Publications

Erratum: Density-functional versus wave-function methods: Toward a benchmark for the jellium surface energy [Phys. Rev. B<b>61</b>, 2595 (2000)]

In Table II, the meta-GGA energies for the 20-electron jellium spheres should have been Ϫ1.782,Ϫ1.901, and Ϫ1.804 eV for r s ϭ3.25, 4.00, and 5.62, respectively.These corrected energies are very close to the GGA values.The incorrect published values arose from a factor-of-two error in the input kinetic energy density.

Workhorse Semilocal Density Functional for Condensed Matter Physics and Quantum Chemistry

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.

Stabilized jellium: Structureless pseudopotential model for the cohesive and surface properties of metals

The ions in a simple metal act on the valence electrons via a pseudopotential. The long-range part is represented by the electrostatic potential from the positive background of the jellium model. The short-range part can be simulated by a constant (over the interior of the metal), chosen to stabilize the metal at its observed bulk valence-electron density. In this structureless pseudopotential model, the bulk properties of a metal depend only upon valence z and bulk density parameter ${\mathit{r}}_{\mathit{s}}$, while the surface properties depend upon ${\mathit{r}}_{\mathit{s}}$ alone (an experimental trend heretofore not understood). These properties are calculated in closed analytic form, and the anomalies of the jellium model (negative surface energy for ${\mathit{r}}_{\mathit{s}}$\ensuremath{\approxeq}2; negative bulk modulus for ${\mathit{r}}_{\mathit{s}}$\ensuremath{\approxeq}6) are found to be rectified. The new model, perhaps the simplest one viable for all ${\mathit{r}}_{\mathit{s}}$, may also be used to study interfaces, metallic clusters, vacancies, electromagnetic response, etc. A variant of the model, which simulates the effects of atomic corrugation, predicts the crystal face dependence of surface properties. This dependence is strong for the electron-density profile, but not for the surface energy, work function, and distance from the centroid of excess charge to the first lattice plane. Results are presented for metallic hydrogen as well as for Al, Pb, Zn, Mg, Ca, Li, Sr, Ba, Na, K, Rb, and Cs.

Generalized gradient approximation for the fermion kinetic energy as a functional of the density

The new observation of C18O (J=1-0) molecular emission in W31

Efficient Visual Saliency Detection via Multi-Cues

Saliency detection has become a valuable tool in computer vision processing, which has been attracting a good deal of attention. Although a lot of research has been done, it cannot obtain ideal performance. In most saliency detection framework, the single difference cue is often used to detect saliency map, but their results were far from satisfaction for low discriminative power of single cue. In addition to the composition of the detection cues during the whole process, the used cues which could only describe the low level information could also lead to poor detection. In order to solve this problem effectively, the paper proposed a novel saliency detection framework by fusing multi-cue difference with high level difference. Basically, the comprehensive information is coupled into multi-cues vectors to remove the non-salient regions and enhance the brightness of the salient area. Specifically, we utilize the fusion of multi-cues and high-level information to improve the ability of understanding images. To further improve the performance of the proposed framework in AUC, we adopt multiple assignments strategy while enhancing the precision of saliency detection. Extensive experiments indicate that the newly constructed multi-cues with high level information could effectively suppress the influence of background information on salient regions. In order to verify the effectiveness of the new algorithm, our experiment uses several standard benchmark datasets (MSRA, ASD, SED1, SED2, and SOD) to test the performance of the algorithm. The experimental results demonstrate that this method has achieved good saliency detection result and good AUC performance in the test. More importantly, the experimental results also show that the proposed method is well complementary to many existing algorithms.

Insensitivity of the error of the minimally empirical hybrid functional revTPSSh to its parameters

We investigate the parameter dependence of the error of the hybrid of the revised Tao-Perdew-Staroverov-Scuseria (revTPSSh) density functional for the exchange-correlation energy within popular molecular test sets. In particular, we allow for satisfaction of a possibly tighter Lieb-Oxford lower bound on the exchange-correlation energy. We are able to improve over the original revTPSSh on average, but in total the variation of the performance of revTPSSh seems to be low when its parameters are changed. We recommend to continue using the original revTPSSh variant rather than our fitted versions, because we expect a broader applicability from the original parameter set.

Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals

Semilocal density functional approximations for the exchange-correlation energy can improperly dissociate a neutral molecule XY (Y not =X) to fractionally charged fragments X(+q)...Y(-q) with an energy significantly lower than X0...Y0. For example, NaCl can dissociate to Na(+0.4)...Cl(-0.4). Generally, q is positive when the lowest-unoccupied orbital energy of atom Y0 lies below the highest-occupied orbital energy of atom X0. The first 24 open sp-shell atoms of the Periodic Table can form 276 distinct unlike pairs XY, and in the local spin density approximation 174 of these display fractional-charge dissociation. Finding these lowest-energy solutions with standard quantum chemistry codes, however, requires special care. Self-interaction-corrected (SIC) semilocal approximations are exact for one-electron systems and also reduce the spurious fractional charge q. The original SIC of Perdew and Zunger typically reduces q to 0. A scaled-down SIC with better equilibrium properties sometimes fails to reduce q all the way to 0. The desideratum of "many-electron self-interaction freedom" is introduced as a generalization of the one-electron concept.

Local and Gradient-Corrected Density Functionals

The generalized gradient approximation (GGA) corrects many of the shortcomings of the local spin-density (LSD) approximation. The accuracy of GGA for ground-state properties of molecules is comparable to or better than the accuracy of conventional quantum chemical methods such as second-order Møller-Plesset perturbation theory. By studying various decompositions of the exchange-correlation energy Exc, we show that the real-space decomposition of Exc facilitates the most detailed understanding of how the local spin-density approximation and the Perdew-Wang 1991 GGA work. The real-space decomposition shows that the near universality of the on-top value for the exchange-correlation hole connects the homogeneous electron gas to inhomogeneous systems such as atoms and molecules. The coupling-constant decomposition shows that the exchange-correlation energy at full coupling strength Exc,λ=1 is approximated more accurately by local and semi-local functionals than is the coupling-constant average Exc. We use this insight both to critique popular hybrid functionals and to extract accurate energies from exact electron densities by using functionals for the exchange-correlation energy at full coupling strength. Finally, we show how a reinterpreted spin density functional theory can be applied to systems with static correlation.

Utilizing Advanced Kinetic Energy Density Based Ingredients for Novel Local Hybrid Mixing Functions

More realistic band gaps from meta-generalized gradient approximations: Only in a generalized Kohn-Sham scheme

Unlike the local density approximation (LDA) and the generalized gradient approximation (GGA), calculations with meta-generalized gradient approximations (meta-GGA) are usually done according to the generalized Kohn-Sham (gKS) formalism. The exchange-correlation potential of the gKS equation is nonmultiplicative, which prevents systematic comparison of meta-GGA band structures to those of the LDA and the GGA. We implement the optimized effective potential (OEP) of the meta-GGA for periodic systems, which allows us to carry out meta-GGA calculations in the same KS manner as for the LDA and the GGA. We apply the OEP to several meta-GGAs, including the new SCAN functional [Phys. Rev. Lett. 115, 036402 (2015)]. We find that the KS gaps and KS band structures of meta-GGAs are close to those of GGAs. They are smaller than the more realistic gKS gaps of meta-GGAs, but probably close to the less-realistic gaps in the band structure of the exact KS potential, as can be seen by comparing with the gaps of the EXX+RPA OEP potential. The well-known grid sensitivity of meta-GGAs is much more severe in OEP calculations.

Pair distribution function of the spin-polarized electron gas: A first-principles analytic model for all uniform densities

We construct analytic formulas that represent the coupling-constant-averaged pair distribution function $\gxcav(r_s,ζ, k_Fu)$ of a uniform electron gas with density parameter $r_s =(9π/4)^{1/3}/k_F$ and relative spin polarization $ζ$ over the whole range $0

ELECTRON DENSITY FUNCTIONALS FROM THE GRADIENT EXPANSION OF THE DENSITY MATRIX: THE TROUBLE WITH LONG-RANGE INTERACTIONS

Divergence and accurate resummation of density functional perturbation theory, with applications to atoms and molecules

One-parameter optimization of a nonempirical meta-generalized-gradient-approximation for the exchange-correlation energy

The meta-generalized-gradient-approximation (meta-GGA) for the exchange-correlation energy, as constructed by Tao, Perdew, Staroverov, and Scuseria (TPSS) [Phys. Rev. Lett. 91, 146401 (2003)], has achieved usefully consistent accuracy for diverse systems and is the most reliable nonempirical density functional (and the most reliable nonhybrid) in common use. We present here an optimized version of this TPSS functional obtained by empirically fitting a single free parameter that controls the approach of the exchange enhancement factor to its rapidly-varying-density limit, while preserving all the exact constraints that the original TPSS functional satisfies. We find that molecular atomization energies are significantly improved with the optimized version and are even better than those obtained with the best hybrid functionals employing a fraction of exact exchange (e.g., the TPSS hybrid), while energy barrier heights are slightly improved; jellium surface energies remain accurate and almost unchanged. The one-parameter freedom of the TPSS functional may be useful even beyond the meta-GGA level, since the TPSS approximation is a natural starting point for the higher-level hyper-GGA.

Long-range van der Waals interaction between nanoclusters

CORRELATION ENERGY DENSITIES: E PLURIBUS UNUM

Polarizabilities and Hyperpolarizabilities of Hydrogen Chains: Is Self-Interaction Correction the Key?