  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 meta-gradient 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.
