Abstract
We demonstrate the existence of different density-density functionals designed to retain selected properties
of the many-body ground state in a non-interacting solution starting from the standard density functional theory
ground state. We focus on diffusion quantum Monte Carlo applications that require trial wave functions with
optimal Fermion nodes. The theory is extensible and can be used to understand current practices in several
electronic structure methods within a generalized density functional framework. The theory justifies and stimulates
the search of optimal empirical density functionals and effective potentials for accurate calculations of the
properties of real materials, but also cautions on the limits of their applicability. The concepts are tested and
validated with a near-analytic model.
