Marcus barrier

Khoshtariya D. E., Dolidze T. D., Zusman L. D. and Waldeck D. H. (2001), Observation of the turnover between the solvent friction (overdamped) and tunneling (nonadiabatic) charge-transfer mechanisms for a Au/Fe(CN)6 " electrode process and evidence for a freezing out of the Marcus barrier , J. Phys. Chem. Alas, 1818-1829. 

If carried through, the physicist s and chemist s theories should lead to the same results. Some concepts are definitely irreconcilable, however. Typical for ET reactions is the exponential dependence on the rate. At a decreasing temperature, nuclear tunneling leads to a weaker decrease of the rate and finally to a constant rate as a function of 1". This is interpreted as a tunneling through the Marcus barrier. In solid-state physics, this is referred to as variable range hopping, which leads to a log(rate) dependence proportional to 1. ... 

In the statistical description of ununolecular kinetics, known as Rice-Ramsperger-Kassel-Marcus (RRKM) theory [4,7,8], it is assumed that complete IVR occurs on a timescale much shorter than that for the unimolecular reaction [9]. Furdiemiore, to identify states of the system as those for the reactant, a dividing surface [10], called a transition state, is placed at the potential energy barrier region of the potential energy surface. The assumption implicit m RRKM theory is described in the next section. 

Klippenstein S J 1992 Variational optimizations in the Rice-Ramsperger-Kassel-Marcus theory calculations for unimolecular dissociations with no reverse barrier J. Chem. Rhys. 96 367-71... 

The symmetry coefficient = —P d nk/dAE is usually close to j, in agreement with the Marcus formula. Turning to the quantum limit, one observes that the barrier transparency increases with increasing AE as a result of barrier lowering, as well as of a decrease of its width. Therefore, k grows faster than the Arrhenius rate constant. At 7 = 0... 

If the intrinsic barrier AGq could be independently estimated, the Marcus equation (5-69) provides a route to the calculation of rate constants. An additivity property has frequently been invoked for this purpose.For the cross-reaction... 

In Eq. (7-21), AGo is the intrinsic barrier, the free energy of activation of the (hypothetical) member of the reaction series having AG" = 0. It is evident that the Marcus equation predicts a nonlinear free energy relationship, although if a limited... 

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. 

Table 15.2 Comparing experimental activation barriers with those calculated by the Marcus equation...

Rates of addition to carbonyls (or expulsion to regenerate a carbonyl) can be estimated by appropriate forms of Marcus Theory. " These reactions are often subject to general acid/base catalysis, so that it is commonly necessary to use Multidimensional Marcus Theory (MMT) - to allow for the variable importance of different proton transfer modes. This approach treats a concerted reaction as the result of several orthogonal processes, each of which has its own reaction coordinate and its own intrinsic barrier independent of the other coordinates. If an intrinsic barrier for the simple addition process is available then this is a satisfactory procedure. Intrinsic barriers are generally insensitive to the reactivity of the species, although for very reactive carbonyl compounds one finds that the intrinsic barrier becomes variable. ... 

The extent to which the effect of changing substituents on the values of ks and kp is the result of a change in the thermodynamic driving force for the reaction (AG°), a change in the relative intrinsic activation barriers A for ks and kp, or whether changes in both of these quantities contribute to the overall substituent effect. This requires at least a crude Marcus analysis of the substituent effect on the rate and equilibrium constants for the nucleophile addition and proton transfer reactions (equation 2).71-72... 

Our analysis of literature data will focus on two closely related questions about the influence of changes in the relative thermodynamic driving force and Marcus intrinsic barrier for the reaction of simple carbocations with Bronsted bases (alkene formation) and Lewis bases (nucleophile addition) on the values of ks/kp determined by experiment. 

To what extent are the variations in the rate constant ratio /cs//cpobserved for changing structure of aliphatic and benzylic carbocations the result of changes in the Marcus intrinsic barriers Ap and As for the deprotonation and solvent addition reactions It is not generally known whether there are significant differences in the intrinsic barriers for the nucleophile addition and proton transfer reactions of carbocations. 

The more favorable partitioning of [1+ ] to form [l]-OH than to form [2] must be due, at least in part, to the 4.0 kcal mol-1 larger thermodynamic driving force for the former reaction (Kadd = 900 for conversion of [2] to [l]-OH, Table 1). However, thermodynamics alone cannot account for the relative values of ks and kp for reactions of [1+] that are limited by the rate of chemical bond formation, which may be as large as 600. A ratio of kjkp = 600 would correspond to a 3.8 kcal mol-1 difference in the activation barriers for ks and kp, which is almost as large as the 4.0 kcal mol 1 difference in the stability of [1]-OH and [2]. However, only a small fraction of this difference should be expressed at the relatively early transition states for the reactions of [1+], because these reactions are strongly favored thermodynamically. These results are consistent with the conclusion that nucleophile addition to [1+] is an inherently easier reaction than deprotonation of this carbocation, and therefore that nucleophile addition has a smaller Marcus intrinsic barrier. However, they do not allow for a rigorous estimate of the relative intrinsic barriers As — Ap for these reactions. 

Table 2 Rate constants, equilibrium constants, and estimated Marcus intrinsic barriers for the formation and reaction of ring-substituted l-phenylethyl carbocations X-[6+] (Scheme 8)°... 

Bunting and Kanter have developed a modified form of the Marcus equation to treat the changes in intrinsic barrier A observed for deprotonation of /J-keto esters and amides.81 It would be useful to consider similar modifications of the Marcus equation to model the variable intrinsic barriers observed for carboca-tion-nucleophile addition reactions. 

The first attempt to describe the dynamics of dissociative electron transfer started with the derivation from existing thermochemical data of the standard potential for the dissociative electron transfer reaction, rx r.+x-,12 14 with application of the Butler-Volmer law for electrochemical reactions12 and of the Marcus quadratic equation for a series of homogeneous reactions.1314 Application of the Marcus-Hush model to dissociative electron transfers had little basis in electron transfer theory (the same is true for applications to proton transfer or SN2 reactions). Thus, there was no real justification for the application of the Marcus equation and the contribution of bond breaking to the intrinsic barrier was not established. 

As with the Marcus-Hush model of outer-sphere electron transfers, the activation free energy, AG, is a quadratic function of the free energy of the reaction, AG°, as depicted by equation (7), where the intrinsic barrier free energy (equation 8) is the sum of two contributions. One involves the solvent reorganization free energy, 2q, as in the Marcus-Hush model of outer-sphere electron transfer. The other, which represents the contribution of bond breaking, is one-fourth of the bond dissociation energy (BDE). This approach is... 

In the context of the Marcus formulation, the lowering of the activation barrier in an inner-sphere process could arise from the reduction of the work term wp as a result of the strong interaction in the ionic products, e.g., [RitSn+ IrCU3 ] and [RitSn+TCNE ]. The electrostatic potential in such an ion pair is attractive and may cause the tetraalkyltin to achieve a quasi five-coordinate configuration in the precursor complex, reminiscent of a variety of trigonal bipyramidal structures already well-known for tin(IV) derivatives, i.e.,... 

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