Accurate optimized-potential-model solutions for spherical spin-polarized atoms: Evidence for limitations of the exchange-only local spin-density and generalized-gradient approximations

Engel, E.; Vosko, S. H.

doi:10.1103/physreva.47.2800

Cited by 257 publications

(192 citation statements)

References 51 publications

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“…[17,18] In spite of these good features, the implementation of the OEP method is very complicated and its computational cost is excessively high. Only spherical atoms, [16,17,19] jellium surfaces, [20] jellium spheres, [21] and periodic solids with a small unit cell [22] have been extensively studied, and there exists no investigation of molecular systems with the OEP method. However, about a decade ago, Krieger, Li, and Iafrate (KLI) proposed an approximation scheme to the OEP, and have shown that the KLI potential with the exact exchange-only energy functional (KLI-x) satisfies the above mentioned properties (i)-(iv) of V KS xc , and accurately reproduces the OEP-x results for spherical atoms.…”

Section: Introductionmentioning

confidence: 99%

Density-functional study of small molecules within the Krieger-Li-Iafrate approximation

1999

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We report density-functional studies of several small molecules (H 2 , N 2 , CO, H 2 O, and CH 4 ) within the Krieger-Li-Iafrate (KLI) approximation to the exact Kohn-Sham local exchange potential, using a threedimensional real-space finite-difference pseudopotential method. It is found that exchange-only KLI leads to markedly improved eigenvalue spectra compared to those obtained within the standard local-density approximation (LDA), the generalized gradient approximation (GGA), and the Hartree-Fock (HF) method. For structural properties, exchange-only KLI results are close to the corresponding HF values. We find that the addition of LDA or GGA correlation energy functionals to the KLI exact exchange energy functional does not lead to systematic improvements.

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Section: Introductionmentioning

confidence: 99%

Density-functional study of small molecules within the Krieger-Li-Iafrate approximation

1999

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“…The wavefunctions R nl are discretized on a semi-logarithmic numerical grid, using the Engel code [78,79].…”

Section: Real Atomsmentioning

confidence: 99%

Kinetic and Exchange Energy Densities near the Nucleus

2016

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Abstract:We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirmed by numerical calculations on real atoms up to two thousands electrons. Based on this model, we propose non-local density-dependent ingredients that are suitable for the description of the kinetic and exchange energy densities in the region close to the nucleus. These non-local ingredients are invariant under the uniform scaling of the density, and they can be used in the construction of non-local exchange-correlation and kinetic functionals.

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“…40 Zhang and Yang ͓revPBE ͑Ref. 12͔͒ relaxed this constraint and optimized by fitting the exchange-only total atomic energies from He to Ar to the exact exchange-only results from the optimized exchange potential method, 41 obtaining ϭ1.245. 12…”

Section: B the Termmentioning

confidence: 99%

The extended Perdew-Burke-Ernzerhof functional with improved accuracy for thermodynamic and electronic properties of molecular systems

Goddard

2004

The Journal of Chemical Physics

170

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Density functional theory ͑DFT͒ has become the method of choice for many applications of quantum mechanics to the study of the electronic properties of molecules and solids. Despite the enormous progress in improving the functionals, the current generation is inadequate for many important applications. As part of the quest of finding better functionals, we consider in this paper the Perdew-Burke-Ernzerhof ͑PBE͒ functional, which we believe to have the best theoretical foundation, but which leads to unacceptable errors in predicting thermochemical data ͑heats of formation͒ of molecular systems ͓mean absolute deviation ͑MAD͒ϭ16.9 kcal/mol against the extended G2 data set of 148 molecules͔. Much improved thermochemistry is obtained with hybrid DFT methods that include part of the Hartree-Fock exchange ͓thus B3LYP ͑Becke's three parameter scheme combining Hartree-Fock exchange, Becke gradient corrected exchange functional and Lee-Yang-Parr correlational functional͒ with MADϭ3.1 kcal/mol and PBE0 ͑Perdew's hybrid scheme using PBE exchange and correlation functionals͒ with MADϭ4.8 kcal/mol͔. However we wish to continue the quest for a pure density-based DFT. Thus we optimized the four free parameters ͑ , , ␣, and ␤͒ in PBE theory against experimental atomic data and the van der Waals interaction properties of Ne 2 , leading to the xPBE extended functional, which significantly outperforms PBE for thermochemical properties MAD reduced to 8.0 kcal/mol while being competitive or better than PBE for predictions of geometric parameters, ionization potentials, electron affinities, and proton affinities and for the description of van der Waals and hydrogen bond interactions. Thus xPBE significantly enlarges the field of applications available for pure DFT. The functional forms thus obtained for the exchange and correlational functionals may be useful for discovering new improved functionals or formalisms.

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Accurate optimized-potential-model solutions for spherical spin-polarized atoms: Evidence for limitations of the exchange-only local spin-density and generalized-gradient approximations

Cited by 257 publications

References 51 publications

Density-functional study of small molecules within the Krieger-Li-Iafrate approximation

Density-functional study of small molecules within the Krieger-Li-Iafrate approximation

Kinetic and Exchange Energy Densities near the Nucleus

The extended Perdew-Burke-Ernzerhof functional with improved accuracy for thermodynamic and electronic properties of molecular systems

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