The method of spin projection was examined by developing and applying computer programs to calculate projected semi-empirical and ab initio unrestricted Hartree-Fock (UHF) wavefunctions. The electronic spectra of naphthalene, anthracene, naphthacene and pentacene were calculated using the Pariser-Pople-Parr (PPP) Π-electron approximations and both UHF and configurational interaction (CI) techniques. The results of both techniques were compared with experimentally determined spectra with reasonable agreement between the CI and projected UHF results. While the CI calculations generally produced lower energies for the triplet states than the UHF calculations, the spectra from UHF calculations were in somewhat better agreement with experiment. Anomalies encountered with degeneracies and the presence of open shell ground states are also discussed. The geometry of monohomocyclooctatetraene anion radical (MHCOT) was studied using spin projection of the UHF INDO wavefunction. The theoretical molecular geometry was varied until the experimental hyperfine coupling constants matched hyperfine constants obtained from using both projected and unprojected UHF wavefunctions. The two types of calculations resulted in slightly different energies and geometries with the projected calculations giving a higher energy for the doublet state; essentially no differences were noted in the bond orders obtained from the two types of calculations. The geometry from the projected calculations was a somewhat more strained conformation than the geometry from the unprojected calculation. Ab initio UHF calculations with spin projection were performed on H₂O(+) to compare the energies of pure spin states from ab initio multiconfigurational self-consistent field with CI. (MCSCF/CI) with those from spin projection. The MCSCF/CI calculations are superior to the UHF plus spin projection calculations. This result will always be observed when the UHF wavefunction is very close to a pure spin state before spin projection. The dissociation of CF₂O was studied using ab initio wavefunctions. The energies of the unprojected UHF wavefunctions were examined along with those for the dissociated CF₂ + O fragments. Good agreement exists between the calculated and experimental vertical ionization potentials for CF₂0 at the equilibrium geometry. / Doctor of Philosophy