Dimensional crossover of the exchange-correlation density functional

In this paper we focus on the dimensional properties of the exchange-correlation (XC) density functional. Due to its universal character, the exact XC functional can be used to describe electron systems confined in any number of dimensions. However, we show that the most popular XC models (the local density and the generalized gradient approximations) fail in this respect. This limitation can be avoided by using nonlocal models, such as the weighted density approximation (WDA). Concretely, we demonstrate that the same WDA functional gives accurate XC energies and pair-correlation functions for both three-dimensional (3D) and 2D homogeneous electron gas. The practical consequences of these dimensional properties are evident when applying the XC functional models to a simple, but more realistic, quasi-2D electron system.