Abstract
Starting from very accurate many-body wave functions, we have constructed essentially exact densities, exchange-correlation potentials, and components of the total energy for helium and two-electron ions. These density-functional results are compared to the corresponding quantities obtained from a variety of commonly used approximate density functionals, namely, the local-density approximation and various generalized gradient approximations, in order to test the accuracy of the approximate functionals. Although the generalized gradient approximations yield improved energies compared to the local-density approximation, the exchange and correlation potentials (especially the latter) obtained from the generalized gradient approximations are in poor agreement with the corresponding exact potentials. The large-distance asymptotic behavior of the exact exchange-correlation potential to O(1/${\mathit{r}}^{4}$) is found to agree with theoretical predictions. The short-range behavior of the exchange-correlation potential is very close to quadratic. The prospects for improved generalized gradient approximations are discussed.
Keywords
PhysicsSeries (stratigraphy)Local-density approximationQuadratic equationHeliumRange (aeronautics)Statistical physicsQuantum mechanicsAtomic physicsDensity functional theoryMathematics
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Publication Info
- Year
- 1994
- Type
- article
- Volume
- 50
- Issue
- 5
- Pages
- 3827-3837
- Citations
- 383
- Access
- Closed
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Cite This
C. J. Umrigar,
Xavier Gonze
(1994).
Accurate exchange-correlation potentials and total-energy components for the helium isoelectronic series.
Physical Review A
, 50
(5)
, 3827-3837.
https://doi.org/10.1103/physreva.50.3827
Identifiers
- DOI
- 10.1103/physreva.50.3827
- PMID
- 9911351