In direct energy Kohn–Sham (DEKS) theory, the density functional theory electronic energy equals the sum of occupied orbital energies, obtained from Kohn–Sham-like orbital equations involving a shifted Hartree exchange–correlation potential, which must be approximated. In the present study, the Fermi–Amaldi term is incorporated into approximate DEKS calculations, introducing the required −1/r contribution to the exchange–correlation component of the shifted potential in asymptotic regions. It also provides a mechanism for eliminating one-electron self-interaction error, and it introduces a nonzero exchange–correlation component of the shift in the potential that is of appropriate magnitude. The resulting electronic energies are very sensitive to the methodologies considered, whereas the highest occupied molecular orbital energies and exchange–correlation potentials are much less sensitive and are similar to those obtained from DEKS calculations using a conventional exchange–correlation functional.