Generalized density-functional theory: extended weighted density approaches.

Abstract

A third-order density-functional theory is introduced by an approach that may be used to find density-functional theories to any higher-order accuracy provided only that known homogeneous state correlation functions are utilized as input. It is constructed from the required knowledge of a single weight function at each order. By way of application results are presented for the melting of classical hard spheres using functionals accurate to a third-order functional Taylor series in the homogeneous limit. Within the framework of the modified weighted density approximation, there is a uniform improvement in the solid phase-free energies, pressures and melting parameters, and further improvement also results when these functionals are optimized in a way that utilizes the close packing limit. The sensitivity of the results to existing and proposed models of the third-order direct correlation function is discussed.