Theory of solvation dynamics

Recent work on the theory of solvation dynamics has attempted to go beyond the linearized MSA model of Wolynes, which considers the rotational dynamics of the solvent as the only relaxation mechanism. Certain translational and hydrodynamic-like motions of the solvent are neglected. 

Figure 3.17 Comparison between experiment (dashed curve) and calculations combining the polarizable continuum model for solute electronic structure and continuum dielectric theory of solvation dynamics in water. SRF(t) stands for S(t) in our notation. The calculations are for a cavity based on a space-filling model of Cl53, while the experiments are for C343. The two sets of theoretical results correspond to using water e(o>) from simulation (full curve) of SPC/E water and from a fit to experimental data (dash-dotted curve). (Reprinted from F. Ingrosso, A. Tani andJ. Tomasi, J. Mol. Liq., 1117, 85-92. Copyright (2005), with permission from Elsevier).

As was discussed in the previous section, continuum theories of solvation dynamics often require as input the nonlocal dielectric susceptibility of the solvent, (r,to), or equivalently, its Fourier transform [54]... 

H. L. Friedman, B.-C. Perng, H. Resat and F. O. Raineri, Applications of a molecular theory of solvation dynamics, J. Phys. Condens. Matter, 6 (1994) A131-A36. 

We describe a classical statistical mechanical theory of solvation dynamics, formulated for general molecular interaiction site models (ISM) of the solute and solvent species. Ba-... 

While there is no unique criterion for choosing 4 E, the selection must lead to an accurate theory of solvation dynamics without invoking two-time many-point correlation functions. We have found that this goal can be achieved with a new theory for the nonequilibrium distribution function in which the renormalized solute-solvent interactions enter linearly. In this theory and are chosen such that the renormalized linear response theory accurately describes the essential solute-solvent static correlations that rule the equilibrium solvation both at t = 0 (when solvent is in equilibrium with the initial charge distribution of the solute) and at 1 = oc (when the solvent has reached equilibrium with the new solute charge distribution). ... 

The RDT theory of solvation dynamics is capable of describing the solvation tcf as well as the evolution of various ancillary observables. ... 

M. Berg, "Comparison of a Viscoelastic Theory of Solvation Dynamics to Tune-Resolved Experiments in a Nonpolar Solution, Chem. Phys. Lett, in press. 

The continuum dielectric theory used above is a linear response theory, as expressed by the linear relation between the perturbation T> and the response , Eq. (15.1b). Thus, our treatment of solvation dynamics was done within a linear response framework. Linear response theory of solvation dynamics may be cast in a general form that does not depend on the model used for the dielectric environment and can therefore be applied also in molecular (as opposed to continuum) level theories. Here we derive this general formalism. For simplicity we disregard the fast electronic response of the solvent and focus on the observed nuclear dielectric relaxation. 

In the Markovian Kramers model discussed in Section 14.4, the friction coefficient y describes the coupling of the reaction coordinate to the thermal environment. In the low friction (underdamped) limit it is equal to the thermal relaxation rate in the reactant well, which is equivalent in the present case to the solvation well of the initial charge distribution. More generally, this rate should depend also on the frequency >s of this well. The theory of solvation dynamics, Chapter 15, does not use a Langevin equation such as (14.39) as a starting point, however it stiU yields an equivalent relaxation rate, the inverse solvation time (tl) , which is used in the present discussion. 

The well-known continuum models and also the microscopic theories of solvation dynamics suggest a close relation between solvation dynamics and DR. This is expressed as tl = (soo/so)td where tl is the longitudinal relaxation time and td is the Debye relaxation time. However, the solvation dynamics of an ion at the protein surface is difficult to understand because of the heterogeneous environment of the protein surface. Therefore, a straightforward application of the continuum model with a multiexponential description of DR is not possible. The continuum theory suggests that at short length scales, the relaxation time is essentially given by the DR time. Therefore, we certainly expect a slow component in the solvation dynamics. 

Approximate analytical theories of solvation dynamics are typically based on the linear response approximation and additional statistical mechanics or continuum electrostatic approximations to Cy(r). The continuum electrostatic approximation requires the frequency-dependent solvent dielectric response For example, the Debye model, for which e(a>) = + (cq - )/(l +... 

The continuum dielectric theory of solvation dynamics is a linear response theory, as expressed by the linear relation between the perturbation D and the response E, Eq. [4.3.2]. Linear response theory of solvation dynamics may be cast in a general form that does not... 

---