In each case, we used photon energies tuned to the analogous optically-allowed transition at the corresponding CASCI(N el , N orb )/6-31G level of theory: hω = 13.65 eV for CASCI(6,7)/6-31G, hω = 13.25 eV for CASCI(6,11)/6-31G, and hω = 13.09 eV for CASCI(6,14)/6-31G. As all of these levels of theory will result in different absolute energies of the polariton states, we compare the Rabi splitting energy (defined as the difference between the upper polariton and lower polariton energies) at each level of theory to the CS-QED-FCI-1/6-31G Rabi splitting for all values of λ y > 0 (see Figure right panel); the Rabi splitting error goes to 0 by definition with λ y = 0. In this system, we see very little difference between the computed Rabi splitting in the photon number and coherent state representations for a given QED-CASCI active space size (see Figure right panel). However, we do see that the error in the Rabi splitting is rather sensitive to the size of the active space, with the largest (6,14) active space having consistently the smallest error in the Rabi splitting, with errors around 1 meV/36 microHartrees at the strongest coupling strength (λ y = 0.05 a.u.). By contrast, the smallest active space (6,7) approaches errors in the Rabi splitting of around 0.1 eV/3.6 mHartree at the strongest coupling strength. The strong dependence of the Rabi splitting error on the active space size suggests that the inclusion of many-body correlation effects along with electron-photon coupling can impact the ability to capture the essential phenomenology of molecular polaritons.