Abstract
By utilizing the knowledge that a Hamiltonian is a unique functional of its ground-state density, the following fundamental connections between densities and Hamiltonians are revealed: Given that are ground-level densities for interacting or noninteracting Hamiltonians ( arbitrarily large) with local potentials ,,,, but given that we do not know which belongs with which , the correct mapping is possible and is obtained by minimizing with respect to optimum permutations of the 's among the 's. A tight rigorous bound connects a density to its interacting ground-state energy via the one-body potential of the interacting system and the Kohn-Sham effective one-body potential of the auxiliary noninteracting system. A modified Kohn-Sham effective potential is defined such that its sum of lowest orbital energies equals the true interacting ground-state energy. Moreover, of all those effective potentials which differ by additive constants and which yield the true interacting ground-state density, this modified effective potential is the most invariant with respect to changes in the one-body potential of the true Hamiltonian. With the exception of the occurrence of certain linear dependencies, density will not generally be associated with any ground-state wave function (is not wave function representable) if that density can be generated by a special linear combination of three or more densities that arise from a common set of degenerate ground-state wave functions. Applicability of the "constrained search" approach to density-functional theory is emphasized for non--representable as well as for -representable densities. In fact, a particular constrained ensemble search is revealed which provides a general sufficient condition for non- representability by a wave function. The possible appearance of noninteger occupation numbers is discussed in connection with the existence of non- representability for some Kohn-Sham noninteracting systems.
- Received 20 October 1981
DOI:https://doi.org/10.1103/PhysRevA.26.1200
©1982 American Physical Society