which are common integrals in CI calculations. For PN-QED-CASCI, these and all subsequent integrals are performed in the canonical MO basis, whereas for CS-QED-CASCI, we transform these and all subsequent integrals to the (orthonormal) QED-HF basis. The elements of ∆ and G involve slightly different integrals for the photon number formulation as compared to the coherent state formulation. The matrix elements of ∆ in the photon number formulation are