Journal
PHYSICAL REVIEW B
Volume 73, Issue 20, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.73.205104
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We propose a model for the angle- and system-averaged exchange-correlation hole of a many-electron system. This hole analyzes the exchange-correlation energy into contributions of various distances u from an electron. The model is reverse-engineered (derived from and not used to derive a density functional). It satisfies known exact hole constraints, including ones that can only be satisfied by a meta-generalized gradient approximation or meta-GGA. It incorporates the exchange-correlation energy density of the Tao-Perdew-Staroverov-Scuseria (TPSS) nonempirical meta-GGA. The hole model is tested for atoms and applied to jellium surfaces. The Fourier transform (u -> k) of the hole is needed for wave-vector interpolation of the jellium surface energy from an exact small-k or large-u asymptote. We find essentially the same surface energies (close to the uncorrected TPSS values) whether we apply the wave-vector interpolation correction to the local spin density approximation, the GGA or the meta-GGA. These and other considerations suggest that these surface energies are accurate. Moreover, we find that the uncorrected TPSS surface energies have a realistic wave-vector analysis. Our TPSS hole model can be used to build the hole model for a TPSS-based global hybrid functional, or for a hyper-GGA that uses full exact exchange.
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