Hybrid density functionals are very successful in describing a wide range of molecular properties accurately. In large molecules and solids, however, calculating the exact ͑Hartree-Fock͒ exchange is computationally expensive, especially for systems with metallic characteristics. In the present work, we develop a new hybrid density functional based on a screened Coulomb potential for the exchange interaction which circumvents this bottleneck. The results obtained for structural and thermodynamic properties of molecules are comparable in quality to the most widely used hybrid functionals. In addition, we present results of periodic boundary condition calculations for both semiconducting and metallic single wall carbon nanotubes. Using a screened Coulomb potential for Hartree-Fock exchange enables fast and accurate hybrid calculations, even of usually difficult metallic systems. The high accuracy of the new screened Coulomb potential hybrid, combined with its computational advantages, makes it widely applicable to large molecules and periodic systems.

A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements

The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The exchange and correlation terms respect two paradigms: one-or twoelectron densities and slowly-varying densities, and so describe both molecules and solids with high accuracy, as shown by extensive numerical tests. This functional completes the third rung of "Jacob's ladder" of approximations, above the local spin density and GGA rungs.PACS numbers: 71.15. Mb,31.15.Ew,71.45.Gm Kohn-Sham spin-density functional theory [1] reduces the many-electron ground state problem to a selfconsistent noninteracting-electron form that is exact in principle for the density and energy, requiring in practice an approximation for the exchange-correlation (xc) energy functional E xc [n ↑ , n ↓ ]. No other method achieves comparable accuracy at the same cost. The exact functional is universal; its approximations should be usefully accurate for both molecules and solids, and thus for intermediate cases (clusters, biological molecules) or combinations (chemisorption and catalysis on a solid surface). The paradigm densities of quantum chemistry (hydrogen atom and electron pair bond) and condensed matter physics (uniform electron gas) thus deserve special respect. Semi-empirical functionals can fail outside their fitting sets [2,3]; those fitted only to molecules can be unsuitable for solids. Alternatively, functionals can be constructed to satisfy exact constraints on E xc [n ↑ , n ↓ ]. Non-empirical functionals are not fitted to actual or computer experiments for real systems, but are validated by such data.The first three rungs of "Jacob's ladder" [4] of approximations can be summarized by the formulawhere n(r) = n ↑ (r) + n ↓ (r) is the total density, andis the kinetic energy density for the occupied Kohn-Sham orbitals ψ iσ (r), which are nonlocal functionals of the density n σ (r). (We use atomic units where = m = e 2 = 1.) The first rung, found by dropping the ∇n σ and τ σ dependences in Eq. (1), is the local spin density (LSD) approximation [1,5], exact for the uniform electron gas and often usefully accurate for solids. The second rung, found by dropping only the τ σ dependence in Eq. (1), is the generalized gradient approximation (GGA) [6,7,8] (useful for molecules as well). The Perdew-Burke-Ernzerhof (PBE) GGA has two non-empirical derivations based on exact properties of the xc hole [7] and energy [8].The third rung of the ladder, the meta-GGA, makes use of all the ingredients shown in Eq. (1). The kinetic energy density τ σ (r) recognizes [9] when n σ (r) has oneelectron character by the condition τ σ (r) = τ W σ (r), where τ W σ (r) = |∇n σ | 2 /8n σ is the von Weizsäcker kinetic energy density for real orbitals. Moreover, Eq. (1) can be correct to fourth-order in ∇ for a slowly-varying density [11]. However, prio...

Successful modern generalized gradient approximations (GGA's) are biased toward atomic energies. Restoration of the first-principles gradient expansion for exchange over a wide range of density gradients eliminates this bias. We introduce PBEsol, a revised Perdew-Burke-Ernzerhof GGA that improves equilibrium properties of densely-packed solids and their surfaces.

This work reexamines the effect of the exchange screening parameter omega on the performance of the Heyd-Scuseria-Ernzerhof (HSE) screened hybrid functional. We show that variation of the screening parameter influences solid band gaps the most. Other properties such as molecular thermochemistry or lattice constants of solids change little with omega. We recommend a new version of HSE with the screening parameter omega=0.11 bohr(-1) for further use. Compared to the original implementation, the new parametrization yields better thermochemical results and preserves the good accuracy for band gaps and lattice constants in solids.

Fullerene single-wall nanotubes (SWNTs) were produced in yields of more than 70 percent by condensation of a laser-vaporized carbon-nickel-cobalt mixture at 1200degreesC. X-ray diffraction and electron microscopy showed that these SWNTs are nearly uniform in diameter and that they self-organize into "ropes," which consist of 100 to 500 SWNTs in a two-dimensional triangular lattice with a lattice constant of 17 angstroms. The x-ray form factor is consistent with that of uniformly charged cylinders 13.8 +/- 0.2 angstroms in diameter. The ropes were metallic, with a single-rope resistivity of <10(-4) ohm-centimeters at 300 kelvin. The uniformity of SWNT diameter is attributed to the efficient annealing of an initial fullerene tubelet kept open by a few metal atoms; the optimum diameter is determined by competition between the strain energy of curvature of the graphene sheet and the dangling-bond energy of the open edge, where growth occurs. These factors strongly favor the metallic (10,10) tube with C5v symmetry and an open edge stabilized by triple bonds.

Time-dependent density-functional ͑TDDFT͒ methods are applied within the adiabatic approximation to a series of molecules including C 70 . Our implementation provides an efficient approach for treating frequency-dependent response properties and electronic excitation spectra of large molecules. We also present a new algorithm for the diagonalization of large non-Hermitian matrices which is needed for hybrid functionals and is also faster than the widely used Davidson algorithm when employed for the Hermitian case appearing in excited energy calculations. Results for a few selected molecules using local, gradient-corrected, and hybrid functionals are discussed. We find that for molecules with low lying excited states TDDFT constitutes a considerable improvement over Hartree-Fock based methods ͑like the random phase approximation͒ which require comparable computational effort.

In order to discriminate between approximations to the exchange-correlation energy E XC ͓ ↑ , ↓ ͔, we employ the criterion of whether the functional is fitted to a certain experimental data set or if it is constructed to satisfy physical constraints. We present extensive test calculations for atoms and molecules, with the nonempirical local spin-density ͑LSD͒ and the Perdew-Burke-Ernzerhof ͑PBE͒ functional and compare our results with results obtained with more empirical functionals. For the atomization energies of the G2 set, we find that the PBE functional shows systematic errors larger than those of commonly used empirical functionals. The PBE ionization potentials, electron affinities, and bond lengths are of accuracy similar to those obtained from empirical functionals. Furthermore, a recently proposed hybrid scheme using exact exchange together with PBE exchange and correlation is investigated. For all properties studied here, the PBE hybrid gives an accuracy comparable to the frequently used empirical B3LYP hybrid scheme. Physical principles underlying the PBE and PBE hybrid scheme are examined and the range of their validity is discussed.