A DFT study of analytical correlated densities

Simple analytical expressions for the charge density of two-electron atomic systems are studied using quantities which are of much interest in the Kohn–Sham formalism of density functional theory. Through the analysis of these quantities the overall performance of such densities can be discussed on a much firmer basis. A recent approximation to Tc[ρ], the kinetic contribution to the exchange-correlation energy in density functional theory, has also been tested on these systems. It is concluded that a very high degree of quality, not only in the charge density but also in its derivatives, is needed to provide meaningful results for density functional theory quantities.