A Phenomenological Symmetry Rule for Chemical Reactivity Under Vibrational Strong Coupling

Symmetry is known to strongly influence the course of a chemical reaction. It has also been found to play a key role in vibrational strong coupling (VSC), where it can influence the outcome of chemical reactions or alter chemical equilibria. However, the precise nature of this effect and its extent remains elusive. To further explore the role of vibrational symmetry, we have investigated the equilibrium constants of different charge transfer complexes, in particular of isomers of trimethyl benzene belonging to different point groups from which a general symmetry rule emerges. We describe the strongly coupled system by a direct product of irreducible representations associated with the complexes and the cavity. As a consequence, the coupled vibration is associated with a new irreducible representation that projects differently on the reaction coordinate of the charge transfer complexation, reflecting the changes in the equilibrium constants. This phenomenological symmetry rule points to a general underlying framework for predicting the outcome of chemical reactivity under VSC.