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Exchange-correlation hole is a central concept in density functional theory.It not only provides justification for an exchange-correlation energyfunctional, but also serves as a local ingredient in nonlocal range-separationdensity functional. However, due to the nonlocal nature, modelig theconventional exact exchange hole presents a great challenge to densityfunctional theory. In this work, we propose a semilocal exchange holeunderlying the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA functional. Thepresent model is distinct from previous models at small separation between anelectron and the hole around the electron. It is also different in the way itinterpolates between the rapidly varying iso-orbital density and the slowlyvarying density, which is determined by the wave vector analysis based on theexactly solvable infinite barrier model for jellium surface. Our numericaltests show that the exchange hole generated from this model mimics theconventional exact exchange hole quite well for atoms. Finally, as a simpleapplication, we apply the hole model to construct a TPSS-based range-separationfunctional. Our tests show that this TPSS-based range-separation functional cansubstantially improve TPSS band gaps and barrier heights, without losing muchaccuracy of molecular atomization energies.

Semilocal exchange hole with an application to range-separation density functional