Reorganization of the solvent molecules

In addition to these interactions, one must take into account that reorganization of the solvent molecules requires the expenditure of some energy Calculations show that this energy for water has values of -60 to -120kJ/mol. 

The reorganization of the solvent molecules can be expressed through the change in the slow polarization. Consider a small volume element AC of the solvent in the vicinity of the reactant it has a dipole moment m = Ps AC caused by the slow polarization, and its energy of interaction with the external field Eex caused by the reacting ion is —Ps Eex AC = —Ps D AC/eo, since Eex = D/eo- We take the polarization Ps as the relevant outer-sphere coordinate, and require an expression for the contribution AU of the volume element to the potential energy of the system. In the harmonic approximation this must be a second-order polynomial in Ps, and the linear term is the interaction with the external field, so that the equilibrium values of Ps in the absence of a field vanishes ... 

Fig. 1 represents schematically the usual physical interpretation of polar SD The solute undergoes vertical electroitic excitation and the dynamic fluorescence Stokes shift arises Ifom the reorganization of the solvent molecules. In the case... 

The results point out the relevant contribution played by electrostatic interactions to the hydration enthalpy of polar solutes. Nevertheless, even for these compounds the non-electrostatic term plays a significant contribution to the hydration enthalpy. The entropic contribution to the hydration is mainly associated with the non-electrostatic terms, which can be mainly attributed to the reorganization of the solvent molecules around the solute cavity, as van der Waals terms are assumed to be essentially enthalpic [31,33],... 

One more methodological problem should be touched upon whose solution is necessary for correct description of mechanisms of reactions in solutions. This problem has to do with the relaxation of the solvent during the dynamic process. In all methods, except the MD scheme, it is assumed that, regardless of the velocity of the process, the medium is equilibrated in each point of the PES of reaction. This assumption is actually one of the necessary conditions for applying the theory of transition state. Clearly, in the case of fast reactions the time of reorganization of the solvent molecules is comparable to the time of realization of these reactions. This justifies the conclusion that the equilibrium of the medium is not always fulfilled. The model calculations by van der Zwan and Hynes [71, 72], later extended to more realistic cases of the 8 2 reactions in polar media [73, 74], bear witness to the dependence of the reaction rate constants upon the degree of nonequilibrium of a given solvent. 

The time taken for reorganization of the solvent molecules around an instantly created dipole is termed as solvation time or solvent relaxation time (r, ) [72]. As the ILs are polar, time-resolved fluorescence studies on dipolar fluorescent molecules provide valuable information on the timescales of reorganization of the constituents of the ILs around a photoexcited molecule. The timescale of solvation depends on the viscosity, temperature, and molecular structure of the surrounding solvent [72]. As ILs are highly viscous, the solvation in ILs is a much slow process compared with that in less viscous conventional solvents. The dynamics of solvation is commonly studied by monitoring the time-dependent fluorescence Stokes shift of a dipolar molecule following its excitation by a short pulse (Scheme 7.2). This phenomenon is called dynamic fluorescence Stokes shift [73], and the solvation dynamics in several ILs has been studied by this method using various fluorescent probes. 

The solvent reorganization term reflects the changes in solvent polarization during electron transfer. The polarization of the solvent molecule can be divided into two components (1) the electron redistribution of the solvent molecules and (2) the solvent nuclear reorientation. The latter corresponds to a slow and rate-determining step involving the dipole moments of the solvent molecules that... 

To obtain an estimate for the energy of reorganization of the outer sphere, we start from the Born model, in which the solvation of an ion is viewed as resulting from the Coulomb interaction of the ionic charge with the polarization of the solvent. This polarization contains two contributions one is from the electronic polarizability of the solvent molecules the other is caused by the orientation and distortion of the... 

It should be kept in mind that this type of study, treated here in terms of single complexes, acquires greater importance when carried out on a series of homologous complexes. This allows one to evaluate how the electronic and/or structural variations of the ligand influence the reorganization processes of the solvent molecules. In fact, such a comparison has recently led to a reinterpretation of the A °c parameter also in terms of the structural reorganisations of the first coordination sphere.18,19 For example, if one compares the A-Sr°c values for... 

For intramolecular vibrations, each site was considered independently. However, the reorganizations in the surrounding solvent are necessarily properties of both sites since some of the solvent molecules involved are shared between reactants. The critical motions in the solvent are reorientations of the solvent dipoles. These motions are closely related to rotations of molecules in the gas phase but are necessarily collective in nature because of molecule—molecule interactions in the condensed phase of the solution. They have been treated theoretically as vibrations by analogy with lattice vibrations of phonons which occur in the solid state.32,33... 

This concept of the prior reorganization of the solvent is best illustrated by a charge shift e.t, something like the self-exchange reaction of a neutral molecule M with its ion M+ see scheme 3 [57]. 

Fig. 13. A hypothetical representation of solvent molecule orientation in the transition state involving electron transfer between two charged reactants. Each solvent molecule possesses a permanent dipole, which in this idealized diagram is depicted by an ellipsoidal shape. Solvent molecules reorganize to the geometry of the transition state. The electronic polarization of the solvent molecules, represented here by the bold arrows, then responds practically instantaneously with electron transfer. Finally, the permanent dipoles of the solvent molecules readjust to the successor state. This model may not be applicable to electron transfer between neutral reetants (see text)...

The nature of the quenching mechanism can be easily confirmed by recording the emission spectrum in a frozen solution (EtOH/MeOH mixture (9 1) at liquid nitrogen temperature). Under these conditions, the relative decrease in fluorescence intensity expressed as I /Iq is equal to 0.82, while at room temperature it is 0.23. Such a reduction in quenching efficiency in a frozen solution is characteristic of an electron transfer mechanism. In fact, immobilization of the solvent molecules in a frozen matrix prevents the reorganization of solvent molecules sur-... 

For simplicity we have assumed that the shapes of the two curves are equal (only one y value in both cases). In consequence the reorganization values arc equal, i.e. Ared = Aox = A. The fluctuation of the solvent molecules leads finally to a broadening of the electronic levels as derived below. 

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