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. / Master of Science