Expanded Density Functionals

The free energy density functional format is increasingly used to represent the structure of non-uniform fluids in thermal equilibrium. This representation can often be simplified and extended by introducing in-principle extraneous densities with respect to which the free energy is stationary and, if possible, a minimum. The virtual necessity of such an expanded framework is illustrated for a periodic one-dimensional classical lattice gas, and its practical effectiveness attested to by the exact solution of a one-dimensional classical fluid with nearest neighbor interactions. A number of current approximation methods, classical and quantum, are either in this form or are shown to fall into it under slight reformulation. Identification of large scale excitations makes it possible to include their images in this framework, leaving only local fluctuations to be accounted for, and the possibility is raised of a meaningful density-effective potential joint representation.