Microscopic description of nonadiabatic, nonequilibrium, and equilibrium solvations for solvated cluster reactions: (H2O)nCl−+CH3Cl→ClCH3+Cl−(H2O)n

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Abstract
A microscopic theory was presented for each of the nonadiabatic‐ and equilibrium‐solvation regimes in microsolvated cluster reactions to examine nonequilibrium‐solvation effects, and applied to the S N 2 reactions: (H2O) n Cl−+CH3Cl→ClCH3+Cl−(H2O) n for n=0–4. To have pictures for nonadiabatic and equilibrium solvations, the potential‐energy surface of the reacting system on the transition‐state region was described with effective normal coordinates defined in each of these solvation limits. The solute dynamics in each of these solvation limits was considered to be determined by the effective frequencies characterizing the motions along the corresponding normal coordinates, and a rate‐constant expression was approximately derived. Ab initio molecular‐orbital calculations were carried out for the microsolvated S N 2 reactions, and the ratio of nonadiabatic‐ to equilibrium‐solvation rate constants was evaluated. It was found that the ratio provides a better approximate value of a transmission coefficient that corresponds to the ratio of the nonequilibrium‐ to equilibrium‐solvation rate constants, for the larger values of number of microsolvated waters. It was supported that the nonadiabatic‐solvation picture appropriately characterizes the dynamics on the transition‐state region in such a reaction that the time scale of the reaction is very short compared to the motions of solvent reorganization. Furthermore, the finding that the transmission coefficients were quite small gave us a new understanding of the importance of the nonequilibrium‐solvation effect. In addition, the activation free energy for the microsolvated reaction in the case of n=4 was found unexpectedly to give most of the activation free energy for the corresponding solution reactions.