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 multireference character. Our results show again that so-called nonempirical DHDFs are outperformed by semiempirical 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-omega B2GP-PLYP, SOS-omega B2PLYP, SOS-omega B2GP-PLYP, SOS-omega B88PP86, SOS-RSX-QIDH, and SOS-omega PBEPP86. When comparing our functional rankings with previous studies on singlet-singlet and singlet-triplet excitations, we recommend TDA-SOS-omega B88PP86 and TDA-SOS-omega PBEPP86 as robust methods for excitation energies in general until further improvements have been achieved that surpass the chemical accuracy threshold for challenging open-shell excitations without increasing the computational effort.

Automated summary

This work is the first comprehensive study of time-dependent double-hybrid density functionals (DHDFs) for calculating doublet-doublet excitation energies. The results show that certain semi-empirical DHDFs have better performance, especially spin-scaled, range-separated DHDFs paired with the TDA.