Open-shell one-electron equations are derived by application of Rootha
an's coupling operator technique to the variational procedure of findi
ng the Kohn-Sham orbitals and minimizing the energy of an open-shell s
ystem, represented within the density functional vector coupling schem
e. The final equations are presented in a form suitable for standard q
uantum-chemical codes using finite basis set Kohn-Sham calculations. E
xamples of multiplets for which the theory is applicable are discussed
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