Solvent fluctuation

In a simple electron transfer reaction, the reactant is situated in front of the electrode, and the electron is transferred when there is a favorable solvent fluctuation. In contrast, during ion transfer, the reactant itself moves from the bulk of the solution to the double layer, and then becomes adsorbed on, or incorporated into, the electrode. Despite these differences, ion transfer can be described by essentially the same formalism [Schmickler, 1995], but the interactions both with the solvent and with the metal depend on the position of the ion. In addition, the electronic level on the reactant depends on the local electric potential in the double layer, which also varies with the distance. These complications make it difficult to perform quantitative calculations. 

Even if we consider a single solvent, e g., water, at a single temperature, say 298K, depends on the solute and in fact on the coordinate of the solute which is under consideration, and we cannot take xF as a constant. Nevertheless, in the absence of a molecular dynamics simulation for the solute motion of interest, XF for polar solvents like water is often approximated by the Debye model. In this model, the dielectric polarization of the solvent relaxes as a single exponential with a relaxation time equal to the rotational (i.e., reorientational) relaxation time of a single molecule, which is called Tp) or the Debye time [32, 347], The Debye time may be associated with the relaxation of the transverse component of the polarization field. However the solvent fluctuations and frictional relaxation occur on a faster scale given by [348,349]... 

The basic ideas presented above correspond to an analysis of a typical unimolecular process, as for instance, SN1 mechanism where the solvent may have achieved the stabilization of the di-ionic quantum state and has favored ionic dissociation as opposed to homolytic dissociation. The chemical interconversion appears here to be a quantum mechanical change of state where the solvent fluctuations would play the role of... 

Picosecond Raman measurements have led to the proposal of a dynamic polarization model." In this model, 5i tS undergoes reversible changes in vibrational frequencies that are induced by solvent fluctuations. The mixing of a perturbing state with interconverts carbon-carbon double bonds with single bonds that leads S tS near the vertical geometry to proceed along the pathway for isomerization. 

How would the distribution of hydrolysis species fit into the general picture of solvent fluctuations Would the reorganization energies, when resolved into contributions from Fe3+, FeOH2+, FeOH2+, form separate distributions, or would the hydrolysis fluctuations be part of a continuum of solvent fluctuations In other words, is it more correct to regard the phenomenon of hydrolysis, as far as its effect on electron transfer, from the point of view of contributions from separate hydrolysis species ... 

Fig. 6. Distribution of Fe2+/Fe3+ reorganization energies found in the MD simulation of electron transfer in a hydrolyzing solution of Fe3+ (the Fe2+ could hydrolyze, but never does) at an apparent pH near 3.9. The strongly overlapping distributions show almost no shift in reorganization energy as a function of hydrolysis, indicating that the hydrolysis fluctuations lie on a continuum with all other solvent fluctuations.

It appears that hydrogen-bonds are potentially fast enough so to allow for bimolecular proton-transfer to occur along relaxed hydrogen-bond links, thus making the preparation of such links, which may involve relatively slow solvent fluctuations, the primary event that establishes the proton transfer coordinate. 

Non-polar Solutes in Polar Solvents the (Solvent Stark EffecP. At first sight a non-polar solute molecule cannot polarize the surrounding solvent since it develops no electric field. However, the solvent fluctuates around the non-polar solute, so that there is a small instantaneous electric field which acts on the solute to produce a fluctuating induced dipole which leads to... 

The sequence of the observed frequencies, resolved on the time scale, may be regrouped in a form giving a quantity S(t) which may be related to a time correlation function CAE(t) which represents the ensemble average of solvent fluctuations. 

These tunneling concepts can be compared with the Marcus theory for electron transfer (Closs and Miller 1988 Kang et al. 1990 Kim and Hynes 1990a,b Marcus and Sutin 1985 McLendon 1988 Minaga et al. 1991 Sutin 1986). In the normal regime, solvent fluctuation is required to equilibrate the reactant and... 

Theories based on the Enskog collision time (84) or other solid-like approaches do not have a strongly temperature-dependent frequency correlation time. But they do have a temperature-dependent factor resulting from the need to create the solvent fluctuations in the first place. Thus, all fast-modulation theories predict that the dephasing rate will go to zero at 0 K. 

Another approach to solvent fluctuation control of reactions in solution based on the Kramer model (Kramer, 1940 Sumi, 1999 and references therein). According to this model a transition over a double-well potential W(q) occurs as a result of zigzag diffusion. An important parameter of the theory is the relaxation time of the average motion of the medium... 

Sumi, H., (1999) Solvent fluctuation control of solution reactions and its manifistation in protein functions, in Jortner, J., Bixon, M. (eds.), Advances in Chemical Physics. 107, Part 2, John Wiley Sons. NY., pp. 611-646. 

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