Adiabatic connection at negative coupling strengths

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 $\alpha \to -\mathrm{\infty }$ 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 $\alpha \to -\mathrm{\infty }$ and the opposite limit of infinitely strong repulsion ($\alpha \to +\mathrm{\infty }$) yields a rather accurate estimate of the second-order correlation energy $E\text{cor}\text{glt}[\rho ]$ 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.