Time-independent (static) density-functional theories for pure excited states: Extensions and unification

Time-independent density-functional theoretic approaches to pure excited states are considered, with special emphasis on the extensions of the constrained search to excited states. Links between the Levy-Nagy and Gorling formulations are revealed. The excited-state analog of the Legendre-transform functional for ground states is constructed. Powerful results for Coulombic systems may facilitate the construction of an excited-state density functional with a simple and universal form.