Non-empirical improvement of PBE and its hybrid PBE0 for general description of molecular properties.

Imposition of the constraint that, for the hydrogen atom, the exchange energy cancels the Coulomb repulsion energy yields a non-empirical re-parameterization of the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) exchange-correlation energy functional, and of the related PBE hybrid (PBE0). The re-parameterization, which leads to an increase of the gradient contribution to the exchange energy with respect to the original PBE functional, is tested through the calculation of heats of formation, ionization potentials, electron affinities, proton affinities, binding energies of weakly interacting systems, barrier heights for hydrogen and non-hydrogen transfer reactions, bond distances, and harmonic frequencies, for some well known test sets designed to validate energy functionals. The results for the re-parameterized PBE GGA, called PBEmol, give substantial improvement over the original PBE in the prediction of the heats of formation, while retaining the quality of the original PBE functional for description of all the other properties considered. The results for the hybrids indicate that, although the PBE0 functional provides a rather good description of these properties, the predictions of the re-parameterized functional, called PBEmolβ0, are, except in the case of the ionization potentials, modestly better. Also, the results for PBEmolβ0 are comparable to those of B3LYP. In particular, the mean absolute error for the bond distance test set is 17% lower than the corresponding error for B3LYP. The re-parameterization for the pure GGA (PBEmol) differs from that for the hybrid (PBEmolβ0), illustrating that improvement at the GGA level of complexity does not necessarily provide the best GGA for use in a hybrid.