The methods presented in Section 3.3.1 provide ways to include screening effects from a classical environment into GW -BSE calculations utilizing additional terms in the screened Coulomb interaction W . In contrast to this internal inclusion of screening, alternative approaches focus on accounting for these effects with what we from now on refer to as external QM/MM. As the name suggests, the calculations for the QM and classical MM regions of such approaches are more separated than, e.g. by evaluating the effects on an environment reaction field via Eq. (81). Instead, the two regions are coupled based solely on electrostatic interactions. A typical workflow of such an external GW -BSE/MM calculation is shown in Figure . The four method ingredients are the classical microelectrostatics model, the DFT calculation for the ground state, as well as the GW and Bethe-Salpeter equation steps, respectively. The classical, polarizable environment in the MM region enters the GW-BSE workflow merely as a specific external In what is sometimes referred to as Thole model, we indicate static atomic multipole moments as Q m t , where t is the multipole rank and m the associated atom in the molecule M. The tensor T mm ′ tu describes the interactions between the multipoles moments Q m t and Q m ′ u . In the polarizable representation, each atom is additionally assigned a polarizability α mm ′ tu with which induced moments ∆Q m t due to the field generated by moments u on a different atom m ′ can be created. Let us consider now a purely classical (MM) system S in state s, which has been split into regions R and R ′ with S = R ∪ R ′ . Molecules in region R (R ′ ) are indicated by M (M ′ ), and atoms in molecule M (M ′ ) by m (m). The total classical energy of the system is then given by