Exact expressions for the height of the interatomic step in the exchange-correlation potential from the derivative discontinuity of the energy

Popular approximations to the exchange-correlation (xc) energy of density functional theory do not yield the spatial `step’ structures in the exact xc potential which are necessary to describe dissociation and electron excitation with the Kohn-Sham (KS) system. Via the discontinuity in the derivative of the xc energy as a function of electron number I derive exact analytic expressions in terms of the KS single-particle energies for the height of the step in the xc potential between a variety of open- and closed-shell atoms within stretched molecules.