Dimensional dependence of a molecular-polariton mode number

Abstract

Vibrational and electronic strong coupling of light with molecular excitations has shown promise for modifying chemical reaction rates. However, the Tavis–Cummings model often used to model such polaritonic chemistry considers only a single discrete cavity mode coupled with the molecular modes, while experimental systems generally consist of a larger number of molecules in cavities with a continuum of modes. Here, we model the polaritonic effects of multimode cavities of arbitrary dimensions and filled with a large number of molecules. We obtain the dependence of the effects on the dimensionality of the cavity, the molecular oscillator strength, and molecular concentration. Combining our model with the transition state theory, we show that polaritonic effects can be altered by a few orders of magnitude compared to including only a single cavity mode, and that the effect is stronger with a larger molecular dipole moment and molecular concentration. However, the change remains negligibly small for realistic chemical systems due to the large number of dark states.