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

TL;DR

This paper proposes a shifted potential in Kohn-Sham theory that allows the exact ground-state energy to be obtained as a simple sum of orbital energies, simplifying the calculation of electronic energies.

Contribution

It introduces a universal density-dependent shift in the effective potential, reducing its variability and discontinuities, offering a new perspective for approximating ground-state energies.

Findings

The shifted potential yields the exact ground-state energy as a sum of orbital energies.

The shifted potential varies less with density changes compared to the traditional potential.

It does not exhibit discontinuities when the electron number crosses an integer.

Abstract

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.