Time-Dependent Long-Range-Corrected Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling: A Comprehensive Analysis of Singlet–Singlet and Singlet–Triplet Excitation Energies

Following the work on spin-component
and spin-opposite scaled (SCS/SOS)
global double hybrids for singlet–singlet excitations by Schwabe
and Goerigk [J. Chem. Theory
Comput. 2017, 13, 4307−4323] and our own works on new
long-range corrected (LC) double hybrids for singlet–singlet
and singlet–triplet excitations [J. Chem. Theory Comput. 2019, 15, 4735−4744 and J. Chem. Phys. 2020, 153, 064106], we present new LC double hybrids with
SCS/SOS that demonstrate further improvement over previously published
results and methods. We introduce new unscaled and scaled versions
of different global and LC double hybrids based on Becke88 or PBE
exchange combined with LYP, PBE, or P86 correlation. For singlet–singlet
excitations, we cross-validate them on six benchmark sets that cover
small to medium-sized chromophores with different excitation types
(local-valence, Rydberg, and charge transfer). For singlet–triplet
excitations, we perform the cross-validation on three different benchmark
sets following the same analysis as in our previous work in 2020.
In total, 203 excitations are analyzed. Our results confirm and extend
those of Schwabe and Goerigk regarding the superior performance of
SCS and SOS variants compared to their unscaled parents by decreasing
mean absolute deviations, root-mean-square deviations, or error spans
by more than half and bringing absolute mean deviations closer to
zero. Our SCS/SOS variants are shown to be highly efficient and robust
for the computation of vertical excitation energies, which even outperform
specialized double hybrids that also contain an LC in their perturbative
part. In particular, our new SCS/SOS-ωPBEPP86 and SCS/SOS-ωB88PP86
functionals are four of the most accurate and robust methods tested
in this work, and we fully recommend them for future applications.
However, if the relevant SCS and SOS algorithms are not available
to the user, we suggest ωPBEPP86 as the best unscaled method
in this work.