  Model Hamiltonians with long-range interaction yield energies that are
corrected taking into account the universal behavior of the electron-electron
interaction at short range. Although the intention of the paper is to explore
the foundations of using density functionals combined with range separation,
the approximations presented can be used without them, as illustrated by a
calculation on Harmonium. In the regime when the model system approaches the
Coulomb system, they allow the calculation of ground states, excited states,
and properties, without making use of the Hohenberg-Kohn theorem.
Asymptotically, the technique is improvable, allows for error estimates that
can validate the results. Some considerations for correcting the errors of
finite basis sets in this spirit are also presented. Being related to the
present understanding of density functional approximations, the results are
comparable to those obtained with the latter, as long as these are accurate.
