Exponential-six potential scaling for the calculation of free energies in molecular simulations

Abstract

An adjustable, scaled form of the exponential-six (exp-6) potential is presented. The potential form allows stable scaling from a fully interacting exp-6 system to a non-interacting reference system for the direct computation of free energy differences or efficient particle growth simulations, particularly for high-density systems. Additional scaling parameters were introduced to overcome known endpoint effects, whereby reducing the potential to an ideal gas state can produce singularities in simulation averages or prohibit the sampling of close particle distances. The scaled potential is validated in several ways, using Hamiltonian thermodynamic integration, by comparison to vapour–liquid and solid–liquid coexistence free energies reported in the literature, and by the application of the Gibbs–Helmholtz equation. Forms of the scaled exp-6 potential for its implementation into molecular simulations and the thermodynamic integration methods are also developed.

Keywords:

• exponential-six potential
• free energy
• potential scaling
• simulation
• thermodynamic integration

Acknowledgements

The authors acknowledge James P. Larentzos (Engility Corporation) for insightful discussions and help in implementing the H-TI into LAMMPS. This research was also supported in part by appointments to the US Army Research Laboratory Postdoctoral Fellowship Program administered by the Oak Ridge Associated Universities through a contract with the US Army Research Laboratory.

Additional information

Funding

The authors acknowledge financial support from various sources, including the Office of Naval Research, the Department of Defense High Performance Computing Modernisation Program Software Application Institute for Multi-scale Reactive Modeling of Insensitive Munitions, ARL under Cooperative Agreement: W911NF-10-2-0039, and the Grant Programme of the Ministry of Education, Youth and Sports under project: LH12020.