Assessment of advanced energy functionals in an exactly solvable model system

Abstract

There is an increasing interest in the use of the random-phase approximation (RPA) and extensions thereof to calculate ground-state correlation energies within the Kohn-Sham formalism. However, current implementations of these RPA-based functionals resort to the use of mean-field-like approximations when obtaining Kohn-Sham eigenorbitals and eigenenergies. In this paper we exactly calculate RPA and related results for a model system in which different correlation regimes can be easily addressed. We explore the reliability of such methods in the limit of strong interactions and pay special attention to the importance of a self-consistent resolution of the corresponding Kohn-Sham equations. In particular, we show that the self-consistent implementation of these methods provides accurate correlation energies and ground-state densities even when mean-field approximations dramatically fail.