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The density-functional theory relates the ground-state properties of an X-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 X = 1 and to the jellium problem. This upper bound is exact for X = 1.

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We discuss the one-particle density-matrix functional theory for the N-particle ground-state problem. Using the variational principle we obtain a set of self-consistent equations which could be useful for practical calculations. The derived relation between the eigenvalues of the density matrix and the chemical potential agrees with that of Gilbert. The present theory is compared with the Kohn–Sham and the Hartree–Fock approach to the ground state problem. It is found that both approaches can be obtained from the present theory under certain assumptions.

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