The exchange energy for pairs of helium and neon atoms was calculated with recently proposed exchange-energy functionals for Hartree-Fock electron densities, and compared with the exact (Hartree-Fock) exchange energy. While all of the functionals calculate the total exchange energies to within 1%, most of the functionals give very poor results for DELTAE(exc), the exchange-energy contribution to the interaction energy. At the positions of the energy minima for the atom pairs, most functionals give DELTAE(exc) in error by over 100%. The reason for the difference in accuracy between the total exchange energy and DELTAE(exc) is that the total exchange energy is dominated by the high density and small gradient regions near the nuclei, while DELTAE(exc) is dominated by the low density and large gradient regions between the atoms. We propose an exchange functional which gives good results for both the total exchange energy and DELTAE(exc). We also show that the Lieb-Oxford bound can only be applied globally, and not locally as some investigators have suggested.
