  We develop a Green's function approach to quasiparticle excitations of
open-shell systems within the GW approximation. It is shown that accurate
calculations of the characteristic multiplet structure require a precise
knowledge of the self energy and, in particular, its poles. We achieve this by
constructing the self energy from appropriately chosen mean-field theories on a
fine frequency grid. We apply our method to a two-site Hubbard model, several
molecules and the negatively charged nitrogen-vacancy defect in diamond, and
obtain good agreement with experiment and other high-level theories.
