We give an overview of the fundamental concepts of density functional
theory. We give a careful discussion of the several density functionals and
their di®erentiability 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 di®erentiability 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 ¯nd a noninteracting v-representable density
arbitrarily close and show that this is su±cient to set up a Kohn-Sham
scheme. We ¯nally describe two systematic approaches for the construction
of density functionals. |