Ground-State Energy as a Simple Sum of Orbital Energies in Kohn-Sham Theory: A Shift in Perspective through a Shift in Potential

It is observed that the exact interacting ground-state electronic energy of interest may be obtained directly, in principle, as a simple sum of orbital energies when a universal density-dependent term is added to $w\left(\left[ \rho \right];\mathbf{r} \right)$, the familiar Hartree plus exchange-correlation component in the Kohn-Sham effective potential. The resultant shifted potential, $\bar{w}\left(\left[ \rho \right];\mathbf{r} \right)$, actually changes less on average than $w\left(\left[ \rho \right];\mathbf{r} \right)$ when the density changes, including the fact that $\bar{w}\left(\left[ \rho \right];\mathbf{r} \right)$ does not undergo a discontinuity when the number of electrons increases through an integer. Thus the approximation of $\bar{w}\left(\left[ \rho \right];\mathbf{r} \right)$ represents an alternative direct approach for the approximation of the ground-state energy and density.