Second, further to the discussion about the Kohn-Sham system, we should keep in mind that, for a single electron, the Kohn-Sham excitation energies equal the exact ones, while the Kohn-Sham electron addition energies are different from the exact ones. So we may expect that, for certain systems, there is a reasonable correspondence for the excitation energies. It is far from obvious that this would also hold true in extended systems with many electrons, and, of course, the Kohn-Sham gap does not equal the optical gap in general. The Kohn-Sham band structure is nevertheless a powerful starting point for calculations using, for example, one-and two-body Green's functions.