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We apply the Green's function coupled cluster singles and doubles (GFCCSD)impurity solver to realistic impurity problems arising for strongly correlatedsolids within the self-energy embedding theory (SEET) framework. We describethe details of our GFCC solver implementation, investigate its performance, andhighlight potential advantages and problems on examples of impurities createdduring the self-consistent SEET for antiferromagnetic MnO and paramagneticSrMnO$_{3}$. GFCCSD provides satisfactory descriptions for weakly andmoderately correlated impurities with sizes that are intractable by existingaccurate impurity solvers such as exact diagonalization (ED). However, our dataalso shows that when correlations become strong, the singles and doublesapproximation used in GFCC could lead to instabilities in searching for theparticle number present in impurity problems. These instabilities appearsespecially severe when the impurity size gets larger and multiple degenerateorbitals with strong correlations are present. We conclude that to fully checkthe reliability of GFCCSD results and use them in fully {\em ab initio}calculations in the absence of experiments, a verification from a GFCC solverwith higher order excitations is necessary.

Testing the GFCCSD impurity solver on real materials within the self-energy embedding theory framework