Solvation in atomic liquids: connection between Gaussian field theory and density functional theory

TL;DR

This paper establishes a connection between Gaussian field theory and classical density functional theory for molecular solvation, compares different DFT approaches, and discusses their limitations and improvements for solvation free-energy calculations.

Contribution

It demonstrates how Chandler's Gaussian field theory results can be recovered and simplified within classical DFT frameworks, and compares various DFT variants for solvation modeling.

Findings

All theories approximate solvent structure well

They fail to accurately predict solvation free energies

Adding a bridge correction improves free energy estimates

Abstract

For the problem of molecular solvation, formulated as a liquid submitted to the external potential field created by a molecular solute of arbitrary shape dissolved in that solvent, we draw a connection between the Gaussian field theory derived by David Chandler [Phys. Rev. E, 1993, 48, 2898] and classical density functional theory. We show that Chandler's results concerning the solvation of a hard core of arbitrary shape can be recovered by either minimising a linearised HNC functional using an auxiliary Lagrange multiplier field to impose a vanishing density inside the core, or by minimising this functional directly outside the core --- indeed a simpler procedure. Those equivalent approaches are compared to two other variants of DFT, either in the HNC, or partially linearised HNC approximation, for the solvation of a Lennard-Jones solute of increasing size in a Lennard-Jones solvent. Compared to Monte-Carlo simulations, all those theories give acceptable results for the inhomogeneous solvent structure, but are completely out-of-range for the solvation free-energies. This can be fixed in DFT by adding a hard-sphere bridge correction to the HNC functional.