(4.2.8) Fromager : An alternative approach to quantum embedding initiated with the seminal work of Knizia and Chan 612 on density-matrix embedding theory (DMET) has been intensively developed in the last few years in both condensedmatter physics and quantum chemistry . At first sight, DMET looks more like a wave-function-based method that has nothing to do with DFT. Nevertheless, connections can be made when the convergence criteria involve diagonal elements of the (one-electron reduced) density matrix only. In this context, the localized "impurity" orbital occupations ρ i ≡ ∑ σ =↑,↓ a † iσ a iσ play the role of the density and the correlation embedding potential, which is used in the full-size system, is a collection of one-electron ("on-site" in lattice models ) energies v i . The latter are adjusted so that the corresponding embedded impurity orbitals have the same occupation as in the full-size system. Referring to a noninteracting Kohn-Sham (full-size) system in this context is appealing because it is a way to "exactify" the embedding procedure.