A recent modification to the traditional Kohn-Sham method (Levy, M.; Zahariev, F. Phys. Rev. Lett 2014, 113, 113002; Levy, M.; Zahariev, F. Mol. Phys. 2016, 114, 1162-1164), which gives the ground state energy as a direct sum of the occupied orbital energies, is discussed and its properties are numerically illustrated on representative atoms and ions. It is observed that current approximate density functionals tend to give surprisingly small errors for the highest occupied orbital energies that are obtained with the augmented potential. The appropriately shifted Kohn-Sham potential is the basic object within this direct-energy Kohn Sham method and needs to be approximated. To facilitate approximations, several constraints to the augmented Kohn Sham potential are presented.