  We apply the Green's function coupled cluster singles and doubles (GFCCSD)
impurity solver to realistic impurity problems arising for strongly correlated
solids within the self-energy embedding theory (SEET) framework. We describe
the details of our GFCC solver implementation, investigate its performance, and
highlight potential advantages and problems on examples of impurities created
during the self-consistent SEET for antiferromagnetic MnO and paramagnetic
SrMnO$_{3}$. GFCCSD provides satisfactory descriptions for weakly and
moderately correlated impurities with sizes that are intractable by existing
accurate impurity solvers such as exact diagonalization (ED). However, our data
also shows that when correlations become strong, the singles and doubles
approximation used in GFCC could lead to instabilities in searching for the
particle number present in impurity problems. These instabilities appears
especially severe when the impurity size gets larger and multiple degenerate
orbitals with strong correlations are present. We conclude that to fully check
the reliability of GFCCSD results and use them in fully {\em ab initio}
calculations in the absence of experiments, a verification from a GFCC solver
with higher order excitations is necessary.
