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, V., Massa, L., Singh, R. & Slamet, M. (2001). Quantal density functional theory of excited states. Physical Review Letters, 87(11). doi: 10.1103/PhysRevLett.87.113002