Are localized broken symmetry solutions acceptable in molecular calculations

The question of localized versus nonlocalized broken symmetry core-hole and low-lying excited states is reviewed with particular emphasis on the role of the overall symmetry. The broken-symmetry solutions, which yield for core-ionization very good results for the energy, if symmetrized give a splitting and perhaps a worse energy. It is argued that when the splitting is smaller than the experimental resolution the appropriate description of the physical state is not a wave function, but a density matrix (statistical ensemble) of broken-symmetry states with correct overall symmetry.