Density functional for the ground-state energy of artificial two-electron atoms with harmonic confinement

An exact analytical expression for the ground-state energy density functional for artificial two-electron atoms, in harmonic confinement, and with an inverse square law interaction u(r(12)) = lambda/r(12)(2) between the electrons, is derived. This is the first time when the ground-state energy is exactly exhibited as a functional of the density in the case of interacting fermions. To achieve this, a generalization for the given interparticle interaction of the 'noninteracting' virial theorem is also shown to be valid.