ELECTRON AND SPIN-DENSITY ANALYSIS OF SPIN-PROJECTED UNRESTRICTED HARTREE-FOCK DENSITY-MATRICES OF RADICALS

Methods have been developed for the electron and spin density analysis of unrestricted Hartree-Fock wave functions of radicals without and with the inclusion of annihilation of the largest spin contaminant via spin projection (PUHF). While UHF wave functions are not eigenfunctions of the [S2] operator, the spin projection method successfully annihilates the main component of the spin contamination. Electron and spin density functions determined at the UHF and PUHF levels are compared. Differences of topological and of integrated properties are discussed. Methyl and allyl radicals are discussed to illustrate the effects of spin annihilation. Representative series of simple binary radicals of first- and second-row atoms, of heteroatom-substituted methyl radicals, of a selected number of unsaturated systems, and of selected aza analogues of allyl radicals also are considered, and trends are discussed. It is found that the electron populations determined with the UHF and PUHF electron density functions differ only marginally but that the spin populations are greatly dependent on the method.