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

TL;DR

This paper investigates the augmented potential in density functional theory, focusing on its behavior at different interaction strengths and correlation regimes, and explores related energy densities and scaling properties.

Contribution

It provides a detailed analysis of the augmented potential's features in the weak and strong interaction limits, including energy densities and their relation to local interpolations.

Findings

Augmented potential shift relates to total energy and orbital energies.

Energy density analysis across correlation regimes.

Insights into classical jellium and uniform gas models.

Abstract

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.