Marcus theory barriers

A key point that must be made is diat quantum mechanical tunneling through the Marcus-theory barrier when it is non-zero can increase the rate for electron transfer just as is true for any other activated process. Because the electron is so light a particle, tunneling can be a major contributor to die overall rate. Models for electron tunneling will not, however, be presented here. 

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... 

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. 

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. ... 

Fig. 4 Predictions of Marcus Theory for the variation of forward (fcf)and reverse (kr) rate coefficients with ApA" for reactions with different intrinsic barriers (X/4)...

One of the most valuable outcomes of the Marcus theory is that it provides a quantitative, albeit simple, description of how the activation barrier varies with the driving force of the reaction. The factors constituting the intrinsic barrier are clearly identified and can be approximately estimated from available data characterizing the structure of the reactants of the products and of the reaction medium. 

Note that calculated energies have been substituted for the more normal free energies of Marcus theory. Equation (2) predicts a low 7.2 kcalmoPM activation energy for the 1 -+ 2. The experimental work in Freon glasses did not reveal the existence of 1, although recent work has shown that it does have a finite lifetime in solution and that the estimated rearrangement barrier is 4.8 kcalmo] [12],... 

A simple diagram depicting the differences between these two complementary theories is shown in Fig. 1, which represents reactions at zero driving force. Thus, the activation energy corresponds to the intrinsic barrier. Marcus theory assumes a harmonic potential for reactants and products and, in its simplest form, assumes that the reactant and product surfaces have the same curvature (Fig. la). In his derivation of the dissociative ET theory, Saveant assumed that the reactants should be described by a Morse potential and that the products should simply be the dissociative part of this potential (Fig. Ib). Some concerns about the latter condition have been raised. " On the other hand, comparison of experimental data pertaining to alkyl halides and peroxides (Section 3) with equations (7) and (8) seems to indicate that the simple model proposed by Saveant for the nuclear factor of the ET rate constant expression satisfactorily describes concerted dissociative reductions in the condensed phase. A similar treatment was used by Wentworth and coworkers to describe dissociative electron attachment to aromatic and alkyl halides in the gas phase. ... 

Results from the dissociative reduction of aryl ethers led to a number of important generalizations. These are classical stepwise systems initially forming jr -type radical anions. In this case, the intrinsic barriers for the formation of the intermediate radical anions are dominated by solvent reorganization with only a small (sometimes negligible) contribution from internal reorganization. Thus, the ETs to these systems are properly described by Marcus theory, in which the harmonic approximation satisfactorily accounts for both outer and inner reorganization factors. On the... 

Of course, Marcus theory does not stop at this juncture but attempts to provide a quantitative relationship between reaction kinetics and thermodynamics. On the basis of Marcus theory the barrier to a particular reaction AG, may be described as a function of a parameter called the intrinsic barrier, AG, and the free energy of the reaction AG°. The particular relationship is presented in (112). The basic idea here is that the barrier height is composed of two contributions, a kinetic component termed the intrinsic... 

One difficulty that arises within the Marcus formulation is that the intrinsic barrier term is ideally treated as a constant. Earlier applications of Marcus theory were based on this assumption (Cohen and Marcus, 1968 Kreevoy and Konasewich, 1970 Kreevoy and Oh, 1973 Albery et al., 1972). However, as regards methyl transfer, this assumption is clearly invalid. 

The above model has been further explored to account for reaction efficiencies in terms of a scheme where nucleophilicities and leaving group abilities can be rationalized by a structure-reactivity pattern. Pellerite and Brau-man (1980, 1983) have proposed that the central energy barrier for an exothermic reaction (see Fig. 3) can be analysed in terms of a thermodynamic driving force, due to the exothermicity of the reaction, and an intrinsic energy barrier. The separation between these two components has been carried out by extending to SN2 reactions the theory developed by Marcus for electron transfer reactions in solutions (Marcus, 1964). While the validity of the Marcus theory to atom and group transfer is open to criticism, the basic assumption of the proposed model is that the intrinsic barrier of reaction (38)... 

The Marcus equation allows AG for RX + Y —> RY + X to be calculated from the barriers of the two symmetrical reactions RX + X - RX + X and RY + Y — RY + Y. The results of such calculations are generally in agreement with the Hammond postulate. Marcus theory can be applied to any single-step process where something is transferred... 

Rate and equilibrium constants have been measured for representative intramolecular aldol condensations of dicarbonyls.60a For the four substrates studied (32 n = 2, R = Me n = 3, R = H/Me/Ph), results have been obtained for both the aldol addition to give ketol (33), and the elimination to the enone (34). A rate-equilibrium mismatch for the overall process is examined in the context of Baldwin s rales. The data are also compared with Richard and co-workers study of 2-(2-oxopropyl)benzaldehyde (35), for which the enone condensation product tautomerizes to the dienol60b (i.e. /(-naphthol). In all cases, Marcus theory can be applied to these intramolecular aldol reactions, and it predicts essentially the same intrinsic barrier as for their intermolecular counterparts. 

Detailed analysis of the rate and equilibrium constants determined for both phases of intramolecular aldol condensation reactions (13 —>15, 16—>18, and 19—>21) in terns of Marcus theory, has established that the intrinsic barriers for die intramolecular reactions are the same as those determined previously for the intermolecular counterparts.31 Consequently, rate constants for intramolecular aldol reactions are predictable from the energetics of the reactions and the effective molarity can be calculated. An associated discussion of Baldwin s rales suggests that they are a consequence of the need to achieve a conformation from which reaction can take place... 

It has been reported that rates of proton transfer from carbon acids to water or hydroxide ion can be predicted by application of multi-dimensional Marcus theory to a model whereby diffusion of the base to the carbon acid is followed by simple proton transfer to give a pyramidal anion, planarization of the carbon, and adjustment of the bond lengths to those found in the final anion.124 The intrinsic barriers can be estimated without input of kinetic information. The method has been illustrated by application to a range of carbon acids having considerable variation in apparent intrinsic barrier. 

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