Tests of a ladder of density functionals for bulk solids and surfaces

The local spin-density approximation (LSDA) and the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) are fully non-empirical realizations of the first two rungs of ``Jacob's ladder'' of exchange-correlation density functionals. The recently proposed non-empirical meta-GGA of Tao, Perdew, Staroverov, and Scuseria (TPSS), featuring the kinetic energy density as an additional local ingredient, completes the third rung. A hierarchy of these functionals, complemented by the meta-GGA of Perdew, Kurth, Zupan, and Blaha (PKZB), is tested in self-consistent Gaussian-type orbital calculations of equilibrium lattice constants, bulk moduli, and cohesive energies for 18 solids, and in studies of the jellium surface energy. The ascent of the ladder generally results in better performance, although most of the improvement for bulk solids occurs in the transition from LSDA to PBE. For the jellium surface energy, PBE is less accurate than LSDA, but PKZB and TPSS are more accurate. We support the idea that most of the error of these functionals for bulk solids arises in the description of core--valence interaction, by demonstrating that it can be removed through adjustment of the corresponding term in the equation of state. Overall, TPSS gives the best description of solids and surfaces, as it was found to do for molecules in earlier work.