Double Excitations in Molecules from Ensemble Density Functionals: Theory and Approximations

Double excitations, which are dominated by a Slater-determinant with both electrons in the highest occupied molecular orbital promoted to the lowest unoccupied orbital(s), pose significant challenges for low-cost electronic structure calculations based on density functional theory (DFT). Here, we demonstrate that recent advances in ensemble DFT [{\it Phys. Rev. Lett.} {\bf 125}, 233001 (2020)], which extend concepts of ground-state DFT to excited states via a rigorous physical framework based on the ensemble fluctuation-dissipation theorem, can be used to shed light on the double excitation problem. We find that the exchange physics of double excitations is reproducible by standard DFT approximations using a linear combination formula, but correlations are more complex. In passing, to analyze correlation, we extend the random-phase approximation to ensembles. We then show, using selected test systems, that standard DFT approximations may be adapted to tackle double excitations based on theoretically motivated simple formulae that employ ensemble extensions of expressions that use the on-top pair density.