Linear free energy relationships for controlling reaction rates in optical cavities

Changes to reaction rates of chemical reactions in optical cavities due to the coupling between molecular vibrations and vacuum field fluctuations have been reported, but the field lacks theoretical explanations. In this work, we report a linear free energy relationship (LFER) derived with perturbation theory based on the permanent dipole, cavity frequency, and frequency-dependent polarizability to not only predict but also control how a reaction rate behaves in-cavity. Typically, the LFER shows that more favorable reactions occur at a faster rate (i.e. Bell-Evans-Polanyi Principle), but interestingly, we found that the cavity frequency can be tuned to cause slower reactions to be more thermodynamically favorable and vice versa. Using Time-Dependent Density Functional Theory (TDDFT), we simulated the Menshutkin, Diels-Alder, and Ullman Coupling reactions and added photons perturbatively to the reactions to modify energies. We verified the predicted LFER with these numerical results. Thus, we provide theoretical insights into how molecular permanent dipoles, polarizabilities, and the cavity frequency affect reaction rates, allowing us to predict, control, and even reverse the Bell-Evans-Polanyi Principle.