All electronic structure computations were executed using the QCHEM software package. We employed the parametrized quantum electrodynamics time-dependent density functional theory (pQED-TD-DFT) approach with the ωB97XD hybrid exchange-correlation functional and the 6-311+G** basis set. The cavity polarization direction ê's alignment with a specific molecular axis, either ê = X or ê = Y, or ê = Z; the example orientation is illustrated in Fig. . Accordingly, the matrix elements ⟨ψ α | μ • X|ψ γ ⟩ and ⟨ψ α | μ • Y|ψ γ ⟩ are input for the interaction term μ • ê and for the DSE term. For the cavity polarization direction ê with respect to the X, Y, and Z directions of the molecule (see Fig. ), the interaction term follows the relationship ê • μ = sin θ cos ϕ X • μ + sin θ sin ϕ Y • μ + cos θ Z • μ. Both ground state energies and electron density differences were determined using the QCHEM package. Results and Discussions.