Construction of a semilocal exchange density functional from a three-dimensional electron gas collapsing to two dimensions

Abstract

In a recent paper an alternative route has been proposed to construct the so-called exchange-correlation (xc) enhancement factor Fxc of density-functional theory, defined as the enhancement of a realistic xc energy density over its local exchange-only counterpart. This new route, based on the ab initio calculation of the exact exchange energy density of a family of electron-density profiles, was implemented on the basis of jellium-slab exact-exchange self-consistent calculations. Here, we follow this route to construct a meta-generalized-gradient approximation (MGGA) for exchange from a nonuniform one-dimensional coordinate scaling, which we implement on the basis of a number of calculations performed for model densities of electrons confined by infinite-barrier walls, as the electron system is shrunk from three to two dimensions. Our MGGA yields exchange energies that approach in the two-dimensional (2D) limit the exact exchange energy of a 2D electron gas, by appealing to a scaling of the MGGA exchange enhancement factor.