3 Results and discussion correlating all electrons (including core electrons) and choosing a def2-TZVPP basis. The nature of the GS and ES reference structures was furthermore checked by performing frequency calculations and computing T 1 diagnostics. We selected these structures as highest-accuracy level reference and performed, for comparison, all-electron PBE0 calculations with the Turbomole program package, first using the def2-TZVPP basis to unravel the effect of the underlying electronic structure method and then increasing the basis set to def2-QZVPP 61 quality to get an estimate for the basis set error. Deviations of PBE0 computations with CP2K to the mentioned EOM-CCSD and PBE0 reference data originate then mainly from core shells being described in terms of pseudopotentials and correspondingly adapted basis sets. More specifically, we used pseudopotentials and basis sets which were optimized for the PBE0 functional with the numerical atom code of CP2K and which are available within the database and distribution of CP2K. To check consistency of the chosen CP2K basis sets and pseudopotentials, we investigated a hierarchy of MOLOPT as well as correlation consistent ccGRB-X basis sets. Benchmark data on vertical singlet excitation energies, geometries of the first excited state, adiabatic excitation and fluorescence energies (for PBE0, ADMM-PBE0 and sTDA kernels based on PBE0 and ADMM-PBE0 references) are given for the two basis set families in comparison to both EOM-CCSD/def2-TZVPP/Gaussian, PBE0/def2-TZVPP/Turbomole, and PBE0/def2-QZVPP/Turbomole references in the supplementary material, demonstrating that MOLOPT and ccGRB-X basis sets yield comparable accuracy and that converged results are in general obtained for triple-zeta basis sets. For the sake of convenience, we therefore restrict the following discussion to subsets of MOLOPT type basis sets, concentrating on the assessment of the mentioned excited-state properties regarding a) the accuracy of ADMM in comparison to conventional hybrid functional TDDFT as well as b) the comparison of semi-empirical sTDA and ADMM-approximated hybrid functional kernels in comparison to highly accurate EOM-CCSD reference data.