We first report the absolute energy error of the pPF(N el ,10) relative to PF-FCI-10 for each basis set, where N el is the number of many-electron basis states used to parameterize the pPF Hamiltonian (see Figure ). We find N p = 10 is more than sufficient to converge the photonic Fock space, and so PF-FCI-10 provides the exact energies for this system in a given orbital basis. We see that the energy error decreases as we increase N el in a given orbital basis, and also decreases with increasing size of the orbital basis. The energy error of pPF(N el ,10)/cc-pVDZ converges to ∼10 microHartrees in the limit that all of the FCI states are used to parameterize the Hamiltonian, while the energy error of pPF(N el ,10)/cc-pVQZ converges to 0.1 microHartrees in the comparable limit (see Figure ). These results are consistent with the argument that the projected dipole self approaches the exact dipole self-energy in the limit that both the orbital and many-electron basis are complete. We also note that t he fraction of electronic states needed for energy convergence increases from around 50 percent in cc-pVDZ to 80 percent in cc-pVQZ.