Density-functional tight binding meets Maxwell: unraveling the mysteries of (strong) light-matter coupling...

Controlling chemical and material properties through strong light-matter coupling in optical cavities has gained considerable attention over the past decade. However, the underlying mechanisms remain insufficiently understood, and a significant gap persists between experimental observations and theoretical descriptions. This challenge arises from the intrinsically multiscale nature of the problem, where nonperturbative feedback occurs across different spatial and temporal scales. Collective coupling between a macroscopic ensemble of molecules and a photonic environment, such as a Fabry-Pérot cavity, can strongly influence the microscopic properties of individual molecules, while microscopic details of the ensemble in turn affect the macroscopic coupling. To address this complexity, we present an efficient computational framework that combines density-functional tight binding (density-functional tight binding (dftb)) with finite-difference time-domain (finite-difference time domain (fdtd)) simulations of Maxwell's equations (dftb + Maxwell). This approach allows for a self-consistent treatment of both the cavity and the microscopic details of the molecular ensemble. We demonstrate the potential of this method by tackling several open questions. First, we calculate nonperturbatively two-dimensional spectroscopic observables that directly connect to well-established experimental protocols. Second, we provide local, molecule-resolved information within collectively coupled ensembles, which is difficult to obtain experimentally. Third, we show how cavity designs can be optimized to target specific microscopic applications. Finally, we outline future directions to enhance the predictive power of this framework, including extensions to finite temperature, condensed phases, and correlated quantum effects. The dftb + Maxwell method enables real-time exploration of realistic chemical parameters on standard computational resources and offers a systematic approach to bridging the gap between experiment and theory.