As a first example of an application of a variant of such a GW /MM embedding scheme, Galleni et al. studied the peak broadening pf photoemission spectra in amorphous polymers. Figure shows as an example the obtained core level and valence region photoelectron spectra of polymethyl methacrylate (PMMA), where the data shown as "charges" correspond roughly speaking to a GW /MM calculation with no polarization in the MM region, while "charges+dipoles" include polarization effects. One can clearly see that intrinsic local inhomogeneities in the electrostatic environment induce a broadening of 0.2-0.7 eV in the binding energies of both core and semivalence electrons. Figure shows in steps the effects of embedding of electron-hole excitations in GW -BSE/MM on the charge-transfer type excitations between two adenine base pairs in solvated double-stranded DNA. The progression from a GW-BSE calculation in vacuum, via a GW -BSE/MM with a non-polarizable environment, to GW -BSE/MM with a polarizable environment shows not only that the charge-transfer excitation energy is affected but that the nature of the electronic excitation is also sensitive to effects from the complex environment. Here, for instance, the amount of transferred charge changes from a partial charge transfer of 0.6 e to an integer charge transfer of 1 e. It is also clear that this is an effect of polarization, as integer transfer is not observed with a static MM environment in Figure (b). This is not only a consequence of the converged GW -BSE/MM calculation having different weights for the respective transitions between occupied and unoccupied single-electron states in Eq. . Additionally, the singleparticle functions themselves are affected by the inclusion of the contribution of polarized electrostatic moments in the external potential of the underlying ground-state calculation.