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.