For example, in the coupled cluster approach, the number of Fock states (i.e., coupled cluster excitation operators) and interaction terms used dramatically increases the computational cost such that only two Fock states have been utilized in recent works, where some benchmarking has been done in model systems, effectively limiting calculations to a specific highcavity-energy regime with minimal relevant electronically excited states. In other methods, such as density functional theory, some implementations are limited to treating the electronic and photonic DOFs using the same exchange-correlation functional, which shows performance similar to that of the Hartree-Fock method. In this way, one sacrifices some part of the problem in order to treat the two parts of the system on the same footing. These current limitations can be alleviated by first solving the more complex molecular subsystem on its own before diagonalizing the full, electron-photon system giving, in principle, the exact electron-photon correlation.