The adiabatic connection of density functional theory (DFT) for electronic systems is generalized here to negative values of the coupling strength α (with attractive electrons). In the extreme limit α→-∞ 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 α→-∞ and the opposite limit of infinitely strong repulsion (α→+∞) yields a rather accurate estimate of the second-order correlation energy EcGL2[ρ] for several different densities ρ, without using virtual orbitals. The same procedure is also applied to the Be isoelectronic series, analyzing the effects of near degeneracy. © 2010 The American Physical Society.