By working with the real functions pix and piy instead of pi+ and pi–, we show how to express the SCF Hamiltonians for the Sigma states of the configurations (piu)3(pig),(piu)3(pig)3, and (1pi)3 (2pi) of diatomic molecules in terms of the Coulomb and exchange operators only. With these results, we have used conventional SCF programs to solve for the wavefunctions of many interesting states of N2, O2, and CO, e.g., the B 3Sigmau– state of O2. For many states, the SCF results are in good agreement with experiment. However, SCF theory runs into serious trouble if electron correlation is important in determining the relative locations of excited states
