Exact-Exchange Density Functional Theory applied to a strongly inhomogeneous electron gas

A recently developed quasi-two-dimensional exact-exchange formalism within the framework of density-functional theory has been applied to a strongly inhomogeneous interacting electron gas. Results are presented for the exchange-hole density at different positions in the system, the exchange-energy density, and the exchange energy per particle. It has been found that the exact exchange hole is strongly nonlocal when evaluated at a point of low density, but that evolves progressively towards a local-density approximation (LDA) hole for increasing density. The exchange-energy density is over (under) estimated by the LDA at the points of high (low) density. The exchange energy per particle shows a pronounced minimum when the system is close to the two-dimensional limit.