Energy surface, chemical potentials, Kohn-Sham energies in spin-polarized density functional theory

On the basis of the zero-temperature grand canonical ensemble generalization of the energy E[N,N_s,v,B] for fractional particle N and spin N_s numbers, the energy surface over the (N,N_s) plane is displayed and analyzed in the case of homogeneous external magnetic fields B(r). The (negative of the) left/right-side derivatives of the energy with respect to N, N_up, and N_down give the fixed-N_s, spin-up, and spin-down ionization potentials/electron affinities, respectively, while the derivative of E[N,N_s,v,B] with respect to N_s gives the (signed) half excitation energy to a state with N_s increased (or decreased) by 2. The highest occupied and lowest unoccupied Kohn-Sham spin-orbital energies are identified as the corresponding spin-up and spin-down ionization potentials and electron affinities. The excitation energies to the states with N_s+2, N_s-2, can be obtained as the differences between the lowest unoccupied and the opposite-spin highest occupied spin-orbital energies, if the (N,N_s) representation of the Kohn-Sham spin-potentials is used. The cases where the convexity condition on the energy does not hold are also discussed. Finally, the discontinuities of the energy derivatives and the Kohn-Sham potential are analyzed and related.Comment: 35 pages, to appear in JCP; text made more precise, Aufbau discussed, T_s derivative discontinuities given too, two Appendices adde

Nonempirical Density Functionals Investigated for Jellium: Spin-Polarized Surfaces, Spherical Clusters, and Bulk Linear Response

Earlier tests show that the Tao-Perdew-Staroverov-Scuseria (TPSS) nonempirical meta-generalized gradient approximation (meta-GGA) for the exchange-correlation energy yields more accurate surface energies than the local spin density (LSD) approximation for spin-unpolarized jellium. In this study, work functions and surface energies of a jellium metal in the presence of ``internal'' and external magnetic fields are calculated with LSD, Perdew-Burke-Ernzerhof (PBE) GGA, and TPSS meta-GGA and its predecessor, the nearly nonempirical Perdew-Kurth-Zupan-Blaha (PKZB) meta-GGA, using self-consistent LSD orbitals and densities. The results show that: (i) For normal bulk densities, the surface correlation energy is the same in TPSS as in PBE, as it should be since TPSS strives to represent a self-correlation correction to PBE; (ii) Normal surface density profiles can be scaled uniformly to the low-density or strong-interaction limit, and TPSS provides an estimate for that limit that is consistent with (but probably more accurate than) other estimates; (iii) For both normal and low densities, TPSS provides the same description of surface magnetism as PBE, suggesting that these approximations may be generally equivalent for magnetism. The energies of jellium spheres with up to 106 electrons are calculated using density functionals and compared to those obtained with Diffusion Quantum Monte Carlo data, including our estimate for the fixed-node correction. Finally we calculate the linear response of bulk jellium using these density functionals, and find that not only LSD but also PBE GGA and TPSS meta-GGA yield a linear-response in good agreement with that of the Quantum Monte Carlo method, for wavevectors of the perturbing external potential up to twice the Fermi wavevector.Comment: 14 pages, 9 figure

Localization and delocalization errors in density functional theory and implications for band-gap prediction

The band-gap problem and other systematic failures of approximate functionals are explained from an analysis of total energy for fractional charges. The deviation from the correct intrinsic linear behavior in finite systems leads to delocalization and localization errors in large or bulk systems. Functionals whose energy is convex for fractional charges such as LDA display an incorrect apparent linearity in the bulk limit, due to the delocalization error. Concave functionals also have an incorrect apparent linearity in the bulk calculation, due to the localization error and imposed symmetry. This resolves an important paradox and opens the possibility to obtain accurate band-gaps from DFT.Comment: 4 pages 4 figure

Empirical analysis of the Lieb-Oxford bound in ions and molecules

Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, inparticular, are important for the construction of improved density functionals. Here we investigate one such universal property -- the Lieb-Oxford lower bound -- for ionic and molecular systems. In recent work [J. Chem. Phys. 127, 054106 (2007)], we observed that for atoms and electron liquids this bound may be substantially tightened. Calculations for a few ions and molecules suggested the same tendency, but were not conclusive due to the small number of systems considered. Here we extend that analysis to many different families of ions and molecules, and find that for these, too, the bound can be empirically tightened by a similar margin as for atoms and electron liquids. Tightening the Lieb-Oxford bound will have consequences for the performance of various approximate exchange-correlation functionals.Comment: 8 pages, 3 color figure

Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids

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 {\it two} paradigms: one- or two-electron 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.Comment: 4 pages, 1 figure, 1 table. updated with minor and yet necessary corrections. New references are adde

Density-Functional-Based Determination of the CH3-CH4 Hydrogen Exchange Reaction Barrier

Due to the overbinding that is inherent in existing {\em local} approximations to the density-functional formalism, certain reaction energies have not been accessible. Since the generalized gradient approximation significantly decreases the overbinding, prospects for density-functional-based reaction dynamics are promising. Results on the generalized-gradient based determination of the CH3-CH4 hydrogen exchange reaction are presented. Including all Born-Oppenheimer effects an energy barrier of 9.5 kcal/Mole is found which is a very significant improvement over the local-density approximation.Comment: 5 twocolumn pages (needs twocolumn.sty), revtex, 3 figures, To appear in Chem.Phys.Let

Vanadium pentoxide (V2O5): a van der Waals density functional study

The past few years has brought renewed focus on the physics behind the class of materials characterized by long-range interactions and wide regions of low electron density, sparse matter. There is now much work on developing the appropriate algorithms and codes able to correctly describe this class of materials within a parameter-free quantum physical description. In particular, van der Waals (vdW) forces play a major role in building up material cohesion in sparse matter. This work presents an application to the vanadium pentoxide (V2O5) bulk structure of two versions of the vdW-DF method, a first-principles procedure for the inclusion of vdW interactions in the context of density functional theory (DFT). In addition to showing improvement compared to traditional semilocal calculations of DFT, we discuss the choice of various exchange functionals and point out issues that may arise when treating systems with large amounts of vacuum.Comment: 5 pages, 4 figures, 1 tabl