Augmented potential, energy densities, and virial relations in the weak- and strong-interaction limits of DFT

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.