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The expansion method for the nonrelativistic Hartree-Fock theory by Roothaan is extended to relativistic cases for general open-shell atoms. Numerical applications of the theory to the first transition elements are carried out. It is shown that the conventional approximation of the exchange potential shifts the energy value considerably, whereas the off-diagonal Lagrange multiplier has little effect on the energy. Some problems in the application of the theory to open-shell atoms are discussed.
T. Kagawa (Mon,) studied this question.