Exact conditions for ensemble density functional theory

Ensemble density functional theory (EDFT) offers a promising path for computing excitation energies via a theory of the ensemble density --- a weighted sum of interacting excited-state densities. Recovering excitation energies is theoretically simple, but practical application requires approximations dependent on weight choice. Here, the authors derive exact conditions for EDFT. Using an exactly solvable model, they illustrate violations of exact conditions, weight-dependent derivative discontinuities in the strong-interaction limit, and ultimately the significance of weight dependence for future functional design.