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

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.

15 pages, 1 table

Cited by in corpus (19)

• Guest Editorial: Special Topic on Data-enabled Theoretical Chemistry
• Neural-network Kohn-Sham exchange-correlation potential and its out-of-training transferability
• Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles
• Ground and excited energy levels can be extracted exactly from a single ensemble density-functional theory calculation
• Ensemble Density Functional Theory of Neutral and Charged Excitations
• A weight-dependent local correlation density-functional approximation for ensembles
• N-centered ensemble density-functional theory for open systems
• Augmented potential, energy densities, and virial relations in the weak- and strong-interaction limits of DFT
• Neutral electronic excitations and derivative discontinuities: An extended $N$-centered ensemble density functional theory perspective
• Exact "exact exchange" potential of two- and one-dimensional electron gases beyond the asymptotic limit
• Exact exchange-correlation potentials for calculating the fundamental gap with a fixed number of electrons
• Extended $N$-centered ensemble density functional theory of double electronic excitations
• On Augmented Kohn-Sham Potential for Energy as a Simple Sum of Orbital Energies
• Density functional theory beyond the Born-Oppenheimer approximation: Exact mapping onto an electronically non-interacting Kohn-Sham molecule
• Quasi-low-dimensional electron gas with one populated band as a testing ground for time-dependent density-functional theory
• Fundamental gaps of quantum dots on the cheap
• Kinetic correlation functionals from the entropic regularisation of the strictly-correlated electrons problem
• Exact exchange-correlation potential of effectively interacting Kohn-Sham systems
• Ensemble density functional theory of excited states: Exact N-centered formalism and practical opportunities