An improvement over the mean-field and singlereference methods can be systematically achieved by increasing the number of reference states (configuration Slater determinants). In electronic structure theory, one can achieve these by building a correlated wavefunction theory starting from HF, such as a configuration interaction (CI) approach that includes all possible singly (S) excited Slater determinants (CIS), 149 or one that includes doubly (D) excited Slater determinants (CISD), or CISD(T), etc. However, the most computationally feasible and accurate methods stem from the coupled cluster (CC) approach. In particular, CCSD, which includes up to two electronic excitation operators in principle but indirectly includes correlation from higher-level excitations due to the location of the excitation operators in an exponential function. As such, this method has been shown to systematically achieve more accurate results compared to the analogous method in CI (eg, CISD method) and sometimes even outperforms the CISDT methods. In this case, it is the most appropriate choice to extend to the QED formalism to correctly capture the correct electronic and electron-photon correlations that will result from coupling to the cavity. Even though this method is too expensive for most medium sized molecules, it provides a useful benchmark for other lower-order methods (e.g., scQED-TD-DFT ).