We agree with Baerends that the quality of the total energy in local and semilocal DFAs is (far) superior to the quality of the Kohn-Sham potential and hence we have decided not to interfere with the total energy of the DFA. Instead, we impose constraints on the effective local potential to reduce the self-interaction errors from it. These constraints, Q rep = N -1 and ρ rep (r) ≥ 0, are enforced with the OEP method, whose mathematical (rather than numerical) problems with finite basis sets are now well understood. The computational cost of these OEP calculations is determined by the matrix elements of the DFA functional derivative, a local potential, and is comparable to performing a small number (about ten) of DFA calculations. Imposing these constraints, the error of the HOMO Kohn-Sham orbital energies for local and semilocal DFAs reduces to about 1 eV. For one-electron systems, the two constraints give correctly a zero Hxc potential. (3.2.18) Kronik : Following the important points raised in contributions (2.1.7) and (3.2.17), I think it is worthwhile to emphasize that piecewise linearity, freedom from self-interaction, and an asymptotically correct Kohn-Sham potential -all three of which are important principles for DFA construction -are somewhat related yet inequivalent properties of the exact density functional. 327 The IP and EA are fundamental properties of atoms, molecules and solids, which are often associated with the orbital energies via Koopmans' theorem 328 in Hartree-Fock theory or Janak theorem 87 in Kohn-Sham DFT; see contribu-tions (2.2.4), (2.4.9), and (3.2.13). However, it is well-known that relaxation and correlation effects are often important in electron detachment and attachment processes, calling for extensions to the theory. From the perspective of fractional charges, an integration approach has been developed for the double-hybrid functionals, 331 whose justification lies in the fact that they are found to fulfil better the piecewise linearity condition (see contribution (2.4.1)) and suffer less from delocalization error. 332 Furthermore, the extended Koopmans' theorem 333 (EKT) can be applied to the double-hybrid (DH) functionals, leading to the EKT-DH methods, which are shown to be capable of describing the breakdowns of the quasi-particle approximations for the inner-valence IPs, at a relatively low computational cost and a high accuracy.