View article

The ground-state energy and density of a many-electron system are often calculated by Kohn-Sham density functional theory. We describe a ladder of approximations for the exchange-correlation energy as a functional of the electron density. At the lowest rung of this ladder, the contribution to the energy from a volume element of 3-dimensional space is determined by the local density there. Higher rungs or levels incorporate increasingly complex ingredients constructed from the density or the Kohn-Sham orbitals in or around this volume element. We identify which additional exact conditions can be satisfied at each level, and discuss the extent to which the functionals at each level may be constructed without empirical input. We also discuss the research that remains to be done at the exact-exchange level, and present our “dreams of a final theory.” “Jacob left Beer-sheba and went toward Haran. He came to a …