Abstract
The electronic exchange energy as a functional of the density may be approximated as ${E}_{x}[n]={A}_{x}\ensuremath{\int}{d}^{3}r{n}^{\frac{4}{3}}F(s)$, where $s=\frac{|\ensuremath{\nabla}n|}{2{k}_{F}n}$, ${k}_{F}={(3{\ensuremath{\pi}}^{2}n)}^{\frac{1}{3}}$, and $F(s)={(1+1.296{s}^{2}+14{s}^{4}+0.2{s}^{6})}^{\frac{1}{15}}$. The basis for this approximation is the gradient expansion of the exchange hole, with real-space cutoffs chosen to guarantee that the hole is negative everywhere and represents a deficit of one electron. Unlike the previously publsihed version of it, this functional is simple enough to be applied routinely in self-consistent calculations for atoms, molecules, and solids. Calculated exchange energies for atoms fall within 1% of Hartree-Fock values. Significant improvements over other simple functionals are also found in the exchange contributions to the valence-shell removal energy of an atom and to the surface energy of jellium within the infinite barrier model.
Keywords
JelliumPhysicsSimple (philosophy)Nabla symbolValence (chemistry)Atom (system on chip)Atomic physicsLocal-density approximationEnergy (signal processing)ElectronDensity functional theoryQuantum mechanics
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Publication Info
- Year
- 1986
- Type
- article
- Volume
- 33
- Issue
- 12
- Pages
- 8800-8802
- Citations
- 4189
- Access
- Closed
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Cite This
John P. Perdew,
Yue Wang
(1986).
Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation.
Physical review. B, Condensed matter
, 33
(12)
, 8800-8802.
https://doi.org/10.1103/physrevb.33.8800
Identifiers
- DOI
- 10.1103/physrevb.33.8800