We explain by quantal density functional theory the physics of mapping from any bound nondegenerate excited state of Schrödinger theory to an S system of noninteracting fermions with equivalent density and energy. The S system may be in a ground or excited state. In either case, the highest occupied eigenvalue is the negative of the ionization potential. We demonstrate this physics with examples. The theory further provides a new framework for calculations of atomic excited states including multiplet structure.
Sahni, Viraht, Massa, Lou, Singh, Ranbir, Slamet, Marlina. "Quantal Density Functional Theory of Excited States." Physical Review Letters 87.11 (2001).