Cavity quantum electrodynamics complete active space self consistent field theory

The qualitative description of strongly correlated systems interacting with quantized cavity modes poses significant theoretical challenges due to the combinatorial scaling of electronic and photonic degrees of freedom. Recent advances addressing this complexity include quantum electrodynamics (QED) generalizations of complete active space configuration interaction (QED-CASCI) and density matrix renormalization group (QED-DMRG) methods. In this work, we introduce a QED extension of state-averaged complete active space self-consistent field theory (QED-SA-CASSCF), which incorporates cavity-induced correlations through a second-order orbital optimization framework with robust convergence properties. The implementation enables symmetry-free orbital relaxations to account for photon-mediated symmetry breaking in polaritonic systems. Numerical validation on the LiH molecule coupled to an optical cavity demonstrates that the QED-SA-CASSCF method achieves significantly improved accuracy in modeling ground-state and polariton potential energy surfaces (PESs) compared to QED-CASCI. This advancement provides a systematic approach for studying cavity-altered chemical landscapes while retaining the balance between static correlation treatment and computational feasibility inherent to multiconfigurational methods.