Abstract
We show that if one uses a screened Coulomb potential V(K)=4\ensuremath{\pi}/(${K}^{2}$+${K}_{s}^{2}$) to calculate ${\ensuremath{\gamma}}_{x}$, the exchange-energy density-functional gradient expansion coefficient, one obtains Sham's result if one takes K\ensuremath{\rightarrow}0 before taking ${K}_{s}$\ensuremath{\rightarrow}0. The exchange energy is by its very definition an unscreened quantity so that the correct order of the limits is ${K}_{s}$\ensuremath{\rightarrow}0 before K\ensuremath{\rightarrow}0, in which case ${\ensuremath{\gamma}}_{x}$=1.42${\ensuremath{\gamma}}_{x}^{\mathrm{Sham}}$. .AE
Keywords
PhysicsOrder (exchange)Energy (signal processing)CoulombAtomic physicsEnergy densityMathematical physicsQuantum mechanicsTheoretical physicsElectron
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Publication Info
- Year
- 1988
- Type
- article
- Volume
- 37
- Issue
- 9
- Pages
- 4634-4636
- Citations
- 82
- Access
- Closed
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Cite This
Leonard Kleinman,
Seongbok Lee
(1988).
Gradient expansion of the exchange-energy density functional: Effect of taking limits in the wrong order.
Physical review. B, Condensed matter
, 37
(9)
, 4634-4636.
https://doi.org/10.1103/physrevb.37.4634
Identifiers
- DOI
- 10.1103/physrevb.37.4634