The Uhlenbeck-Ford model: Exact virial coefficients and application as a reference system in fluid-phase free-energy calculations

TL;DR

This paper computes exact virial coefficients for the Uhlenbeck-Ford model and demonstrates that scaled versions serve as effective reference systems for accurate fluid-phase free-energy calculations in molecular simulations.

Contribution

It provides new exact virial coefficients for the UF model and introduces scaled UF models as robust reference systems for fluid free-energy calculations.

Findings

Scaled UF models enable accurate free-energy calculations.

UF models are too soft, but scaled versions are stable and effective.

Fluid phase is the only stable phase for a wide range of scaled UF models.

Abstract

The Uhlenbeck-Ford (UF) model was originally proposed for the theoretical study of imperfect gases, given that all its virial coefficients can be evaluated exactly, in principle. Here, in addition to computing the previously unknown coefficients B11 through B13, we assess its applicability as a reference system in fluid-phase free-energy calculations using molecular simulation techniques. Our results demonstrate that, although the UF model itself is too soft, appropriately scaled Uhlenbeck- Ford (sUF) models provide robust reference systems that allow accurate fluid-phase free-energy calculations without the need for an intermediate reference model. Indeed, in addition to the accuracy with which their free energies are known and their convenient scaling properties, the fluid is the only thermodynamically stable phase for a wide range of sUF models. This set of favorable properties may potentially put the sUF fluid-phase reference systems on par with the standard role that harmonic and Einstein solids play as reference systems for solid-phase free-energy calculations.