EQUIVALENCE OF 2 FREE-ENERGY MODELS FOR THE INHOMOGENEOUS HARD-SPHEREFLUID

It is shown that the free-energy model for the inhomogeneous hard-sphe re fluid introduced by Rosenfeld [Phys. Rev. Lett. 63, 980 (1989)], wh ich contains both vector and scalar contributions, and the fully scala r expression proposed subsequently by Kierlik and Rosinberg [Phys. Rev . A 42, 3382 (1990)] represent two equivalent forms of the same functi onal. This unexpected result was partly obscured by a sign error in th e original derivation of the vector part.