fully-flexible molecule using one set of simulations to compute the solid absolute chemical potential and one set of simulations to compute the solid-liquid free energy difference. With this combination, only a handful of simulations are needed, whereby the absolute quantities of the chemical potentials are obtained, for use in other property calculations, such as the characterization of crystal polymorphs or the determination of the entropy. Using the LAMMPS molecular simulator, the Frenkel and Ladd and pseudo-supercritical path techniques are adapted to generate 3rd order fits of the solid and liquid chemical potentials. Results yield the thermodynamic melting point Tm = 488.75 K at 1.0 atm. We also validate these calculations and compare this melting point to one obtained from a typical superheated simulation technique.

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

“…In doing so, the only difference introduced to our computed absolute solid free energies is the analytic finite size correction associated with fixing the center of mass and total momentum. Along with the finite-size correction from harmonic crystal approximation, 43,44 they comprise all the finite-size corrections that are usually important to be included in theoretical studies of, e.g., Lennard-Jones (LJ) or hard spheres (HSs) crystals, where uncertainties can be as small as 0.001 k B T per molecule. 34,38 However, for solubility predictions of more complex molecular crystals, these finite-size corrections are negligible compared to other sources of error.…”

“…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.…”

Challenges in the use of atomistic simulations to predict solubilities of drug-like molecules

“…However, it is possible that the interaction removal could be achieved with a weaker value of the restraint constant, and this would in turn reduce the number of simulations to add or remove harmonic restraints. This should also be discussed in the context of ways to reduce the amount of simulation expense observed for these calculations.Finally, the authors should consider including the additional papers of Sellers et al 2016 1 and Schilling and Schmid 2009 2  who also explore the use of atomistic simulation to compute absolute solid free energies. These articles also discuss how to apply restraints in a manner that preserves the indistinguishability of certain particles.…”

“…Finally, the authors should consider including the additional papers of Sellers et al 2016 1 and Schilling and Schmid 2009 2  who also explore the use of atomistic simulation to compute absolute solid free energies. These articles also discuss how to apply restraints in a manner that preserves the indistinguishability of certain particles.…”