  We introduce 'single-particle-exact density functional theory' (1pEx-DFT), a
novel density functional approach that represents all single-particle
contributions to the energy with exact functionals. Here, we parameterize
interaction energy functionals by utilizing two new schemes for constructing
density matrices from 'participation numbers' of the single-particle states of
quantum many-body systems. These participation numbers play the role of the
variational variables akin to the particle densities in standard orbital-free
density functional theory. We minimize the total energies with the help of
evolutionary algorithms and obtain ground-state energies that are typically
accurate at the one-percent level for our proof-of-principle simulations that
comprise interacting Fermi gases as well as the electronic structure of atoms
and ions, with and without relativistic corrections. We thereby illustrate the
ingredients and practical features of 1pEx-DFT and reveal its potential of
becoming an accurate, scalable, and transferable technology for simulating
mesoscopic quantum many-body systems.
