A Meta-Generalized Gradient Approximation for the Cavity-Dependent Exchange-Correlation Interaction in Strongly...

Strong light-matter coupling in optical cavities enables the manipulation of chemical and physical properties without altering molecular composition. Theoretical modeling of such phenomena requires exchange-correlation (XC) functionals that account for both electron-electron and electron-photon (ep) interactions within quantum electrodynamical density functional theory (QEDFT). In this work, we develop a meta-generalized gradient approximation (meta-GGA) specifically targeting the cavity-dependent XC interaction in strongly coupled light-matter systems. This novel approximation is built upon a new semilocal polarizability approximation, which draws from the jellium-with-a-gap model, and can be extended to a "global hybrid" variant that goes beyond the isotropic model from previous approximations. The polarizability model yields significantly improved dispersion coefficients and benchmark calculations with the cavity-dependent XC functional demonstrate improved agreement with QED Hartree-Fock (QED-HF) reference energies. Application to the regioselectivity of brominated nitrobenzene intermediates reveals the functional's capacity to capture cavity-induced energetic shifts. Our results advance the Jacob's ladder of functionals for QEDFT and provide a practical tool for modeling polaritonic chemistry.