Within the framework of the symmetrized Kohn - Sham ( KS) formalism an effective exact- exchange approach, the open-shell localized Hartree - Fock (OSLHF) method, is derived. The derivation relies on an approximation of energy denominators in KS one- particle Greens functions, the approximation of average magnitudes of eigenvalue differences, which is introduced. With the OSLHF method open- shell molecules can be treated efficiently and numerically stable without running into the symmetry problem encountered in conventional KS methods. The self- interaction free Hamiltonian operator of the OSLHF approach is in all cases non- spin- polarized and exhibits the full molecular point group symmetry in real space. Results for atoms as well as small and medium size molecules are presented. A procedure is introduced which yields special basis sets required for an efficient construction of the Slater potential which enters the effective KS potential of localized Hartree -Fock methods. (C) 2003 American Institute of Physics.