Kohn-Sham representability of an interacting ground-state density is its realization as the density of a noninteracting ground state in
a common local potential. Ensemble representability permits positive trace-class
density operators of trace one supported on the noninteracting ground eigenspace.
For three spinful electrons and a real spin-independent potential , the noninteracting Hamiltonian is
Penz, M.; Tellgren, E. I.; Csirik, M. A.; Ruggenthaler, M.; and Laestadius, A. "The Structure of the Density-Potential Mapping. Part
I: Standard Density-Functional Theory." ACS Phys. Chem. Au3,
334-347, 2023. https://doi.org/10.1021/acsphyschemau.2c00069.
, the noninteracting Hamiltonian is
