Three recent weighted-density-functional (WDF) theories are critically examined in terms of their ability to describe correctly the structure of a hard-sphere fluid at a hard wall. A new derivation of the Curtin-Ashcroft WDF theory is given that clarifies the basic approximations behind this formulation and brings out the close relationship between their work and the WDF theories of Meister-Kroll and Groot–van der Eerden. The condition that the second functional derivative of the approximate Helmholtz free-energy functional yields the correct two-particle direct-correlation function in the homogeneous limit is found to be of crucial importance in determining good liquid structures.

• Received 22 May 1990

DOI:https://doi.org/10.1103/PhysRevA.42.4806