Classes of admissible exchange-correlation density functionals for pure spin and angular momentum states

We analyze the various approaches to construct exchange-correlation functionals which are able to describe states of definite spin multiplicity in the DFT realm and outline the characteristics of possible functionals consistent with the Kohn-Sham theory. To achieve this goal the unitary group technique is applied to label many-electron states of definite total spin and to calculate the corresponding analogs of the Roothaan coupling coefficients. The possibility of using range separated Coulomb potential of electron-electron interaction for constructing functionals discriminating multiplet states in the d-shells is explored and a tentative system of state-specific functionals, covering nontrivial correlations in d-shells of transition metal ions, is proposed for the Fe^{2+} ions.