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

HOROWITZ, C.M.; PROETTO, C.R.; PITARKE, J.M.

Physical Review B

American Physical Society

Año: 2023 vol. 108 p. 1151191 - 1151198

2469-9950

In a recent paper [Horowitz, Phys. Rev. B 107, 195120 (2023)2469-995010.1103/PhysRevB.107.195120], 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.