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 spatial `step' structures in exact xc potential which are necessary describe dissociation and electron excitation with Kohn-Sham (KS) system. Via discontinuity derivative as a function number I derive analytic expressions terms KS single-particle energies for height step between variety open- closed-shell atoms within stretched molecules.