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 twoelectron 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 EGL2 c [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.