Strictly correlated electrons in density-functional theory

Electrons at a fixed density approach a strictly correlated limit as their Coulomb interaction is scaled to infinity. We find the exact energy for strictly correlated electrons in spherical two-electron densities, and a useful gradient expansion for general densities. We also propose a model for the coupling-constant dependence, which interpolates between the weak- and strong-interaction limits. This model defines a density functional which predicts accurate ground-state correlation energies for real atoms and the two-dimensional uniform electron gas.