In the DMET scheme, one adopts an orthonormal atomic basis (such as the Löwdin basis used in here) and divides the basis functions according to the fragment they reside on: those on the impurity (ϕ µ ∈ A, chromophore in the context of this article), and those on its environment (ϕ ν ∈ E, solvent molecules). Let us write the occupied orbitals from full-system KS-DFT calculations as