Solvent dynamical effects

The present approach has been applied to the experiment done by Nelsen et ah, [112], which is a measurement of the intramolecular electron transfer of 2,7-dinitronaphthalene in three kinds of solvents. Since the solvent dynamics effect is supposed to be unimportant in these cases, we can use the present theory within the effective ID model approach. The basic parameters are taken from the above reference except for the effective frequency. The results are shown in Fig. 26, which shows an excellent agreement with the experiment. The electronic couphng is quite strong and the perturbative treatment cannot work. The effective frequencies used are 1200, 950, and 800 cm for CH3CN, dimethylformamide (DMF), and PrCN [113]. 

The TST rate constant for electronically adiabatic ET reactions is the well-known Marcus rate constant kjjj [27-29], In the language of this chapter, solvent dynamical effects can alter the actual rate from this limit due to the friction influence. The corresponding GH equations for kct = / kfj are strictly analogous... 

Actually, all of the above results are in contradiction to the currently conventional view [32-35] that solvent dynamical effects for electronically adiabatic ET reactions are determined by solvent dynamics in the R and P wells, and not the barrier top region. This misses the correct picture, even for fairly cusped barrier. Instead, it is the solvent dynamics occurring near the barrier top, and the associated time dependent friction, that are the crucial aspects. It could however be thought possible that, for cusped barrier adiabatic ET reactions in much more slowly relaxing solvents, the well dynamics could begin to play a significant role. However, MD simulations have now been carried out for the same ET solute in a solvent where the... 

Phelps, D. K., Weaver, M. J. and Ladanyi, B. M. Solvent dynamic effects in electron transfer molecular dynamics simulations of reactions in methanol, Chem. Phys., 176 (1993), 575-588... 

VIII. SOLVENT DYNAMIC EFFECTS ON ET REACTIONS AT ELECTRODES... 

Many questions in the analysis of solvent dynamics effects for isomer-izations in solution have arisen, such as (1) when is a frequency-dependent friction needed (2) when does a change of solvent, of pressure, or of temperature change the barrier height (i.e., the threshold energy), and (3) when is the vibrational assistance model needed, instead of one based on Eq. (1.1) or its extensions ... 

The RRKM theory is a ubiquitous tool for studying dissociation or isomerization rates of molecules as a function of their vibrational energy. Still highly active in the theoretical field, Marcus has tackled such issues as the semiclassical theory for inelastic and reactive collisions, devising reaction coordinates, new tunneling paths, and exploring solvent dynamics effects on unim-olecular reactions in clusters. 

K. Ando and S. Kato, Dielectric relaxation dynamics of water and methanol solutions associated with the ionization of /V,/V-dimcltiylanilinc theoretical analyses, J. Chem. Phys., 95 (1991) 5966-82 D. K. Phelps, M. J. Weaver and B. M. Ladanyi, Solvent dynamic effects in electron transfer molecular dynamics simulations of reactions in methanol, Chem. Phys., 176 (1993) 575-88 M. S. Skaf and B. M. Ladanyi, Molecular dynamics simulation of solvation dynamics in methanol-water mixtures, J. Phys. Chem., 100 (1996) 18258-68 D. Aheme, V. Tran and B. J. Schwartz, Nonlinear, nonpolar solvation dynamics in water the roles of elec-trostriction and solvent translation in the breakdown of linear response, J. Phys. Chem. B, 104 (2000) 5382-94. 

How would these paths differ if one assumed that equilibrium solvation (ES) applied rather than nonequilibrium solvation (NES), i.e. if one ignored any solvent dynamical effects This ES condition is imposed by requiring the free energy with respect to the solvent coordinate s is a minimum at each value of r and 8, so that s is equal to its equilibrium value jeq(r, 8) ... 

A case of solvent-driven electronic relaxation has been observed [76] for [Re(Etpy)(CO)3(bpy)]+ in ionic liquids TRIR spectra have shown at early times a weak signal due to the II. state, in addition to much stronger bands of the 3MLCT state. Although no accurate kinetic data are available, the II. state converts to MI.CT with a rate that is commensurate with the solvent relaxation time. Fluorescence up-conversion provided an evidence [10] for population of an upper II. state in MeCN, which converts to CT with a much faster lifetime of 870 fs (Table 1). The solvent dynamic effect on the 3IL—>3CT internal conversion can be rationalized by different polarities of the II. and JCT states, Fig. 11. The solvent relaxation stabilizes the 3CT state relative to II., driving the conversion. 

Experiments aimed at probing solvent dynamical effects in electrochemical kinetics, as in homogeneous electron transfer, are only of very recent origin, fueled in part by a renaissance of theoretical activity in condensed-phase reaction dynamics [47] (Sect. 3.3.1). It has been noted that solvent-dependent rate constants can sometimes be correlated with the medium viscosity, t] [101]. While such behavior may also signal the onset of diffusion-rather than electron-transfer control, if the latter circumstances prevail this finding suggests that the frequency factor is controlled by solvent dynamics since td and hence rL [eqn. (23), Sect. 3.3.1] is often roughly proportional to... 

There is little experimental information on possible solvent dynamical effects for electron transfer in aqueous solution. However, water is a dynamically "fast solvent, vos being determined by "solvent inertial effects so that the usual transition-state formula [eqn. (22)] should be applicable for determining vn (Sect. 3.2.1). Consequently, solvent dynamical effects in this and other "low friction media (e.g. acetonitrile) should be controlled by the rotational frequency of individual solvent molecules and limited to reactions involving only very small inner-shell barriers (Sect. 3.3.1). 

Dynamical solvent effect on ket- The solvent dynamical effect can be examined by the so called frequency factor, vn. in the usual TST like format,... 

The timescale of environmental (solvent) motions that determine the solvent dynamical effect on the process of interest should be shorter than the timescale on which the solvent can be described as a harmonic medium. 

Solvent dynamical effects on relaxation and reaction process were considered in Chapters 13 and 14. These effects are usually associated with small amplitude solvent motions that do not appreciably change its configuration. However, the most important solvent effect is often equilibrium in nature — modifying the free energies of the reactants, products, and transition states, thereby affecting the free energy of activation and sometime even the course of the chemical process. Solvation energies relevant to these modifications can be studied experimentally by calorimetric and spectroscopic methods, and theoretically by methods of equilibrium statistical mechanics. 

The relationship between the rate constants kei for an electrode reaction and fee for the corresponding self-exchange electron transfer reaction is not obvious because kgi can be strongly influenced by the nature and history of the electrode surface and by solvent dynamic effects if present. Electrode properties, however, are not expected to be sensitive to pressures in the 0-200 MPa range. Moreover, the signature of solvent dynamical effects is a dependence of reaction rate on solvent viscosity, but the viscosity of water is effectively independent of such pressures at near-ambient temperatures. Consequently, for typical aqueous electrode reactions, Ai/, = O.SAV, regardless of any involvement of solvent dynamics, and so AVg can be predicted from transition state theory (TST) according to Eqs (5.5)-... 

High-pressure kinetics indicate the absence of solvent dynamical effects in outer-sphere bimolecular self-exchange reactions in non-aqueous media, even in the most favorable experimentally accessible case (the Fe(phen)j couple) - on the contrary, expectations based on TST alone are generally met, and AV is negative. 

At the same time, AV(, is invariably positive for electrode reactions in organic solvents, signaling rate control by solvent friction. Solvent dynamics dominate electrode kinetics in non-aqueous media even when the corresponding self-exchange reactions clearly conform to the TST model. In short, pressure effects reveal that electrode reactions are subject to solvent dynamical effects in non-aqueous media at least, but the corresponding self-exchange reactions are not, regardless of the solvent. 

Since the electron is coupled to the polarization modes of the solvent molecule, the rate of the reaction can be affected significantly by the dynamics experienced along the reaction coordinate. The dynamics can even be rate-determining if it is much slower than the time it takes to cross the barrier in the absenee of solvent dynamics effects. 

Here we only briefly describe the analysis of solvent effects on the electron transfer reaction, with emphasis on the physical picture. In the study of solvent dynamic effects on the rate of any chemical reaction (here the rate of an electron transfer reaction), the usual approach is to invoke a phenomenological description where the solvent dynamic effect is included through a friction coeflBcient, f(s) [20]. So, the theoretical study involves two steps. First, we derive an expression for the rate in the presence of solvent forces. Second, we derive an expression for the friction. 

What is presented above is really a rather nice and physically appealing picture of the lack of solvent dynamics effects on a large class of electron transfer reactions in water where the Marcus theory is accurate. 

Electron Transfer Rate Theory Incorporated Solvent Dynamic Effect... 

Nelsen and co-workers measured the ET rates within the 2,7-dinitro-naphthalene anion radical in different solvents and noted that the solvent dynamic effect was not important. They thus tried to use the Marcus formula or the BJ theory in the perturbation limit to explain their experimental results. However, both cannot explain the experimental results correctly because the electronic coupling is not weak enough. Since the solvent dynamics are fast, here we can use the rate expression (eqn (12.17)) with ZN transition probability. Indeed, the predicted rates are in excellent agreement with the experiment. The results are shown in Figure 12.6. In the calculations, the reorganization energy and electronic coupling are estimated by Nelsen s measurement. 

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