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The extrapolation technique of Savin [J. Chem. Phys. 140, 18A509 (2014)], which was initially applied to range-separated ground-state-density-functional Hamiltonians, is adapted in this work to ghost-interaction-corrected (GIC) range-separated ensemble density-functional theory (eDFT) for excited states. While standard extrapolations rely on energies that decay as μ in the large range-separation-parameter μ limit, we show analytically that (approximate) range-separated GIC ensemble energies converge more rapidly (as μ) towards their pure wavefunction theory values (μ → +∞ limit), thus requiring a different extrapolation correction. The purpose of such a correction is to further improve on the convergence and, consequently, to obtain more accurate excitation energies for a finite (and, in practice, relatively small) μ value. As a proof of concept, we apply the extrapolation method to He and small molecular systems (viz., H, HeH, and LiH), thus considering different types of excitations such as Rydberg, charge transfer, and double excitations. Potential energy profiles of the first three and four singlet Σ excitation energies in HeH and H, respectively, are studied with a particular focus on avoided crossings for the latter. Finally, the extraction of individual state energies from the ensemble energy is discussed in the context of range-separated eDFT, as a perspective.

Combining extrapolation with ghost interaction correction in range-separated ensemble density functional theory for excited states