Adiabatic connection at negative coupling strengths

Abstract

The adiabatic connection of density functional theory (DFT) for electronic systems is generalized here to negative values of the coupling strength $\ensuremath{\alpha}$ (with attractive electrons). In the extreme limit $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ 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 $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ and the opposite limit of infinitely strong repulsion ($\ensuremath{\alpha}\ensuremath{\rightarrow}+\ensuremath{\infty}$) yields a rather accurate estimate of the second-order correlation energy ${E}_{\mathrm{c}}^{\mathrm{GL}2}[\ensuremath{\rho}]$ for several different densities $\ensuremath{\rho}$, without using virtual orbitals. The same procedure is also applied to the Be isoelectronic series, analyzing the effects of near degeneracy.