In the right panel of Figure , we show the ground-state potential energy stretch of the LiH both outside the cavity (dashed black line) and inside the cavity. For the latter, we compute the PES using PN-QED-FCI-1 and CS-QED-FCI-1 as a minimal photonic basis and CS-QED-FCI-6 as a fully converged photonic basis based on th behavior of the mean absolute error shown in the left panel of Figure . We see that all in-cavity PESs are above the cavity-free PES as expected. We also see CS-QED-FCI-6 is a lower bound to both curves in a minimal photonic basis, which follows from the variational nature of these calculations. Consistent with the idea that the coherent state formulation provides a more efficient photonic basis, we can see that the CS-QED-FCI-1 curve lies below the PN-QED-FCI-1 curve and is visually nearly identical to the fully converged result (see Figure right panel).