Is the Kohn-Sham Oscillator Strength Exact at the Ionization Threshold?

It is well-established that the highest occupied orbital of the exact Kohn-Sham potential of any system is at -I, where I is the ionization energy. Therefore, in optical response, the non-interacting Kohn-Sham electrons in the ground-state potential have a first ionization threshold that exactly matches that of the real system[1]. We show that corresponding the Kohn-Sham oscillator strength is not exact at the first ionization threshold by explicit demonstration for the helium atom. We use a simple fit of the entire photoabsorption spectrum of both the Kohn-Sham potential for helium and that of real helium. We use oscillator strength sum rules[2] to determine the fit parameters, so this fit should be generally useful. [1] M. A. L. Marques, C. A. Ullrich, F. Nogueira, et al. Time-Dependent Density Functional Theory. Springer-Verlag, Berlin, 2006 [2] U. Fano and J. W. Cooper. Rev. Mod. Phys., 40(3), 441-507, 1968