  Two electrons at the threshold of ionization represent a severe test case for
electronic structure theory. A pseudospectral method yields a very accurate
density of the two-electron ion with nuclear charge close to the critical
value. Highly accurate energy components and potentials of Kohn-Sham density
functional theory are given, as well as a useful parametrization of the
critical density. The challenges for density functional approximations and the
strength of correlation are also discussed.
