The corresponding density of the inactive region is determined from this n I (r) as n II (r) = n(r)n I (r). With this initial partitioning of the total reference density into two subsystem densities, one now considers the active density as a variable in the subsystem I. A set of effective equations for requires the addition of an embedding potential accounting for the electrostatic and exchange-correlation interactions with the electrons in subsystem II. At the same time, it must be ensured that the Pauli exclusion principle is not violated between the orbitals forming the densities of both subsystems. The main idea in projector-based embedding that fulfills both objectives is to raise the energies of orbitals associated with subsystem II to very high values during the calculation for subsystem I.