  Self-interactions (SIs) are a major problem in density functional
approximations and the source of serious divergence from experimental results.
Here, we propose to optimize density functional total energies in terms of the
effective local potential, under constraints for the effective potential that
guarantee it is free from SI errors and consequently asymptotically correct.
More specifically, we constrain the Hartree, exchange and correlation potential
to be the electrostatic potential of a non-negative effective repulsive density
of $N-1$ electrons. In this way, the optimal effective potentials exhibit the
correct asymptotic decay, resulting in significantly improved one-electron
properties.
