Assessing recent time-dependent double-hybrid density functionals on doublet-doublet excitations

This work is the first thorough investigation of time-dependent double hybrid density functionals (DHDFs) for the calculation of doublet- doublet excitation energies. It sheds light on the current state-of-the-art techniques in the field and clarifies if there is still room for future improvements. Overall, 29 hybrid functionals and DHDFs are investigated. We separately analyze the individual impacts of the Tamm-Dancoff approximation (TDA), range separation, and spin-component/opposite scaling (SCS/SOS) on 45 doublet-doublet excitations in 23 radicals before concluding with an overarching analysis that includes and excludes challenging excitations with double-excitation or multi-reference character. Our results show again that so-called ’non-empirical’ DHDFs are outperformed by semi-empirical ones. While the best assessed functionals are DHDFs, some of the worst are also DHDFs and outperformed by all assessed hybrids. SCS/SOS is particularly beneficial for range-separated DHDFs. Spin-scaled, range-separated DHDFs paired with the TDA belong to the best tested methods here and we particularly highlight SCS-ωB2GP-PLYP, SOS-ωB2PLYP, and SOS- ωB2GP-PLYP, SOS-ωB88PP86, SOS-RSX- QIDH, and SOS-ωPBEPP86. When comparing our functional rankings with previous studies on singlet-singlet and singlet-triplet excitations, we recommend TDA-SOS-ωB88PP86 and TDA-SOS-ωPBEPP86 as robust methods for excitation energies in general until further improvements have been achieved that surpass the chemical accuracy threshold for challenging ex- citations without increasing the computational effort.