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The Tao-Perdew-Staroverov-Scuseria (TPSS) meta-generalized-gradient-approximation (MGGA) and its revised version, the revTPSS, are implemented self-consistently within the framework of the projector-augmented-wave (PAW) method, using a plane wave basis set. Both TPSS and revTPSS yield accurate atomization energies for the molecules in the AE6 set, better than those of the standard Perdew-Burke-Ernzerhof (PBE) generalized-gradient-approximation. For lattice constants and bulk moduli of 20 diverse solids, revTPSS performs much better than PBE, and on average as well as PBEsol and Armiento-Mattsson (AM05), GGAs designed for solids. The latter two overestimate the atomization energies for molecules to an unacceptable degree. However, the revTPSS presents only a slight improvement over PBEsol for the prediction of cohesive energies for solids, and some deterioration with respect to PBE. We also study the magnetic properties of Fe, for which both TPSS and revTPSS predict the right ground-state solid phase, the ferromagnetic body-centered-cubic (bcc) structure, with an accurate magnetic moment. [ABSTRACT FROM AUTHOR]

Computationally efficient semilocal approximations of density functional theory at the level of the local spin density approximation (LSDA) or generalized gradient approximation (GGA) poorly describe weak interactions. We show improved descriptions for weak bonds (without loss of accuracy for strong ones) from a newly developed semilocal meta-GGA (MGGA), by applying it to molecules, surfaces, and solids. We argue that this improvement comes from using the right MGGA dimensionless ingredient to recognize all types of orbital overlap. [ABSTRACT FROM AUTHOR]

The van der Waals coefficients between quasispherical nanostructures can be modeled accurately and analytically by those of classical solid spheres (for nanoclusters) or spherical shells (for fullerenes) of uniform valence electron density, with the true static dipole polarizability. Here, we derive analytically and confirm numerically from this model the size dependencies of the van der Waals coefficients of all orders, showing, for example, that the asymptotic dependence for C6 is the expected n2 for pairs of nanoclusters An-An, each containing n atoms, but n2.75 for pairs of single-walled fullerenes Cn-Cn. Large fullerenes are argued to have much larger polarizabilities and dispersion coefficients than those predicted by either the standard atom pair-potential model or widely used nonlocal van der Waals correlation energy functionals. [ABSTRACT FROM AUTHOR]

Computationally efficient semilocal approximations of density functional theory at the level of the local spin density approximation (LSDA) or generalized gradient approximation (GGA) poorly describe weak interactions. We show improved descriptions for weak bonds (without loss of accuracy for strong ones) from a newly developed semilocal meta-GGA (MGGA), by applying it to molecules, surfaces, and solids. We argue that this improvement comes from using the right MGGA dimensionless ingredient to recognize all types of orbital overlap.

Semilocal density functionals for the exchange-correlation energy are needed for large electronic systems. The Tao-Perdew-Staroverov-Scuseria (TPSS) meta-generalized gradient approximation (meta-GGA) is semilocal and usefully accurate, but predicts too-long lattice constants. Recent "GGA's for solids" yield good lattice constants but poor atomization energies of molecules. We show that the construction principle for one of them (restoring the density gradient expansion for exchange over a wide range of densities) can be used to construct a "revised TPSS" meta-GGA with accurate lattice constants, surface energies, and atomization energies for ordinary matter.

Popular modern generalized gradient approximations are biased toward the description of free-atom energies. Restoration of the first-principles gradient expansion for exchange over a wide range of density gradients eliminates this bias. We introduce a revised Perdew-Burke-Ernzerhof generalized gradient approximation that improves equilibrium properties of densely packed solids and their surfaces.