Single-particle-exact density functionals

We introduce a novel kind of density functionals for interacting many-fermion systems in the spirit of the Levy—Lieb constrained search. In our approach all single-particle contributions to the energy are represented by exact functionals, and only the functional for the interaction energy requires an approximation in terms of the single-particle eigenstates. We discuss schemes for constructing the required approximate density matrices and report on benchmarking exercises that deliver ground-state energies, occupation numbers, and particle densities through evolutionary algorithms.