Large-Z atoms in the strong-interaction limit of DFT: Implications for gradient expansions and for the Lieb-Oxford bound

TL;DR

This paper investigates the strong-interaction limit of the exchange-correlation functional in density functional theory for atoms, revealing similarities with the weak-interaction limit and implications for the Lieb-Oxford bound.

Contribution

It provides a detailed numerical analysis of the strong-interaction limit, compares gradient expansions at different interaction strengths, and evaluates the accuracy of models and bounds in DFT.

Findings

Gradient expansions at strong and weak interactions are similar in magnitude but opposite in sign.

The point-charge plus continuum model accurately estimates the strong-coupling gradient expansion coefficient.

Standard GGA functionals like PBE underestimate the strong-interaction gradient coefficient.

Abstract

We study numerically the strong-interaction limit of the exchange-correlation functional for neutral atoms and for Bohr atoms as the number of electrons increases. Using a compact representation, we analyse the second-order gradient expansion, comparing it with the one for exchange (weak interaction limit). The two gradient expansions, at strong and weak interaction, turn out to be very similar in magnitude, but with opposite signs. We find that the point-charge plus continuum model is surprisingly accurate for the gradient expansion coefficient at strong coupling, while generalized gradient approximations such as PBE and PBEsol severely underestimate it. We then use our results to analyse the Lieb-Oxford bound from the point of view of slowly-varying densities, clarifying some aspects on the bound at fixed number of electrons.