  The combination of density-functional theory with other approaches to the
many-electron problem through the separation of the electron-electron
interaction into a short-range and a long-range contribution (range separation)
is a successful strategy, which is raising more and more interest in recent
years. We focus here on a range-separated method in which only the short-range
correlation energy needs to be approximated, and we model it within the
"extended Overhauser approach". We consider the paradigmatic case of the H$_2$
molecule along the dissociation curve, finding encouraging results. By means of
very accurate variational wavefunctions, we also study how the effective
electron-electron interaction appearing in the Overhauser model should be in
order to yield the exact correlation energy for standard Kohn-Sham density
functional theory.
