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 mu and kappa parameters (keeping beta 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 mu and kappa 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.