Stationary conditions for excited states: the surprising impact of density-driven correlations

Typical density functional theory (DFT) and approximations thereto solve the many-electron ground state problem by working from a non-interacting Kohn-Sham reference system. In practice, DFT benefits from useful minimization conditions that let approximate solutions iteratively approach the optimal energy and density. The present work reveals that stationary conditions also apply to all excited states of general electronic systems; and may be defined straightforwardly from ensemble extensions of DFT. However, it also reveals that the stationary condition for the non-interacting Kohn-Sham reference systems that make density functional theory numerically efficient is more complex than the ground state problem. The extra complexity reflects a contribution from density-driven correlations. Some implications for approximations and self-consistency are discussed.