Fitting a Round Peg into a Round Hole -- Constructing an Asymptotically Correct Generalized Gradient Approximation.

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 infinite N and Z. In this limit, LDA becomes relatively exact and the correction to it provides a norm for the systematic construction of GGA's. We use the leading correction for neutral atoms to design an asymptotically corrected correlation GGA as a compromise between the two constructions of PBE, one which becomes relatively more accurate for atoms with increasing atomic number. When paired with an asymptotically correct model for exchange, this acGGA satisfies more exact conditions than PBE. Combined with the known density-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 show 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.