The SS-FNO scheme described above can only reduce the size of the virtual space in the IP-EOM-CCSD* method. As the core orbitals are generally localized, one can reduce the dimension of the occupied space by using a quantum embedding scheme. We have used the projector-based embedding scheme advocated by Manby, Miller, and co-workers 68 . In the projector-based embedding calculation, the initial calculation of the entire system is at the desired level of theory for the environment. The molecular orbitals (M.O.s) orbitals are assigned to either the active or environment subsystems based on some localization based criteria. The total system density,  , is then divided into subsystem densities A  and B  , corresponding to the active and environment subsystems, respectively.