The paper introduces a new theoretical approach called Cavity Quantum Electrodynamics Complete Active Space Configuration Interaction (QED-CASCI) to study molecular polaritons, which are excited states of molecules coupled to quantized photon fields. This method aims to provide a rigorous and balanced description of strong correlation effects between electronic and photonic degrees of freedom. The authors present two formulations of QED-CASCI: one using photon number (PN) states and the other using coherent states (CS). They demonstrate the accuracy of the method through benchmark calculations on model systems, showing that the coherent state formulation converges faster and provides more accurate results compared to the photon number formulation. The study also explores the impact of active space size and photon basis completeness on the accuracy of the method, highlighting the importance of a large active space and a fully converged photon basis. The results are validated using benchmark calculations on systems like LiH, H₂O²⁺, BH₃, and C10H8, demonstrating the method's ability to capture the essential phenomenology of molecular polaritons.The paper introduces a new theoretical approach called Cavity Quantum Electrodynamics Complete Active Space Configuration Interaction (QED-CASCI) to study molecular polaritons, which are excited states of molecules coupled to quantized photon fields. This method aims to provide a rigorous and balanced description of strong correlation effects between electronic and photonic degrees of freedom. The authors present two formulations of QED-CASCI: one using photon number (PN) states and the other using coherent states (CS). They demonstrate the accuracy of the method through benchmark calculations on model systems, showing that the coherent state formulation converges faster and provides more accurate results compared to the photon number formulation. The study also explores the impact of active space size and photon basis completeness on the accuracy of the method, highlighting the importance of a large active space and a fully converged photon basis. The results are validated using benchmark calculations on systems like LiH, H₂O²⁺, BH₃, and C10H8, demonstrating the method's ability to capture the essential phenomenology of molecular polaritons.