Assessment of density functional approximations: long-range correlations   and self-interaction effects
  The complex nature of electron-electron correlations is made manifest in the very simple but non-trivial problem of two electrons confined within a sphere. The description of highly non-local correlation and self-interaction effects by widely used local and semi-local exchange-correlation energy density functionals is shown to be unsatisfactory in most cases. Even the best such functionals exhibit significant errors in the Kohn-Sham potentials and density profiles. 
J. Jung and P. Garc\'ia-Gonz\'alez and J. E. Alvarellos and R. W.   Godby