The interaction between the two regions is explicitly evaluated via the term V QM/MM 12 , implying that electrostatic interactions between the two subsystems are handled during the computation of the electronic wave function by adding the external potential of the multipoles in the MM region to the QM Hamiltonian as one-electron operators. In turn, the explicit electrostatic field from the QM density is used to polarize the MM region. For the GW -BSE approach, several such QM densities can be employed, depending on the state of interest (s). If s is a quasiparticle excitation, we define