for a Kohn-Sham calculation with E DFA xc [ρ σ s (r)] and also for a generalized Kohn-Sham calculation with E DFA xc [ρ σ s (r , r)] in the work of Cohen, Moris-Sanchez and Yang (Rows 2 and 4 in Table ). Note that these identifications are based on the assumption that E DFA xc [ρ σ s (r)] and E DFA xc [ρ σ s (r , r)] have an explicit and continuous dependence on its variables ρ σ s (r) and ρ σ s (r , r). But no locality is assumed. With these identifications, the use of HOMO/LUMO energy to approximate -I/ -A was then established, building on the PPLB condition for fractional number of electrons and its results for chemical potentials. The quality of the approximation of ε H to -I and/or ε L to -A just reflects the quality of the DFAs used, where the delocalization error of the DFA plays a key role; see contribution (2.2.15).