Different thermodynamic pathways to the solvation free energy of a spherical cavity in a hard sphere fluid

TL;DR

This study compares various thermodynamic pathways, including a new density route, to accurately compute the solvation free energy of a spherical cavity in a hard sphere fluid using the hydrostatic linear response integral equation.

Contribution

It introduces a new density pathway for calculating solvation free energy and demonstrates its accuracy across a wide range of cavity sizes.

Findings

The new density route provides accurate solvation free energies.

Hydrostatic linear response integral equation effectively models nonuniform hard sphere fluids.

Results are consistent with the Gaussian Field Model for related calculations.

Abstract

This paper determines the excess free energy associated with the formation of a spherical cavity in a hard sphere fluid. The solvation free energy can be calculated by integration of the structural changes induced by inserting the cavity using a number of different exact thermodynamic pathways. We consider three such pathways, including a new density route derived here. Structural information about the nonuniform hard sphere fluid in the presence of a general external field is given by the recently developed hydrostatic linear response (HLR) integral equation. Use of the HLR results in the different pathways gives a generally accurate determination of the solvation free energy for cavities over a wide range of sizes, from zero to infinity. Results for a related method, the Gaussian Field Model, are also discussed.