Chemical equilibrium constants in cavities beyond the single-mode approximation

Despite the plethora of theoretical studies, it is still not well-understood how Fabry-Pérot cavities change chemical reactivity. In order to make progress, we take a step back and lift some of the approximations that nearly all reactivity studies are based on, namely the single mode approximation and the neglect of Coulombic intermolecular interactions. By restraining ourselves to statistical properties, such as the equilibrium constant, we can cast the problem into the framework of discretised path integrals. This allows us to circumvent the explicit simulation of the continuum of electromagnetic modes; instead, we capture their effect in an influence functional. With this method we can calculate how adding a pair of mirrors changes the equilibrium constant of a small ensemble of molecules represented by double-well potentials. Based on what experimental features this approach can and cannot capture, we hope to shed light on which approximations are valid, and spur a systematic analysis of which thus-far neglected effects could play an important role changing chemical reactivity.