Generalized ¥ gradient approximations (GGA's) for the exchange-correlation energy improve upon the ¦ local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation § of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) © GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.

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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

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Density functional approximations for the exchange-correlation energy E xc DFA of an electronic system are often improved by admixing some exact exchange E x : E xc ϷE xc DFA ϩ͑1/n͒͑E x ϪE x DFA ͒. This procedure is justified when the error in E xc DFA arises from the ϭ0 or exchange end of the coupling-constant integral ͐ 0 1 d E xc, DFA. We argue that the optimum integer n is approximately the lowest order of Görling-Levy perturbation theory which provides a realistic description of the coupling-constant dependence E xc, in the range 0рр1, whence nϷ4 for atomization energies of typical molecules. We also propose a continuous generalization of n as an index of correlation strength, and a possible mixing of second-order perturbation theory with the generalized gradient approximation.

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.

We present a novel approach for constructing hybrid functionals by using a local mix of regular density functional theory (DFT) exchange and exact Hartree–Fock (HF) exchange. This local hybrid approach is computationally feasible for a wide range of molecules. In this work, the local mix of HF and DFT exchange is driven by the ratio of τW=|∇ρ|2/8ρ, the Weizsäcker kinetic energy density, with τ, the exact kinetic energy density. This particular choice of local mix yields 100% of exact exchange in one-electron regions. Dissociation energy curves, binding energies, and equilibrium geometries for two-center, three-electron symmetric radical cations can be modeled accurately using this scheme. We also report encouraging results for reaction energy barriers, and somewhat disappointing atomization energies for the small G2 set.