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A Coulomb density is special because it determines not only its Hamiltonian but the degree of excitation as well. We derive Euler equations for excited-state energies and densities that depend only on the electron density. Unlike existing formulations, additional functions and indices are not required; with these functionals, the equations of excited-state density functional theory strongly resemble those of ground-state theory. A critical analysis of the new functionals is included.
Ayers et al. (2012) studied this question.