Approximately Self-Consistent Ensemble Density Functional Theory: Toward Inclusion of All Correlations.

Recent theory developments in ensemble density functional theory (EDFT) promise to bring decades of work for ground states to the practical resolution of excited states, provided newly discovered "density-driven correlations" can be dealt with and adequate effective potentials can be found. This Letter introduces simple theories for both and shows that EDFT using these theories outperforms ΔSCF DFT and time-dependent DFT for low-lying gaps in most of the small atoms and molecules tested, even when all use the same density functional approximations. It thus establishes EDFT as a promising tool for low-cost studies of low-lying excited states and provides a clear route to practical EDFT implementation of arbitrary functional approximations.