A new formula is introduced for the energy expectation value of multi-
determinantal single configuration states with arbitrary open shells i
n terms of the 4-indexed electronic repulsion integrals. Applying the
variational principle to this expression and introducing 2-indexed Cou
lomb and exchange operators, new forms of Hartree-Fock and Hartree-Foc
k-Roothaan equations for open shell systems are obtained. They are bas
ed entirely on the restricted Hartree-Fack formalism. (C) 1998 Elsevie
r Science B.V.