In this sense, the basis states are optimized (or are allowed to respond to interactions with the photon DOFs) to achieve a minimization of the energy, subject to the underlying approximations of the theory (e.g. density functional theory). Further, the electron-electron, electron-photon, and photon-photon correlations are forced to be described on the same footing. In the following, we will focus our description to direct diagonalization techniques to achieve the exact electron-photon correlation, making use of standard electronic structure packages that have been thoroughly tested and are both freely and commercially available. In the last section (Sec. 3.2), we will briefly motivate cases where a self-consistent approach would be advantageous and outline the idea behind such schemes.