Here, all subsystem electron densities ρ I (r) are optimized iteratively, either sequentially in freeze-and-thaw iterations or simultaneously. In the latter case, the electron density of the environment is kept frozen, and only the electron density of the active subsystem is optimized. This case is commonly referred to as Frozen Density Embedding (FDE). For extensive discussion of its theoretical foundations, we refer to Ref. as well as the recent work in Refs. 8, 9.