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Anions and radicals are important for many applications includingenvironmental chemistry, semiconductors, and charge transfer, but are poorlydescribed by the available approximate energy density functionals. Here we testan approximate exchange-correlation functional based on the exactstrong-coupling limit of the Hohenberg-Kohn functional on the prototypical caseof the He isoelectronic series with varying nuclear charge $Z<2$, whichincludes weakly bound negative ions and a quantum phase transition at acritical value of $Z$, representing a big challenge for density functionaltheory. We use accurate wavefunction calculations to validate our results,comparing energies and Kohn-Sham potentials, thus also providing usefulreference data close to and at the quantum phase transition. We show that ourfunctional is able to bind H$^-$ and to capture in general the physics ofloosely bound anions, with a tendency to strongly overbind that can be provenmathematically. We also include corrections based on the uniform electron gaswhich improve the results.

Energy Density Functionals From the Strong-Coupling Limit Applied to the Anions of the He Isoelectronic Series