Pair interactions of rare-gas atoms as a test of exchange-energy-density functionals in regions of large density gradients

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 E₄ₗ₂, the exchange-energy contribution to the interaction energy. At the positions of the energy minima for the atom pairs, most functionals give E₄ₗ₂ in error by over 100%. The reason for the difference in accuracy between the total exchange energy and E₄ₗ₂ is that the total exchange energy is dominated by the high density and small gradient regions near the nuclei, while E₄ₗ₂ 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 E₄ₗ₂. We also show that the Lieb-Oxford bound can only be applied globally, and not locally as some investigators have suggested.