Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation

The electronic exchange energy as a functional of the density may be approximated as Eₗn=Aₗd^3rn^4{3}F (s), where s=||2{k₅n}, k₅= (3{^2n) }^1{3}, and F (s) = (1+1. 296{s^2+14s^4+0. 2s^6) }^1{15}. The basis for this approximation is the gradient expansion of the exchange hole, with real-space cutoffs chosen to guarantee that the hole is negative everywhere and represents a deficit of one electron. Unlike the previously publsihed version of it, this functional is simple enough to be applied routinely in self-consistent calculations for atoms, molecules, and solids. Calculated exchange energies for atoms fall within 1% of Hartree-Fock values. Significant improvements over other simple functionals are also found in the exchange contributions to the valence-shell removal energy of an atom and to the surface energy of jellium within the infinite barrier model.