This is similar to the case of LiF and NaF, where GW/BSE-in-DFT underestimated the optical gap by close to 1 eV when compared to periodic GW/BSE calculations. In fact, it has been an overall trend that GW/BSE excitation energies are in general 1 eV lower than CC2 values, with or without embedding.
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This lack of a clear trend can be attributed to the varying shapes of the clusters, which result in inconsistent contributions from surface and edge-localized states (see ref ( 114 )).