Theoretical investigations play a crucial role in understanding new principles in this emerging field and have suggested interesting reaction mechanisms enabled by cavity quantum electrodynamics (QED). 9, In recent works, traditional electronic structure methods have been generalized to include the effects of light-matter interactions and used to solve the polaritonic states of the moleculecavity hybrid systems. To name a few, these efforts include the cavity QED density functional theory (QED-DFT), time-dependent DFT (QED-TD-DFT), coupled cluster (QED-CC) and its equation-of-motion extension (QED-EOM-CC), or full configuration interaction (FCI) methods. In this way, the light and matter description are calculated on the same footing in their respective methodologies, where the to-tal polariton wavefunction is expressed as the linear combination of different configurations (e.g., Slater determinants of single-particle states), with each configuration composed as a tensor product of the electronic configuration and the photonic configuration. In this work, these schemes will be denoted as self-consistent quantum electrodynamical (scQED) methods.