Analytic example of a free energy functional

We use the ideas of Percus for the construction of classical density functi onals for two model interactions: simple hard spheres and adhesive hard:sph eres (AHSs). The required input, the properties of the uniform fluid, is ta ken from the analytic mean spherical solution for these two systems. For ha rd spheres we derive-via a bilinear decomposition of the direct correlation functions-a set of basis functions, which is the same as the one presented by Rosenfeld in his fundamental measure theory framework. For AHSs additio nal basis functions have to be considered to ensure the bilinear decomposit ion of the direct correlation functions; we present an expression for the f ree energy functional for the one-component case.