A THEORETICAL-MODEL FOR S(N)1 IONIC DISSOCIATION IN SOLUTION .2. NONEQUILIBRIUM SOLVATION REACTION-PATH AND REACTION-RATE

The theoretical formulation developed in the preceding article [Kim, H. J.; Hynes, J. T. J. Am. Chem. Soc., preceding paper in this issue] is applied to determine the reaction path and rate constant for the S(N)1 ionization process in solution RX --> R+ + X-, illustrated for t-BuCl. It is found that the intrinsic solution reaction path (SRP), which is the analogue of the familiar minimum energy path of gas-phase reaction studies, differs considerably from the conventionally assumed equilibrium solvation path (ESP). In particular, the SRP near the transition state lies mainly along the RX separation coordinate r. There is little motion in the solvent coordinate s; the solvent lags the solute nuclei motion and there is nonadiabatic nonequilibrium solvation. Near the reactant configuration RX, however, the critical motion initiating the reaction is that of the solvent, i.e., the solvent orientational polarization. The contrasts with activated electron transfer are also pointed out. The connection of the two-dimensional (r, s) free energy surface to the potential of mean force is made, particularly in connection with the ionization activation free energy, as is the connection to the conventional transition-state theory (TST) rate constant k(TST), which assumes equilibrium solvation. The deviation of the actual rate constant k from its TST approximation (the transmission coefficient kappa = k/k(TST)) due to nonequilibrium solvation is examined, via both linear and nonlinear variational transition state theory. Despite the pronounced anharmonicity of the (r, s) free energy surface arising from the electronic mixing of the covalent and ionic valence bond states, a simple harmonic nonadiabatic solvation analysis is found to be suitable. This analysis predicts progressively larger and more significant departures from equilibrium solvation TST with increasing solvent polarity.