McWeeny has developed a method which utilizes the steepest descent technique in solving the Hartree-Fock equations. The mathematical development is presented and discussed. The method achieves convergence for several otherwise recalcitrant systems.

The following systems are investigated and discussed:

1. the π-electron systems of p-benzoquinone and calicene,

2. the all-valence-electron systems of the calicene dianion, nitrobenzene and m-chloronitrobenzene,

3. the first complete SCFMO binding energy curves for the Cl₂-benzene charge-transfer complex, including several configurations,

4. studies of selectivity for the protonation of (addition of Bronsted acids to) propylene, and the chlorination of nitrobenzene and m-chloronitrobenzene (These studies proved to be far more complex than initially foreseen, and firm conclusions were not obtained.).

Recommendations for further investigation of these systems are also given.