find that at FCI/6-31G level, the third singlet excited-state with an excitation energy of 13.07 eV has a strong transition dipole moment oriented along the y-axis in the coordinate system illustrated in Figure . We first compute the polariton energies at the CS-QED-FCI-1/6-31G level (see Figure ) for a range of coupling strengths up to λ y = 0.05 a.u. We then computed the polariton energies at the same coupling strengths at the QED-CASCI-1(6,14)/6-31G, QED-CASCI-1(6,11)/6-31G and QED-CASCI-1(6,7)/6-31G in both photon number and coherent state representations.