New approach to the calculation of density functionals

The density-functional theory relates the ground-state properties of an $N$-electron system to a universal functional of the charge density. In this paper we discuss a functional which avoids the problems of the Hohenberg-Kohn theory. We show that this functional can be calculated exactly, at least in principle. We present an upper bound for this functional, which is applied to the case $N=1\mathrm{}$ and to the jellium problem. This upper bound is exact for $N=1\mathrm{}$.