Electrons can have a given smooth density distribution $\rho \mathrm{}\left(r\right),$ even if their Coulomb interaction is scaled to infinity. This strong-interaction limit of density-functional theory provides essential information on the correlation energy of real electron systems. The simple concept of strictly correlated electrons (SCE) is analyzed here as a model for that limit. SCE is solved exactly for any one-dimensional (1D) N-electron density and, in particular, for any 3D spherical two-electron system, such as the helium atom. Both the SCE interaction energy and the SCE external potential, which are obtained here as density functionals, obey all the relations known for the corresponding quantities in the unknown true strong-interaction limit. At large but finite interaction, the electrons are still strongly correlated, performing zero-point oscillations about the SCE limit.

• Received 25 March 1999

DOI:https://doi.org/10.1103/PhysRevA.60.4387