Exchange-energy density functional: Reparametrization of Becke’s formula and derivation of second-order gradient correction

Two studies are carried out on the density functional for the Hartree-Fock exchange energy. (1) Becke's semiempirical formula for the exchange energy [Phys. Rev. A 38, 3098 (1988)] is reparametrized and applied to selected molecules. The results are excellent. (2) A new theoretical derivation is given of the coefficient {β} in the standard second-order gradient expansion for the exchange energy. The {β} value obtained is 0.001 429.