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 coordinate for electron-transfer and other chemical reactions has generated great interest in solvation dynamics, the study of how the solvent responds to changes 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 the excited solute's energy gap should behave identically to the relaxation dynamics of the unperturbed solute following a natural fluctuation of the gap away from equilibrium. Despite the fact that the addition of a fundamental unit of charge to a small solute results in a solvation energy that is tens or hundreds of kT, computer simulations of solvation dynamics have found, with only a few exceptions, that LR is obeyed for changes in solute charge. Essentially none of this work, however, accounts for the fact that the solutes in real chemical reactions undergo changes in size and shape as well as in charge distribution. In this paper, we compare the results of molecular simulations of polar and nonpolar solvation dynamics for a simple Lennard-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 dramatically: 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, result in inward translational motions of solvent molecules that affect the solute's energy gap by destabilizing the energy of the (unoccupied) ground state. The inward motions involved in the nonequilibrium relaxation are not present at equilibrium because the destabilization of the ground state is much larger than kT. Because the energetically most important solvent molecules, 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 translational motions resulting from the size change and those resulting from electrostriction, the net io