Comparison of excitation energies from perturbative Ensemble Density Functional Theory approaches in real space

Ensemble density functional theory (EDFT) is promising as an alternative to time-dependent density functional theory (TDDFT) for low-cost prediction of excitation energies and can handle double excitations more naturally. In particular, two perturbative approaches are the Direct Ensemble Correction (DEC), which has been tested on model systems and atoms [Yang et al., Phys. Rev. Lett. 119, 033003 (2017)], and the Ensemble "HOMO-LUMO gap" (or pEDFT), which has been benchmarked on small molecules [Gould et al., Phys. Chem. Lett. 13, 2452-2458 (2022)]. To assess how these EDFT based approaches handle more complicated systems, we implement these methods in the real-space Octopus code, which allows calculations of not only bigger systems, but also small model systems for comparison. Octopus has support for different theory levels and a variety of exchange-correlation functionals. We calculate excited states from DEC and pEDFT for various benchmark systems, and we compare results and convergence characteristics in real space to other standard excited-state approaches like linear-response TDDFT and TD Hartree-Fock.