Molecular dynamics of a model S N1 reaction in water

Results are presented from a computer simulation of the dynamics of a model SN1 reaction in water, very loosely based on the reaction t-BuCl→t-Bu++Cl−. Two diabatic electronic states are considered, covalent and ionic, which cross in the presence of the polar solvent. The curve crossing is treated in the electronically adiabatic limit, which gives rise to coupled reagent and solvent dynamics involving a mixed covalent/ionic adiabatic potential surface. The reaction dynamics are analyzed in terms of a simple solute reaction coordinate defined to be the t-Bu to Cl separation distance. By employing constraint dynamics techniques, the potential of mean force is determined as a function of this reaction coordinate. The time evolution of the reaction is followed in terms of the full molecular dynamics of all reagent and solvent atoms. Beginning with the largely covalently bound reactant t-BuCl, the following was observed: (i) how energy flows out of the water solvent bath into a solvent–reactant fluctuation driving the system to the top of the barrier, (ii) how barrier recrossings lower the reaction rate below the transition state theory prediction, and (iii) how the products slide down the barrier toward separated t-Bu+ and Cl−, dissipating their excess energy back into the solvent. The calculated transmission coefficient measuring the departure of the rate constant from its transition state theory value is 0.53±0.04. This is found to agree with the Grote–Hynes theory prediction, and also with its nonadiabatic solvation, frozen solvent limit, to within the estimated error bars. By contrast, Kramers’ theory incorrectly predicts a much smaller value.