To further provide a benchmark of our QED-TDDFT approach against that of the high-level QED-CCSD provided in Ref. 4, Fig. and Fig. explore the X-, Y-, and Z-directions of cavity field polarization using the TS geometries provided in Ref. 4. Fig. shows the TS barrier height E ‡ = E 0 (R TS ) -E 0 (R reac ) in the ground polaritonic state |Φ 0 (R)⟩ as a function of the light-matter coupling strength A 0 for the three primary cavity field polarization directions, (blue) X, (orange) Y, and (green) Z, for the (a) endo and (b) exo isomers. In both the endo and exo pathways (Fig. ), the TS barrier increases for the X-polarized cavity (blue curve) by 7.2 kcal/mol and 6.7 kcal/mol at A 0 = 0.3 a.u., respectively, compared to outside the cavity (A 0 = 0.0 a.u.). The X-polarized cavity is not expected to offer selectivity for this reaction due to the simultaneous and unfavorable increase in TS barrier energy for the two isomers. In contrast, the Y-direction shows a decreases in both the endo (5.3 kcal/mol) and exo (1.3 kcal/mol) pathways. The endo isomer exhibits an additional 3.0 kcal/mol reduction in the TS barrier compared to the exo isomer, thus offering a significant selectivity toward the endo isomer. The Z-direction also offers a cavitymediated selectivity, now favoring the exo isomer. In this case, the endo isomer's TS barrier is increased by 1.5 kcal/mol while the exo barrier height is decreased by 1.8 kcal/mol, generating a 3.3 kcal/mol difference in TS barrier height between isomers. In the Y-and Z-polarization cases, we expect the endo product yields to be P endo = exp[-E ‡ endo /k B T ]/Z = 99.9% and 0.4%, respectively, where