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 $w([\rho ];\mathit{r})$, the familiar Hartree plus exchange-correlation component in the Kohn-Sham effective potential. The resultant shifted potential, $\overline{w}([\rho ];\mathit{r})$, actually changes less on average than $w([\rho ];\mathit{r})$ when the density changes, including the fact that $\overline{w}([\rho ];\mathit{r})$ does not undergo a discontinuity when the number of electrons increases through an integer. Thus, the approximation of $\overline{w}([\rho ];\mathit{r})$ represents an alternative direct approach for the approximation of the ground-state energy and density.