A density functional theory based on the universality of the free energy density functional

A methodology for classical density functional theory is proposed which expresses the first order direct correlation function for nonuniform systems in terms of the second order direct correlation function and the bridge function of the corresponding uniform systems. Its applicability to nonuniform systems is verified by applying the approach to three concrete cases, namely, to a hard sphere fluid in a spherical cavity, a hard sphere fluid near a hard wall, and a hard sphere fluid near a 9–3 soft wall. The present density functional theory (DFT) provides a recipe by which the integral equation theories for uniform systems can be transformed into the corresponding DFTs for nonuniform systems.