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The standard description of cavity-modified molecular reactions typicallyinvolves a single (resonant) mode, while in reality the quantum cavity supportsa range of photon modes. Here we demonstrate that as more photon modes areaccounted for, physico-chemical phenomena can dramatically change, asillustrated by the cavity-induced suppression of the important and ubiquitousprocess of proton-coupled electron-transfer. Using a multi-trajectory Ehrenfesttreatment for the photon-modes, we find that self-polarization effects becomeessential, and we introduce the concept of self-polarization-modifiedBorn-Oppenheimer surfaces as a new construct to analyze dynamics. As the numberof cavity photon modes increases, the increasing deviation of these surfacesfrom the cavity-free Born-Oppenheimer surfaces, together with the interplaybetween photon emission and absorption inside the widening bands of thesesurfaces, leads to enhanced suppression. The present findings are general andwill have implications for the description and control of cavity-drivenphysical processes of molecules, nanostructures and solids embedded incavities.

Effect of Many Modes on Self-Polarization and Photochemical Suppression in Cavities