  Anions and radicals are important for many applications including
environmental chemistry, semiconductors, 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.
