On the degeneracy of atomic states within exact-exchange (spin-) density   functional theory
  The problem of degenerate ground states of open-shell atoms is investigated in spin-restricted and unrestricted density functional theory using the exact exchange energy functional. For the spin-unrestricted case, spurious energy splittings of the order of 2 to 3 kcal/mol are found for atoms of the second and third period which is larger than the splittings obtained from recently proposed approximate exchange functionals depending explicitly on the current density. In remarkable contrast, for spin-restricted calculations the degeneracy of different atomic ground states is recovered to within less than 0.6 kcal/mol. 
S. Pittalis, S. Kurth, E.K.U. Gross