Nonlinear, Nonpolar Solvation Dynamics in Water:  The Roles of Electrostriction and Solvent Translation in the Breakdown of Linear Response

Abstract

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 ion-dipole attraction between the charged solute and the polar solvent, combine in an additive fashion. When the solute both gains a charge and expands, the translational motions resulting from electrostriction nearly cancel those from the outward solute expansion so that rotational motions dominate the solvent response; the small net expansion that remains results in only a minor breakdown of LR. The additional inward solvent translations beyond those required by electrostriction, which are necessary when the solute becomes charged and its size decreases, on the ...

Solvation Dynamics in Water: 2. Energy Fluxes on Excited- and Ground-State Surfaces

“…13-which allows the frequency shift Eq.5 to be expressed exclusively in terms of real work contributions-is quite similar in character to approximations commonly used in "linear response theory" discussions of the frequency shift, particularly in a time correlation function context. [1][2][3][4][5][6][7][8][9][10][11][12][13][14]17,26,32,33 We will see in Section III C that the approximation works reasonably well even for the relatively challenging 17 case of a single localized charge extinction. Equation 14 shows that the experimental frequency shift can be understood (approximately) in terms of a sum of two real work contributions.…”

“…[17][18][19][20][21][22][23][24][25][26][27][28][29] Thanks to this system's simplicity, the frequency shift is identical to the excited state ion-water solvent Coulomb energy. Consequently, the resulting excess energy's time variation could be readily expressed in terms of a sum of contributions of work on the solvent (and solute) configurational degrees of freedom.…”

Solvation Dynamics in Liquid Water. 1. Ultrafast Energy Fluxes

“…It is to be noted that, besides its qualitative character, this tcf approach suffers from additional limitations. Most importantly, it invokes the validity of linear response theory, which is an issue to consider here, given the large perturbations inherent to the creation or alteration of a charge distribution; indeed linear response is not always applicable to the solvation dynamics problem [46][47][48][49] . Even when such a treatment does a reasonable job on the overall time dependence, this is no guarantee that detailed analysis involving molecular features within this formulation is completely reliable.…”

“…Indeed, a large part of the present insight on solvation relaxation comes from the study of simple ions [15][16][17]46,48,[54][55][56][57] or dipoles 50,58,59 . We note that in this case, for which the solute is initially neutral, the frequency shift can be directly identified with the Coulomb energy of the solute-solvent interaction 50 (see below).…”

Ultrafast dynamics of solvation: the story so far

“…On the other hand, continuum 83 and microscopic 84 models as well as simulations 85,86 indicate that very different mechanisms underlie the similar-looking temporal profiles of polar and non-polar solvation dynamics. For example, dielectric continuum models used to successfully describe polar solvation dynamics are based on dipole-dipole interactions between solvent molecules.…”