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We revisit the two derivations of the PBE correlation functional: Thereal-space cut-off of the exchange-correlation hole and the imposition of exactconditions. These differ in the Lieb-Simon limit, exemplified by the scaling ofneutral atoms to large $N$ and $Z$, in which LDA becomes relatively exact. Weuse the leading correction to this limit for neutral atoms to design anasymptotically corrected correlation GGA as a compromise between these twoconstructions which becomes relatively more accurate for atoms with increasingatomic number. When paired with a similar correction for exchange, this acGGAsatisfies more exact conditions than PBE. Combined with the known$r_s$-dependence of the gradient expansion for correlation, this correctionaccurately reproduces correlation energies of closed shell atoms down to Be. Wetest this acGGA for atoms and molecules, finding substantial improvements overPBE, but also showing that optimal global hybrids of acGGA do not improve uponPBE0, and are similar to meta-GGA values. We discuss the relevance of theseresults to Jacob's ladder of non-empirical density functional construction.

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