Marcus theory solvent effects

Other measures of nucleophilicity have been proposed. Brauman et al. studied Sn2 reactions in the gas phase and applied Marcus theory to obtain the intrinsic barriers of identity reactions. These quantities were interpreted as intrinsic nucleo-philicities. Streitwieser has shown that the reactivity of anionic nucleophiles toward methyl iodide in dimethylformamide (DMF) is correlated with the overall heat of reaction in the gas phase he concludes that bond strength and electron affinity are the important factors controlling nucleophilicity. The dominant role of the solvent in controlling nucleophilicity was shown by Parker, who found solvent effects on nucleophilic reactivity of many orders of magnitude. For example, most anions are more nucleophilic in DMF than in methanol by factors as large as 10, because they are less effectively shielded by solvation in the aprotic solvent. Liotta et al. have measured rates of substitution by anionic nucleophiles in acetonitrile solution containing a crown ether, which forms an inclusion complex with the cation (K ) of the nucleophile. These rates correlate with gas phase rates of the same nucleophiles, which, in this crown ether-acetonitrile system, are considered to be naked anions. The solvation of anionic nucleophiles is treated in Section 8.3. 

Azo-bridged ferrocene oligomers also show a marked dependence on the redox potentials and IT-band characteristics of the solvent, as is usual for class II mixed valence complexes 21,22). As for the conjugated ferrocene dimers, 2 and 241 the effects of solvents on the electron-exchange rates were analyzed on the basis of the Marcus-Hush theory, in which the t/max of the IT band depends on (l/Dop — 1 /Ds), where Dop and Ds are the solvent s optical and static dielectric constants, respectively (155-157). However, a detailed analysis of the solvent effect on z/max of the IT band of the azo-bridged ferrocene oligomers, 252,64+, and 642+, indicates that the i/max shift is dependent not only on the parameters in the Marcus-Hush theory but also on the nature of the solvent as donor or acceptor (92). 

Table 6.6 lists some reactions of the electron in water, ammonia, and alcohols. These are not exhaustive, but have been chosen for the sake of analyzing reaction mechanisms. Only three alcohols—methanol, ethanol, and 2-propanol—are included where intercomparison can be effected. On the theoretical side, Marcus (1965a, b) applied his electron transfer concept (Marcus, 1964) to reactions of es. The Russian school simultaneously pursued the topic vigorously (Levich, 1966 Dogonadze et al, 1969 Dogonadze, 1971 Vorotyntsev et al, 1970 see also Schmidt, 1973). Kestner and Logan (1972) pointed out the similarity between the Marcus theory and the theories of the Russian school. The experimental features of eh reactions have been detailed by Hart and Anbar (1970), and a review of various es reactions has been presented by Matheson (1975). Bolton and Freeman (1976) have discussed solvent effects on es reaction rates in water and in alcohols. 

A well defined theory of chemical reactions is required before analyzing solvent effects on this special type of solute. The transition state theory has had an enormous influence in the development of modern chemistry [32-37]. Quantum mechanical theories that go beyond the classical statistical mechanics theory of absolute rate have been developed by several authors [36,38,39], However, there are still compelling motivations to formulate an alternate approach to the quantum theory that goes beyond a theory of reaction rates. In this paper, a particular theory of chemical reactions is elaborated. In this theoretical scheme, solvent effects at the thermodynamic and quantum mechanical level can be treated with a fair degree of generality. The theory can be related to modern versions of the Marcus theory of electron transfer [19,40,41] but there is no... 

Our approach to these problems has been to study S 2 reactions in the gas phase. Ion-molecule studies have proven very effective in understanding equilibrium behavior of ions in solution (4), and we think there is great potential in the dynamic areas. As it happens, we find that Marcus theory may be especially applicable, in that the process of interest is a unimolecular one and obviates dealing with encounters, work terms, etc. Thus, we can readily extract solvent free quantities of interest. 

One of the most important new areas of theory of charge transfer reactions is direct molecular simulations, which allows for an unprecedented, molecular level view of solvent motion during reactions in this class. One of the important themes for research of this type is to ascertain the validity at a molecular level of the linear response theory estimates of solvent interactions that are inherent in Marcus theory and related approaches. In addition, the importance of dynamic solvent effects on charge transfer kinetics is being examined. Recent papers on this subject have been published by Warshel [71], Hynes [141] and Bader and Chandler [137, 138],... 

Inner-sphere electron transfers are characterized by (a) temperature-independent rate constants that are greatly higher and rather poorly correlated by Marcus theory (b) weak dependence on solvent polarity (c) low sensitivity to kinetic salt effects. This type of electron transfer does not produce ion radicals as observable species but deals with the preequilibrium formation of encountered complexes with the charge-transfer (inner-sphere) nature (see also Rosokha Kochi 2001). 

However, even for the simple methyl transfer reactions, there is considerable confusion and some disagreement about the details of the mechanism. Some authors (Sneen, 1973) have suggested that ionization of RX always precedes attack by the nucleophile, while others have maintained that the nucleophile attacks the covalent substrate. Extensive references to both points of view are given by McLennan (1976). In the present review the application of the Marcus theory of atom transfer (Marcus, 1968a) allows us to deduce values of the parameter a which describes the symmetry of the transition state. We shall compare this information about the transition state with that from changing the solvent, from isotope effects, and from Hammett relations. We shall then attempt to deduce a model for the transition state which is consistent for all the different types of data. 

These various values are displayed in Fig. 24. Hitherto most authors have agreed that the transition state is to be found near A. This area accommodates very well the evidence from charge development (based on Z), the solvent isotope effect and the cr-deuterium isotope effect. This is true for the er-deuterium isotope effect whether one uses the Shiner argument or the analysis presented in this review. But the problem with a transition state at A is that Marcus theory suggests that a must be close to 0.5. We believe this to be true regardless of whether one believes in... 

Picosecond absorption spectroscopy studies of the contact ion pairs formed in the photo-initiated, S N 1 reaction of three substituted benzhydryl acetates (18) provided the rate constants for the k and k2 steps of the reaction (Scheme 10), in acetonitrile and DMSO.83 The activation parameters for the k and k2 steps were obtained from the temperature dependence of these steps and the transition state energies were calculated from the rate constants. This allowed the energy surfaces for three substituted substrates to be calculated in each solvent. The effect of solvent reorganization on the reactions of the unsubstituted and methyl-substituted benzhydryl contact ion pairs (CIP) was significant, causing a breakdown of transition state theory for these reactions. The results indicated that it will be very difficult to develop a simple theory of nucleophilicity in, S N1 reactions and that Marcus theory cannot be applied to SnI processes. 

To fully understand the relaxation pathways for photoinduced charge-transfer reactions in solutions we need to take solvent effects into account. For that reason it is necessary to recall some basic principles of the classical Marcus Theory for electron-transfer reactions in solution. 

The Br0nsted plots (Fig. 3) give information on this point. The higher curvature of the plot for DMSO compared to methanol is indicative of a lower intrinsic barrier to proton transfer for the dipolar aprotic solvent. Since in the extended Marcus theory the solvent effect has already been taken into account, one would expect the intrinsic barrier for proton transfer to be identical in the two systems. This is not the case. Therefore it appears that separation of the mechanism into reagent positioning with concomitant solvent reorganization is not warranted. 

Static solvent effect — is widely understood as the dependence of -> reaction rate on solvent -> permittivity. The most systematic studies of this effect were stimulated by the early version of -> Marcus theory and mostly consisted in experimental verification of Mar-... 

The use of the energy-gap reaction coordinate allows us to calculate solvent reorganization energies in a way analogous to that in the Marcus theory for electron transfer reactions.19 The major difference here is that the diabatic states for electron transfer reactions are well-defined, whereas for chemical reactions, the definition of the effective diabatic states is not straightforward. The Marcus theory predicts that... 

Therefore, if the Marcus theory describes properly the effect of solvents of k, a linear correlation between In and ( op -fis ) should be observed in the experimental results. Before turning to the experimental studies, the (Sop - s ) parameter for various solvents used in electrochemical work is presented in Table 1. Inspection of these data reveals that the largest difference of the (Cop -Ss ) parameter for the listed solvents amounts to 0.263. Thus, on the basis of the Marcus theory for the outer-sphere electrode reactions, the largest change of the reaction rate for different solvents should amount to exp (const 0.263). In this estimation any double-layer effect on the rate constant was neglected. 

We would like to present somewhat more extensively the results of the work of Dzhavakhidze et al. [Ill], who studied the role of the spatial dispersion of the solvent dielectric permittivity and field penetration into a metal in determining the kinetics of electrode reactions. Considering the particular case of the field penetration effect on the reorganization energy, they found [111] that the AG value obtained is greater than predicted by the Marcus theory. Moreover, under some eonditions the dependence of AG on the reactant-electrode distance d) exhibits an anti-Mar-cusian behavior. 

From earlier investigations, one should mention the work of Sahami and Weaver [113] on the electroreduction of CoEn " (En = ethylenediamine), Co(NH3)6 and Co(NH3)5F. They found that solvent effects do not agree with predictions of the Marcus theory. The discrepancies between theory and experiment (experimentally observed changes were higher than those theoretically predicted) were ascribed to contributions to the energy of activation from extensive reorientation of solvent molecules. 

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