Two-Dimensional Scan of the Performance of Generalized Gradient Approximations with Perdew-Burke-Ernzerhof-Like Enhancement Factor.

We assess the performance of the whole class of functionals defined by the Perdew-Burke-Ernzerhof (PBE) exchange-correlation enhancement factor, by performing a two-dimensional scan of the μ and κ parameters (keeping β fixed by the recovery of the local density approximation linear response). We consider molecular (atomization energies, bond lengths, and vibrational frequencies), intermolecular (hydrogen-bond and dipole interactions), and solid-state (lattice constant and cohesive energies) properties. We find, for the energetical properties, a whole family of functionals (with μ and κ interrelated) giving very similar results and the best accuracy. Overall, we find that the original PBE and the recently proposed APBE functional [Phys. Rev. Lett.2011, 106, 186406], based on the asymptotic expansion of the semiclassical neutral atom, give the highest global accuracy, with a definite superior performance of the latter for all of the molecular properties.