  From a simplified version of the mathematical structure of the strong
coupling limit of the exact exchange-correlation functional, we construct an
approximation for the electronic repulsion energy at physical coupling
strength, which is fully non-local. This functional is self-interaction free
and yields energy densities within the definition of the electrostatic
potential of the exchange-correlation hole that are locally accurate and have
the correct asymptotic behavior. The model is able to capture strong
correlation effects that arise from chemical bond dissociation, without relying
on error cancellation. These features, which are usually missed by standard DFT
functionals, are captured by the highly nonlocal structure, which goes beyond
the Jacob's ladder framework for functional construction, by using integrals of
the density as the key ingredient. Possible routes for obtaining the full
exchange-correlation functional by recovering the missing kinetic component of
the correlation energy are also implemented and discussed.
