. Thus, we have demonstrated that the cavity can offer a novel approach toward the selective isomeriza- tion of this DA reaction and that our pQED-TDDFT approach is in agreement with Ref. 4 at the QED-CCSD level. Fig. presents a more direct comparison between the pQED-TDDFT of the current work using pQED-TDDFT and that of the high-level scQED-CCSD of Ref. 4 by showing the exact QED-TDDFT and QED-CCSD TS barrier energies as well as the product energies with an interpolated spline grid portraying the rest of the potential energy surface as a schematic. In gen-eral, we find only minor quantitative differences between the two approaches that can be rationalized by the known deviations between standard CCSD and DFT methodologies, which are expected to reach 1-5 kcal/mol. Here, such deviations reach up to 3.0 kcal/mol for the Endo pathway and 2.6 kcal/mol for the Exo pathway, signifying that our pQED-TDDFT is well within the expected error of the bare manybody approach itself. More importantly, our pQED-TDDFT results portray the same qualitative behavior of the endo and exo potential energy surfaces as the scQED-CCSD for all data points except two: the X-and Z-polarization directions for the endo product energies. In the X-polarization direction, the scQED-CCSD approach predicts an increase in energy for the endo product, while our pQED-TDDFT method indicates a slight decrease. In the Zpolarization direction, the scQED-CCSD results show a minor decrease in product energy, whereas the pQED-TDDFT approach shows an increase. A more detailed analysis of these subtle differences is available in the Supporting Information. Furthermore, the differences in the QED-CCSD and pQED-TDDFT energies are less than 2 kcal/mol and well within the error expected between the standard TDDFT and CCSD methodologies and thus acceptable for our qualitative exploration of this DA reaction which, for the rest of the work, only focuses on the correctly reproduced TS barrier geometries/energies.