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Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation
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.
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Cited by
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Metadata
- Authors
- Perdew, J. P., & Yue, W.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1986-06-15
- Volume
- 33
- Issue
- 12
- Pages
- 8800-8802
- ISSN
- 0163-1829 (ISSN-L)
- OpenAlex
- W2090135568
- Cited by
- 4,316
- References
- 0
- FWCI
- 6.09
- Type
- journal article
- Language
- en
- Open access
- closed
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