  The adiabatic connection of density functional theory (DFT) for electronic
systems is generalized here to negative values of the coupling strength
$\alpha$ (with {\em attractive} electrons). In the extreme limit
$\alpha\to-\infty$ a simple physical solution is presented and its implications
for DFT (as well as its limitations) are discussed. For two-electron systems (a
case in which the present solution can be calculated exactly), we find that an
interpolation between the limit $\alpha\to-\infty$ and the opposite limit of
infinitely strong repulsion ($\alpha\to+\infty$) yields a rather accurate
estimate of the second-order correlation energy $E\cor\glt[\rho]$ for several
different densities $\rho$, without using virtual orbitals. The same procedure
is also applied to the Be isoelectronic series, analyzing the effects of
near-degeneracy.
