To illustrate the convergence behavior of the photon basis, we first consider doing PN-QED-FCI and CS-QED-FCI on the bond stretch of the LiH diatomic molecule in a 6-311G basis. We consider this system coupled to a photon with energy tuned to the lowest singlet excitation (hω = 3.29 eV) and with λ z = 0.05 atomic units, polarized along the internuclear axis (see Figure ). We choose this large value of the field to draw out a clear difference in the convergence behavior of the photon number and coherent state formulations. To explore this convergence behavior, the maximum photon occupation number is systematically increased from N p = 1 to N p = 10, where we could gauge that the photon space is fully converged by N p = 6 since the further increase of N p does not change the energies of any of the eigenvalues to within the convergence criteria of the Davidson solver (≈ 10 -9 Hartrees). We examine the mean absolute error of the PES computed using PN-QED-FCI-N p and CS-QED-FCI-N p as a function of N p , and we see that this error is an order of magnitude smaller for the minimal photonic basis in the coherent-state formulation (see Figure right panel). We see that the error decreases approximately linearly as a function of the size of the photonic basis for both formulations, with both approaching the convergence threshold of our Davidson solver by N p ≈ 6 (see Figure right panel). We use CS-QED-FCI-10 as the exact benchmark for computation of the mean absolute errors displaced in the left panel of Figure .