A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basisfunction products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant ('RI-LVL'), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree-Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2-1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron manybody perturbation theory with significantly reduced computational and memory cost.

We test the accuracy of the revised Perdew-Burke-Ernzerhof exchange-correlation density functional (PBEsol) for metallic bulk and surface systems. It is shown that, on average, PBEsol yields equilibrium volumes and bulk moduli in close agreement with the former generalized gradient approximation (PBE) and two gradient level functionals derived from model system approach (LAG and AM05). On the other hand, for close-packed metal surfaces, PBEsol has the same performance as AM05, giving significantly larger surface energies than PBE and LAG.