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Density driven correlations in ensemble density functional theory: insights from simple excitations in atoms

Ensemble density functional theory extends the usual Kohn-Sham machinery to quantum state ensembles involving ground- and excited states. Recent work by the authors [Phys. Rev. Lett. 119, 243001 (2017); 123, 016401 (2019)] has shown that both the Hartree-exchange and correlation energies can attain unusual features in ensembles. Density-driven(DD) correlations -- which account for the fact that pure-state densities in Kohn-Sham ensembles do not necessarily reproduce those of interacting pure states -- are one such feature. Here we study atoms (specifically $S$--$P$ and $S$--$S$ transitions) and show that the magnitude and behaviour of DD correlations can vary greatly with the variation of the orbital angular momentum of the involved states. Such estimations are obtained through an approximation for DD correlations built from relevant exact conditions Kohn-Sham inversion, and plausible assumptions for weakly correlated systems.