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

Abstract

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.

Time-dependent fluorescence in nanoconfined solvents: Linear-response approximations and Gaussian statistics

“…The agreement is better at shorter times. The dynamic linear-response approximation, C g (t), describes the ∼150 fs inertial solvation dynamics quite well, consistent with previous reports for other models 9,14,15 and attributed to the similarity between the nonequilibrium inertial motion and the equilibrium dynamics in the ground state. An intermediate time scale in the solvation dynamics corresponding to diffusive solvent reorientation, is also reasonably represented in the linear response results, though its amplitude is not.…”

“…linear-response behavior. 8,9 By a detailed examination of the trajectories, it was possible to identify a distinct transition in dynamics when the CN rotor pushed an argon atom out of the first solvation shell. The dynamics prior to this event are well described by linear response while those following it are not.…”

On the connection between Gaussian statistics and excited-state linear response for time-dependent fluorescence

“…͑8͔͒, which assumes that the excited-state dynamics are not far removed from the ground-state dynamics. 8,13,18 This implies that the approximation may have a wider validity for complex systems-e.g., timedependent fluorescence in nanoconfined solvents where the ground-and excited-state statistics can be dramatically different due to the dependence of the solute position on the electronic state-than indicated by the traditional linearresponse approximation.…”

“…[8][9][10][11][12][13] Such cases are sometimes considered to represent a breakdown of the linear-response approximation, though, for example, Tao and Stratt argue, but do not prove, that a stronger condition is more appropriate-one based on whether the energy gap exhibits Gaussian statistics, since "linear-response predictions are obeyed exactly if the liquid fluctuations obey Gaussian statistics." 13 Skaf and Ladanyi found that the linear-response approximation can be unsatisfactory even when the ground-and excited-state correlation functions are the same. 14 Since the derivation of the excitedstate correlation function from Eq.…”

Reactivity and Dynamics at Liquid Interfaces

“…The difference between equilibrium and non-equilibrium rotational relaxation reflects, in part, the difference between the equilibrium structure of the solutesolvent complex. 468,483 The insight gained from studying a simple diatomic solute has been useful for understanding the rotational behavior of large dye molecules. 484 Let us now consider the reorientation dynamics at the liquid/liquid interface.…”