  Exchange-correlation hole is a central concept in density functional theory.
It not only provides justification for an exchange-correlation energy
functional, but also serves as a local ingredient in nonlocal range-separation
density functional. However, due to the nonlocal nature, modelig the
conventional exact exchange hole presents a great challenge to density
functional theory. In this work, we propose a semilocal exchange hole
underlying the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA functional. The
present model is distinct from previous models at small separation between an
electron and the hole around the electron. It is also different in the way it
interpolates between the rapidly varying iso-orbital density and the slowly
varying density, which is determined by the wave vector analysis based on the
exactly solvable infinite barrier model for jellium surface. Our numerical
tests show that the exchange hole generated from this model mimics the
conventional exact exchange hole quite well for atoms. Finally, as a simple
application, we apply the hole model to construct a TPSS-based range-separation
functional. Our tests show that this TPSS-based range-separation functional can
substantially improve TPSS band gaps and barrier heights, without losing much
accuracy of molecular atomization energies.
