  It has recently been observed [Phys. Rev. Lett. 113, 113002 (2014)] that the
ground-state energy may be obtained directly as a simple sum of augmented
Kohn-Sham orbital energies, where it was ascertained that the corresponding
one-body shifted Kohn-Sham effective potential has appealing features. With
this in mind, eigenvalue and virial constraints are deduced for approximating
this potential.
