Testing One-Parameter Hybrid Exchange Functionals in Confined Atomic Systems

In this work the Perdew-Burke-Ernzerhof exchange functional coupled with the exact-exchange is applied on closed-shell atoms confined by impenetrable and penetrable walls. When the Hartree-Fock method is used as the reference, one-parameter hybrid exchange functionals qualitatively give a good description of atoms enclosed by a sphere surrounded by an infinite potential. For atoms confined by a finite potential, however, the same hybrid exchange functionals predict results appreciably different to the reference for small confinement radii. The main reason of this result is the Laplacian of the electron density involved in the exchange potential and, consequently, the effective potential diverges at the nucleus, which cannot be remedied by the inclusion of the exact exchange. Localization and delocalization exhibited by the electron density are used as arguments to explain the differences found between various exchange functionals tested in this article. We show that generalized-gradient functionals are unable to give a good description of the corresponding system when the electron density is squeezed by finite potentials over small regions and how one-parameter hybrid exchange functionals alleviate some of the encountered problems. Although the model of the confined atom is extremely simple, it can reproduce some features predicted by sophisticated methods of electronic structure designed for crystal systems, therefore, this model can be useful to test exchange functionals defined within the Kohn-Sham density functional-theory.