Strictly speaking, PbE methods do not primarily partition the electron density, but are based on a separation of orbitals into sets for different subsystems. In the original work by Manby, Miller and co-workers , this was applied in a top-down fashion. In this case, the calculation starts with an SCF calculation on the supersystem, followed by an orbital localization. Then, the orbitals for the active system may be defined in a certain way (see below), while all orbitals not selected for the active system constitute the environment system and are incorporated into the projection operator. Since a supermolecular SCF calculation is needed, this approach cannot offer efficiency gains compared to the totalsystem calculation. However, such PbE calculations often form the starting point for more advanced wavefunction-in-DFT embedding calculations with covalent bonds between the wavefunction and the DFT region. Since the active region usually contains much fewer electrons than the total system, large computational savings might be expected.