Fitting a round peg into a round hole: asympotically correcting the generalized gradient approximation for correlation

TL;DR

This paper introduces an asymptotically corrected GGA for correlation energy that improves accuracy for atoms and molecules by incorporating the correct large-$N$ and $Z$ scaling behavior, surpassing PBE in many cases.

Contribution

It develops a new correlation functional that asymptotically corrects the PBE GGA, satisfying more exact conditions and improving accuracy for large atoms.

Findings

Improves correlation energy calculations for atoms and molecules.

Outperforms PBE in accuracy for closed-shell atoms.

Shows that hybrid functionals of acGGA do not surpass PBE0.

Abstract

We revisit the two derivations of the PBE correlation functional: The real-space cut-off of the exchange-correlation hole and the imposition of exact conditions. These differ in the Lieb-Simon limit, exemplified by the scaling of neutral atoms to large $N$ and $Z$, in which LDA becomes relatively exact. We use the leading correction to this limit for neutral atoms to design an asymptotically corrected correlation GGA as a compromise between these two constructions which becomes relatively more accurate for atoms with increasing atomic number. When paired with a similar correction for exchange, this acGGA satisfies more exact conditions than PBE. Combined with the known $r_s$-dependence of the gradient expansion for correlation, this correction accurately reproduces correlation energies of closed shell atoms down to Be. We test this acGGA for atoms and molecules, finding substantial improvements over PBE, but also showing that optimal global hybrids of acGGA do not improve upon PBE0, and are similar to meta-GGA values. We discuss the relevance of these results to Jacob's ladder of non-empirical density functional construction.