Projection-based embedding is a formally exact DFT-in-DFT embedding scheme, introduced by Manby et al. . They proposed to partition the density of a full reference system n(r) into the densities of two subsystems n I (r) and n II (r), such that n(r) = n I (r) + n II (r). Then, one considers one of them (from now on n I (r)) as active while the other (from now on n II (r)) is regarded as an inactive embedding density. A set of effective Kohn-Sham equations for the (orbitals forming) active density embedded in the inactive density can be derived, and the resulting total energy of the embedded system can be made to agree exactly with the total energy of the full system. The first step of the algorithm is to perform a reference self-consistent DFT calculation on the complete system employing the full-molecule AO basis as described in Section 2.5. Then, a unitary transformation is used to transform the N occupied canonical molecular orbitals, ϕ i (r) for i = 1, ... N, into localized orbitals, ϕ LO i (r). Note that this step leaves the total density of the system unchanged. Following this localization, an initial active density is constructed by selecting those localized orbitals with a significant Mulliken population q I i > q t on the atoms of the chosen subsystem I, yielding: