Regarding the performed benchmark, a coupling parameter with a default value of a EX = 0.2 was chosen for the exchange contribution for sTDA computations throughout the following discussion. As noted in the supplementary information (SI), adjustments only had to be made in the case of Formylchloride to avoid dissociation upon ES geometry optimization. A default value for a EX might not correspond to an optimal choice, but a thorough and careful optimization of a EX for the investigated benchmark sets and the assessed extended materials is beyond the scope of this work. The general idea of ADMM is to reduce computational costs of the exact exchange contribution by trading in basis-set incompleteness with a GGA correction term. The introduced error is then, however, dependent on both the auxiliary basis-set size as well as the chosen exchange density functional. To discriminate between the two error sources, the discussed ADMM calculations for the molecular benchmark set are performed without correction. An optimally chosen GGA exchange functional contribution could improve the discussed results, with the latter representing thus the lowest limit for the ADMM accuracy. It was e.g. shown in Ref. that exchange functionals like KT3X and OPTX improve over PBEX for ground-state properties, but analogous investigations for the excited state are left for future work. For the subsequently discussed assessment of computational timings for periodic systems, we however included a PBEX exchange functional correction to account for the additionally required resources.