Compared to projection-based embedding, the subsystem-DFT (sDFT) approach does not start from a plain DFT reference calculation of the full system. Instead, the idea here is to perform Kohn-Sham-like calculations on fragments and then to determine the full-system density from the fragment densities. This way, the embedding region II can actually be split further into all molecular fragments. For the sake of presentation, we continue with the two region notation. Then, as in the projection-based embedding, the total electron density is given as n(r) = n I (r) + n II (r), and each subsystem density is obtained from Kohn-Sham equations with constrained electron density (KSCED). To calculate the molecular orbitals of subsystem I in the frozen density n II of subsystem II, these KSCED equations read :