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Based on the work of Gorling and that of Levy and Nagy, density-functionalformalism for many Fermionic excited-states is explored through a careful andrigorous analysis of the excited-state density to external potential mapping.It is shown that the knowledge of the ground-state density is a must to fix themapping from an excited-state density to the external potential. This is theexcited-state counterpart of the Hohenberg-Kohn theorem, where instead of theground-state density the density of the excited-state gives the true many-bodywavefunctions of the system. Further, the excited-state Kohn-Sham system isdefined by comparing it's non-interacting kinetic energy with the true kineticenergy. The theory is demonstrated by studying a large number of atomicsystems.Comment: submitted to J. Chem. Phy

Exploring foundations of time-independent density functional theory for excited states