Embedded Many-Body Green's Function Methods for Electronic Excitations in Complex Molecular Systems

Many-body Green's function theory in the GW approximation with the Bethe--Salpeter equation (BSE) provides a powerful framework for the first-principles calculations of single-particle and electron-hole excitations in perfect crystals and molecules alike. Application to complex molecular systems, e.g., solvated dyes, molecular aggregates, thin films, interfaces, or macromolecules, is particularly challenging as they contain a prohibitively large number of atoms. Exploiting the often localized nature of excitation in such disordered systems, several methods have recently been developed in which GW-BSE is applied to a smaller, tractable region of interest that is embedded into an environment described with a lower-level method. Here, we review the various strategies proposed for such embedded many-body Green's functions approaches, including quantum-quantum and quantum-classical embeddings, and focus in particular on how they include environment screening effects either intrinsically in the screened Coulomb interaction in the GW and BSE steps or via extrinsic electrostatic couplings.