The formally exact density embedding method developed by Manby, Miller and
J. Chem. Theory Comput.
(2012), 8, pp. 2564. , 659 Acc. Chem. Res.
(2019), 52, pp. 1359. affords a step further than electrostatic embedding in the description of chemical environment. This embedding scheme allows for the partition of a system into two interacting subsystems that are treated at two different levels of QM theories, e.g., coupled cluster embedded in DFT. This type of embedding fully accounts for polarization as well as quantum mechanical exchange, as calculated from the super-molecular embedding density and the exchange correlation functional used. The goal of this embedding theory is to perform a higher-level QM (DFT or WFT) calculation in an environment described by a lower-level QM theory.