A steepest descent procedure which can be used in an iterative calculation of the unrestricted bond order matrices for any system is described. The method is used to calculate unrestricted bond order matrices for the ions and lowestπtriplet states of naphthalene, anthracene, phenanthrene and azulene. Spin densities and net charges on each carbon atom in these systems together with triplet excitation energies and ionization potentials are found and compared with experiment. Unrestricted wave functions are not in general eigenfunctions of the total spin operator but this situation can be improved by using projection operators and annihilators. Spin properties of the wave function both before and after a single annihilation are discussed together with the effect of annihilation on spin densities and energy values.