Time-independent density functional theory for degenerate excited states of Coulomb systems

In this third paper of a series [Refs. Ayers–Levy–Nagy (Phys Rev A 85:042518, 2012; J Chem Phys 143:191101, 2015) are papers I and II], time-independent universal functionals of ensemble densities are identified for individual degenerate excited levels of Coulomb systems. We prove that the ensemble Coulomb densities determine not only the Hamiltonian but also the degree of excitation. The Euler equation depending on only the ensemble density of the given degenerate excited level is derived. The corresponding non-interacting system is shown, and the appropriate system of Kohn–Sham equations is derived.