A theory is presented for enforcing spatial symmetry and equivalence with unrestricted Hartree-Fock (UHF) wavefunctions. This generalized UHF (GUHF) wavefunction is a simple way to obtain qualitatively correct ab initio spin densities, for comparison with polarized neutron diffraction experiments. Quasi Newton-Raphson equations are presented, based on generalized energy expressions which use coupling coefficients, and an exponential parametrization of orbital rotation parameters. The coupling coefficients for the common case of a high spin partially occupied degenerate shell are given. The new method is applied to the triplet oxygen atom, and used to calculate spin densities for the FeCl^4-₆ anion. It is found that the energy of the GUHF wavefunction lies above the symmetry broken UHF wavefunction, but below the restricted Hartree-Fock methods, and that the expectation value of S² is worsened (i.e., spin contamination increases).