The molecular origins of nonlinear response in solute energy relaxation: the example of high-energy rotational relaxation.

A key step in solution-phase chemical reactions is often the removal of excess internal energy from the product. Yet, the way one typically studies this process is to follow the relaxation of a solute that has been excited into some distribution of excited states quite different from that produced by any reaction of interest. That the effects of these different excitations can frequently be ignored is a consequence of the near universality of linear-response behavior, the idea that relaxation dynamics is determined by the solvent fluctuations (which may not be all that different for different kinds of solute excitation). Nonetheless, there are some clear examples of linear-response breakdowns seen in solute relaxation, including a recent theoretical and experimental study of rapidly rotating diatomics in liquids. In this paper we use this rotational relaxation example to carry out a theoretical exploration of the conditions that lead to linear-response failure. Some features common to all of the linear-response breakdowns studied to date, including our example, are that the initial solute preparation is far from equilibrium, that the subsequent relaxation promotes a significant rearrangement of the liquid structure, and that the nonequilibrium response is nonstationary. However, we show that none of these phenomena is enough to guarantee a nonlinear response. One also needs a sufficient separation between the solute time scale and that of the solvent geometry evolution. We illustrate these points by demonstrating precisely how our relaxation rate is tied to our liquid-structural evolution, how we can quantitatively account for the initial nonstationarity of our effective rotational friction, and how one can tune our rotational relaxation into and out of linear response.