Density functional approach to the many-body problem: Key concepts and exact functionals

We give an overview of the fundamental concepts of density functional theory. We give a careful discussion of the several density functionals and their differentiability properties. We show that for nondegenerate ground states we can calculate the necessary functional derivatives by means of linear response theory, but that there are some differentiability problems for degenerate ground states. These problems can be overcome by extending the domains of the functionals. We further show that for every interacting v-representable density we can find a noninteracting v-representable density arbitrarily close and show that this is sufficient to set up a Kohn-Sham scheme. We finally describe two systematic approaches for the construction of density functionals