to locate the true global minimum. In particular, the iteration process will not break any symmetries of the Hamiltonian which are not broken by the starting charge and spin-densities, even though the global minimum of the HF energy functional frequently does break at least some of these symmetries. To counter such problems, it is usually a good idea to introduce small artificial terms in the Hamiltonian which break the continuous symmetries and help the iterative process to reach the lowest energy state. In this problem, the iterative process is also hampered by severe convergence problems at zero temperature connected with the localization of HF quasiparticle wavefunctions and the long range nature of the Coulomb interactions. A small change in the energy of a particular orbital may involve a substantial rearrangement of the charges. These problems can be mitigated by always working at a temperature which is comparable to the finite-size quasiparticle energy level spacing and which scales to zero as the system size increases. The Zeeman term in the Hamiltonian, for which we choose typical experimental values, reduces the SU(2) spin symmetry to a U(1) symmetry. In order to break the continuous U(1) symmetry we introduce an artificial (but very 