  The augmented potential introduced by Levy and Zahariev [Phys. Rev. Lett.
113, 113002 (2014)] is shifted with respect to the standard
exchange-correlation potential of Kohn-Sham density functional theory by a
density-dependent constant that makes the total energy become equal to the sum
of the occupied orbital energies. In this work we analyze several features of
this approach, focusing on the limit of infinite coupling strength, and
studying the shift and the corresponding energy density at different
correlation regimes. We also study other definitions of the energy density in
relation to local interpolations along the adiabatic connection, present and
discuss coordinate scaling properties, and use the shift to analyze the
classical jellium and uniform gas models.
