Generalization of the density-functional theory with application to three-body interactions in classical fluids

An external field coupled with the two-body density distribution function leads to a generalization of the density-functional theory in which the free energy is regarded as a functional not only of the density but also of the two-body distribution function. The generalized formalism is applied to the liquid-structure theory in the presence of a weak three-body potential. In the first-order calculation, the three-body effects are fully taken into account through modification of the pair potential; the structure of the pair-potential theory remains intact. Such a renormalizability, which was proven diagrammatically, is ascribed to the variational property of the free-energy functional. An approximate expression for the nonadditive correction which is amenable to the numerical computations is obtained within the hypernetted-chain theory