Energy density functionals from the strong-coupling limit applied to the anions of the He isoelectronic series

Anions and radicals are important for many applications including environmental chemistry, semi- conductors, and charge transfer, but are poorly described by the available approximate energy density functionals. Here we test an approximate exchange-correlation functional based on the exact strong- coupling limit of the Hohenberg-Kohn functional on the prototypical case of the He isoelectronic series with varying nuclear charge Z < 2, which includes weakly bound negative ions and a quantum phase transition at a critical value of Z, representing a big challenge for density functional theory. We use accurate wavefunction calculations to validate our results, comparing energies and Kohn-Sham potentials, thus also providing useful reference data close to and at the quantum phase transition. We show that our functional is able to bind H- and to capture in general the physics of loosely bound anions, with a tendency to strongly overbind that can be proven mathematically. We also include corrections based on the uniform electron gas which improve the results.