Solvent reaction coordinate for an S$_N$2 reaction

We study the prototypical SN2 reaction Cl$^-$ + CH$_3$Cl $\to$ CH$_3$Cl + Cl$^-$ in water using quantum mechanics / molecular mechanics (QM/MM) computer simulations with transition path sampling and inertial likelihood maximization. We have identified a new solvent coordinate to complement the original atom-exchange coordinate used in the classic analysis by Chandrasekhar, Smith, and Jorgensen [Ref1]. The new solvent coordinate quantifies instantaneous solvent induced polarization relative to the equilibrium average charge density at each point along the reaction pathway. On the basis of likelihood scores and committor distributions, the new solvent coordinate improves upon the description of solvent dynamical effects relative to previously proposed solvent coordinates. However, it does not increase the transmission coefficient or the accuracy of a transition state theory rate calculation.