INTRINSIC BARRIER MARCUS EQUATION

Symbolized by A, the reorganization energy of a one-electron transfer reaction is that energy needed for all structural adjustments, not only in the two reactants but in the neighboring solvent molecules as well, required for the two reactants to assume the correct configuration needed to transfer the sole electron. See Intrinsic Barrier Marcus Equation... 

REORGANIZATION ENERGY INTRINSIC BARRIER MARCUS EQUATION Repeatability,... 

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. ... 

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... 

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... 

If the intersecting curves are parabolic in form, then the reactivity pattern expected is described by the Marcus equation (Marcus, 1964, 1977). The magnitude of a may then be shown to be that in (82). Here AGjisthe intrinsic barrier for reaction and AG° the free energy of reaction. 

The increase in double bond character is assumed to increase the intrinsic barrier for reaction at the a-carbon atom. As this increase is greatest for the thermodynamically least stable (CF3-substituted) carbocation, changes in thermodynamic driving force and intrinsic barrier oppose each other. The constancy of the values of kn2o thus reflects a change in intrinsic barrier overriding the second and third terms in the Marcus expression of Equation (20). This is a more radical effect than the lesser variation preserving the linearity of the plots for the reaction families in Fig. 3 (p. 77), for which only the third term is overridden. 

The interpretation of reactivities here provides a particular challenge, because differences in solvation and bond energies contribute differently to reaction rates and equilibria. Analysis in terms of the Marcus equation, in which effects on reactivity arising from changes in intrinsic barrier and equilibrium constant can be separated, is an undoubted advantage. Only rather recently, however, have equilibrium constants, essential to a Marcus analysis, become available for reactions of halide ions with relatively stable carbocations, such as the trityl cation, the bis-trifluoromethyl quinone methide (49), and the rather less stable benzhydryl cations.19,219... 

Marcus5 8 taught us that the most appropriate and useful kinetic measure of chemical reactivity is the intrinsic barrier (AG ) rather than the actual barrier (AG ), or the intrinsic rate constant (kQ) rather than the actual rate constant (k) of a reaction. These terms refer to the barrier (rate constant) in the absence of a thermodynamic driving force (AG° = 0) and can either be determined by interpolation or extrapolation of kinetic data or by applying the Marcus equation.5 8 For example, for solution phase proton transfers from a carbon acid activated by a ji-acceptor (Y) to a buffer base, Equation (1), k0 may be determined from Br A ns ted-type plots of logki or... 

Here, the first two terms jointly define an intrinsic barrier quantity that is determined by the averaged/and G quantities and by the resonance energy of the transition state, due to the avoided crossing, while the third term gives the effect of the reaction thermodynamics (taken only to first order). Equations 6.10 and 6.11 also form a bridge to the popular Marcus equation that is used in physical organic chemistry (13) to analyze the barrier in terms of an intrinsic barrier, Aand a thermodynamic attenuation factor ... 

The intrinsic barrier in the Marcus equation plays an important role, but is essentially unknown and has to be determined either by averaging the barriers... 

Rate constants for electron transfer may be related to the free energy AG° of the reaction through the classical Marcus equation Eq. (5), where AGq is the intrinsic activation barrier of the reaction process [90, 91]. 

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