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An overview of several recent developments in density functional theory forclassical inhomogeneous liquids is given. We show how Levy's constrained searchmethod can be used to derive the variational principle that underlies densityfunctional theory. An advantage of the method is that the Helmholtz free energyas a functional of a trial one-body density is given as an explicit expression,without reference to an external potential as is the case in the standardMermin-Evans proof by reductio ad absurdum. We show how to generalize theapproach in order to express the internal energy as a functional of theone-body density distribution and of the local entropy distribution. Here thelocal chemical potential and the bulk temperature play the role of Lagrangemultipliers in the Euler-Lagrange equations for minimiziation of thefunctional. As an explicit approximation for the free-energy functional forhard sphere mixtures, the diagrammatic structure of Rosenfeld's fundamentalmeasure density unctional is laid out. Recent extensions, based on theKierlik-Rosinberg scalar weight functions, to binary and ternary non-additivehard sphere mixtures are described.

Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory