Reaction Rate Theory for Electric Field Catalysis in Solution

The application of an external, oriented electric field has emerged as an attractive technique for manipulating chemical reactions. Because most applications occur in solution, a theory of electric field catalysis requires treatment of the solvent, whose interaction with both the external field and the reacting species modifies the reaction energetics and thus the reaction rate. Here, we formulate such a transition state theory using a dielectric continuum model, and we incorporate dynamical effects due to solvent motion via Grote-Hynes corrections. We apply our theory to the Menshutkin reaction between $\mathrm{CH_3I}$ and pyridine, which is catalyzed by polar solvents, and to the symmetric $\mathrm{S_N2}$ reaction of $\mathrm{F^-}$ with $\mathrm{CH_3F}$, which is inhibited by polar solvents. At low applied field strengths when the solvent responds linearly, our theory predicts near-complete quenching of electric field catalysis. However, a qualitative treatment of the nonlinear response (i.e., dielectric saturation) shows that catalysis can be recovered at appreciable field strengths as solvent molecules begin to align with the applied field direction. The Grote-Hynes corrrection to the rate constant is seen to vary nonmonotonically with increasing solvent polarity due to contrasting effects of the screening ability, and the longitudinal relaxation time of the solvent.