Fig. (ii) examines the effects on the product energy ∆E p = E 0 (R Prod ) -E 0 (R Reac ) on the polariton ground state |Φ 0 (R)⟩ as a function of coupling strength A 0 with the same cavity frequency of ω c = 3.0 eV. The effects of the cavity for the product energy are reduced for the X-polarization, in comparison to the TS, while increased for the Z-polarization. Similarly to the TS geometry, the X-polarization presents a continuous increase to the energy while the Z-polarization shows a slight decrease. The influence of the Z-polarized cavity on ∆E ‡ (panel b(i)) and ∆E p (panel b(ii)) obtained from the pQED-TD-DFT calculation is also consistent with the previous work using the scQED-CC approach. In particular, with the Zpolarization and a coupling strength of A 0 = 0.22 a.u., the difference between the prediction of ∆E ‡ obtained from the pQED-TD-DFT and scQED-CC methods is less than 10 meV. For ∆E p , the difference between the two methods is less than 5 meV. This further exemplifies that the pQED-TD-DFT method and the scQED-CC methods provide the same quantitative description for the prediction of ∆E p and ∆E ‡ , without the additional effort of developing new DFT functionals. That said, the accuracy of the electronic structure method (which provide the electronic energy and transition dipole moments, see Fig. ) do play an important role role for providing accurate polariton eigenstates.