Nonuniversality of commonly used correlation-energy density functionals

The correlation energies of the helium isoelectronic sequence and of Hooke's atom isoelectronic sequence have been evaluated using an assortment of local, gradient, and metagradient density functionals. The results are compared with the exact correlation energies, showing that while several of the more recent density functionals reproduce the exact correlation energies of the helium isoelectronic sequence rather closely, none is satisfactory for Hooke's atom isoelectronic sequence. It is argued that the uniformly acceptable results for the helium sequence can be explained through simple scaling arguments that do not hold for Hooke's atom sequence, so that the latter system provides a more sensitive testing ground for approximate density functionals. This state of affairs calls for further effort towards formulating correlation-energy density functionals that would be truly universal at least for spherically symmetric two-fermion systems.