A family of model Kohn-Sham potentials for exact exchange

The exact-exchange Kohn-Sham potential is partitioned into Slater's averaged exchange charge potential and a correction. A family of nonempirical approximations to the correction term is proposed based on the known second-order gradient expansion of the exact potential. By taking the uniform electron gas limit of the correction term and using alternative definitions of the average relative electron momentum that are motivated by analysis of the Negele-Vautherin density matrix expansion, we recover the "modified Slater potential" of Harbola and Sen and the much more accurate Becke-Johnson approximation [J. Chem. Phys. 124, 221101 (2006)]. Inclusion of an explicit gradient-dependent term in the Becke-Johnson model yields an even more realistic approximation, as demonstrated by comparing the shapes of these potentials and integrated exchange energies for a series of atoms.