Specifically, we monitor the total number of determinants comprising Eq. 7, the memory size of the σ and CI vectors, and the total time required to converge eigenstates for a series of CS-QED-CASCI(12,12)-N p /cc-pVDZ calculations. For each calculations, we set hω = 5.92 eV, λ = (0, 0.01, 0) a.u., and solve for the 5 lowest roots of the Hamiltonian. As expected, the number of determinants increases linearly with the size of the photonic basis, specifically as (N p + 1) × N e det where N e det is the number of determinants in the electronic subspace that is determined by a given active space size (see Table ). The size of σ and CI vectors are calculated for the iteration when the maximum size of the subspace is reached during the Davidson iterations; we set the threshold for this maximum value to be 12 for all calculations reported in Table , which limits the total size of these vectors to be proportional to 12 × 5 × (N p + 1) × N det , where 5 again comes from the number of roots being solved for. The time to solution tends to be close to linear with the total number of determinants, with the longest time to solution of < 4 hours seen for the N p = 100 case (see Table ).