Towards a universal exchange enhancement factor in density functional theory

Abstract

A broadly used strategy to go beyond the well-known local-density approximation of density functional theory relies on the choice of a so-called exchange-correlation (xc) enhancement factor Fxc, defined as the enhancement of a realistic xc energy density over its local exchange-only counterpart. To date, this density functional, Fxc, has been constructed by following either semiempirical strategies or nonempirical schemes that impose the fulfillment of exact constraints. Here, we follow a totally different route, which is based on an attempt to construct a universal exchange enhancement factor Fx from the exact exchange energy density of a given family of electron density profiles and which we implement on the basis of jellium-slab exact-exchange self-consistent calculations. We find that such an enhancement factor can, indeed, be built which obeys, within our sample of electron-density profiles, most exact constraints and thus represents a benchmark towards the construction of a universal exchange enhancement factor suitable for all electron densities. We provide, in particular, an analytical parametrization of our ab initio calculations at the level of the generalized gradient approximation.