Nonlinear, nonpolar solvation dynamics in water: The roles of electrostriction and solvent translation in the breakdown of linear response

The fact that the motion of solvent molecules defines the reaction coordina te for electron-transfer and other chemical reactions has generated great i nterest in solvation dynamics, the study of how the solvent responds to cha nges in a solute's electronic state. In the limit of linear response (LR), when the perturbation caused by the solute is "small", the relaxation of th e excited solute's energy gap should behave identically to the relaxation d ynamics of the unperturbed solute following a natural fluctuation of the ga p away from equilibrium. Despite the fact that the addition of a fundamenta l unit of charge to a small salute results in a solvation energy that is te ns or hundreds of kT, computer simulations of solvation dynamics have found , with only a few exceptions, that LR is obeyed for changes in solute charg e. Essentially none of this work, however, accounts for the fact that the s olutes in real chemical reactions undergo changes in size and shape as well as in charge distribution. In this paper, we compare the results of molecu lar simulations of polar and nonpolar solvation dynamics for a simple Lenna rd-Jones solute in a flexible-water solution to explore the validity of LR. We find that, when short-range forces are involved, LR breaks down dramati cally: both the inertial and diffusive components of the relaxation differ from those predicted by LR. For increases in solute size, expansion of the solute drives the first-shell solvent molecules into the second shell. The resulting nonequilibrium relaxation takes advantage of translation-rotation coupling that does not occur at equilibrium, resulting in faster solvation than that predicted by LR. Decreases in solute size, on the other hand, re sult in inward translational motions of solvent molecules that affect the s olute's energy gap by destabilizing the energy of the (unoccupied) ground s tate. The inward motions involved in the nonequilibrium relaxation are not present at equilibrium because the destabilization of the ground state is m uch larger than kT. Because the energetically most important solvent molecu les, those closest to the solute, are just as likely to be moving away from the solute as toward it at the time of excitation. solvation for decreases in size is much slower than predicted by LR. In the most realistic cases, when both the size and the charge of the solute change, the solvent transla tional motions resulting from the size change and those resulting from elec trostriction, the net ion-dipole attraction between the charged solute and the polar solvent, combine in an additive fashion. When the solute both gai ns a charge and expands, the translational motions resulting from electrost riction nearly cancel these from the outward solute expansion so that rotat ional motions dominate the solvent response; the smell net expansion that r emains results in only a minor breakdown of LR. The additional inward solve nt translations beyond those required by electrostriction, which are necess ary when the solute becomes charged and its size decreases, on the other ha nd, result in a severe breakdown of LR. All of the results are compared wit h previous experimental and theoretical studies of solvation dynamics, and the implications for solvent-driven chemical reactions are discussed.