Marcus equation transfers

Equation (3.34) without the H X ) and the H 2la terms is identical to the Marcus equation for methyl transfer reactions (Ref. 13). This equation predicts, at the range ( AG0 < a), a linear relationship between AAG0 and AAg by... 

When R is CH3 the process is called methyl transfer. For such reactions, the work terms and are assumed to be very small compared to AG° and can be neglected, so that the Marcus equation simplifies to... 

Excited state electron transfer also needs electronic interaction between the two partners and obeys the same rules as electron transfer between ground state molecules (Marcus equation and related quantum mechanical elaborations [ 14]), taking into account that the excited state energy can be used, to a first approximation, as an extra free energy contribution for the occurrence of both oxidation and reduction processes [8]. 

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. 

Figure 5, Relationship of the activation free energy for electron transfer with the electrode potentials of various FeL33 according to Equation 6 (left), and the driving force according to the Marcus Equation 4 (right).

Figure 16. Relationship between the activation jree energy and the driving force for electron transfer for alkylmetals to TCNE (left) and IrCl6z (right) according to Marcus Equation 4.

As can be seen, the increase in separation between the electrode surface and the redox-active site operated by the variable-in-length carbon chain from (CH2)3 to (CH2)n makes the process change from electrochemically reversible to irreversible. In fact, in agreement with the (simplified) Marcus equation, ket = 1013/e, the rate of the electron transfer is considerably reduced with the distance d. 

In the previous section, we alluded to the Franck Condon factors (FCF) in controlling electron transfer rates. For this topic, detailed reviews of theory and experiment are provided elsewhere. In sum, it is now well known that the reaction free energy required to transfer charge can be reduced by the reaction free energy, AG°, as summarized in the famous Marcus equation AG = (AG° — where X, the reorganization energy, is related to the degree of... 

On the basis of the very negative activation entropies, the transition states for the addition are highly ionic, i.e. there is a large degree of electron transfer in the transition state as with the hydroxyalkyl radicals (Sect. 2.1.1). In support of this is the fact that the rate constants for addition depend on the reduction potentials of the nitrobenzenes, varied by the substituent R3 in a way describ-able by the Marcus equation for outer-sphere electron transfer [19]. 

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... 

Electron-pair donor (or Lewis base), NUCLEOPHILE ELECTRON SINK ELECTRON SPIN RESONANCE ELECTRON TRANSEER MARCUS EQUATION ELECTRODE KINETICS Electron transfer mechanism,... 

By measuring the temperature dependence of kex, activation parameters (Aff and AS ) could be calculated and were reported. However, I am not sure how to physically interpret these numbers. The temperature dependence of rate can be fit to other expressions, and here it is fit to the Marcus equation for nonadiabatic electron transfer in the case of degenerate electron transfer (e.g., AG° = 0)... 

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... 

The ICoCHjOVl "electron exchange reaction proceeds It) limes taster than prcdMCd hy ihe Marcus equation. Whal docs this suggest. ibwit Hie mechanism of electron transfer ... 

Using mutant proteins as well as a variety of redox pairs and electron-transfer distances the validity of the Marcus equation with respect to the thermodynamic driving force and distance dependence has been verified.153 This is even true for cytochrome c mutants functioning in living yeast cells.146... 

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... 

---