  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.
