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 E_x[n]=A_x∫d³rn^4/3F(s), where s=|∇n|/2k_Fn, k_F=(3π²n)^1/3, and F(s)=(1+1.296s²+14s⁴+0.2s⁶)^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.