Fig. presents the results of molecular polaritons generated by coupling the excited electronic states of the formaldehyde molecule with a singlemode cavity for various cavity frequencies ω c and coupling strength A 0 . We chose this system and parameters based on the recent theoretical simulations in Ref. 31 using the scQED-TD-DFT scheme. Here, we use the pQED-TD-DFT procedure to obtain the polariton PES and transition density (see Theoretical Details) for the coupled moleculecavity hybrid systems. Fig. presents the two lowest-energy 1 A 1 -symmetry excited states of the formaldehyde molecule as a function of the C-O bond length, which are denoted as |ψ A 1 ⟩ and |ψ A 1 2 ⟩. They are the adiabatic states of Ĥel . The C-O bond length was scanned by changing only the location of the oxygen atom, keeping all other nuclei frozen. At the C-O bond length of 1.22 Å, these two states correspond to |ψ 4 (R)⟩ and |ψ 7 (R)⟩. At other C-O bond lengths, these two states may correspond to different labels of the adiabatic states due to the presence of other adiabatic states with a different symmetry and trivial crossings with these two states. The symmetry of the adiabtic state determines the orientation of the non-zero transition dipole. Note that there is an avoided crossing near 1.3-1.4 Å of the C-O bond, with a energy gap of roughly 75 meV (see inset) for this level of theory. Fig. ,c present the polaritonic PESs E j (R) (defined in Eq. 4) for the system in a cavity with the polarization direction ê along the C-O bond, and a cavity photon frequency of hω c = 6.5 eV (Fig. ) and hω c = 9.5 eV (Fig. ), respectively. The character of the polaritonic excited state are color coded according to the photon number in the cavity (right). In Fig. , the green-colored curve is largely composed of the photon-dressed ground state |ψ 0 (R)⟩⊗ |1⟩ ≡ |ψ 0 (R), 1⟩. Near to a C-O bond length of 1.45 Å, the |ψ 0 (R)⟩⊗|1⟩ state crosses the |ψ A 1 1 (R)⟩⊗|0⟩ state, which is an excited state with 0 photons (thick gray curve in Fig. ). The light-matter interaction (in Eq. 1) hybridizes the two states and generates the polaritonic states, with the energy splitting generated commonly referred to as the Rabi splitting. At this nuclear configuration, both polariton states contain roughly equal contributions of the excitonic and photonic character (indicated as 50% on the colorbar as black). Further, the molecule-cavity interaction produces hybridized states with mixed ground and excited adiabatic character. The original adiabatic potential energy minima located near the C-O bond length of 1.5 Å for the lower-energy ψ A 1 state (see panel a) has now been removed (see panel b). The new lowest-energy excited-state polariton now has a totally downward slope toward the same minimum location as the ground polariton state |Φ 0 (R)⟩, with nearly 100% photonic character (green color) in that region.