and easily sees that the reaction field appears both in the dielectric function and again in the modified Coulomb interaction. Tölle et al. provided additional details about the implementation of the above for several subsystem fragments in different bases within the resolution-of-identity (RI) method in Refs. , and we point the interested reader to the original work. The authors then reported the results of DFT-embedded GW -BSE calculations on an ammonia-benzene dimer, aqueous methylenecyclopropane, and a water-solvated adenine-thymine dimer. In Figure , we reprint from their work the dependence of the quasiparticle energy of the HOMO of ammonia in the ammonia-benzene dimer at different intermolecular separations (Fig. of ). One can clearly see that for both sDFT (here labeled as 'Naddkin') and projection-based-embedding (PbE), the plain embedded GW calculations without accounting for environment screening (blue open circles) from the benzene molecule yield lower quasiparticle energies than the supermolecular full system reference (open squares). The difference is largest for the closest dimer separation (around 0.2 eV) and becomes progressively smaller for larger distances. Note that HOMO Kohn-Sham energies for the HOMO already differ by about 0.05 eV in the respective ground state calculations for the shortest intermolecular separation (cf., Fig. of Ref. ). The inclusion of the environment screening here from the single benzene molecule (red crosses) brings the quasiparticle energies in very close agreement with the full calculations. The authors observed similar behavior for the quasiparticle energies of methylenecyclopropane with a variable number of water molecules as solvent and in water-solvated adenine-thymine dimers.