Barrier for the electron-transfer reaction

Now we will be interested in the barrier height when the first of these possibilities occurs. 

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Barrier Means a Cost of Opening the Closed Shells Barrier for the Electron Transfer Reaction (15 (g))... 

The fact that excited states of these complexes are not generally quenched by water or acid in solution suggests that barriers for the electron-transfer process render it too slow to compete with excited state decay. The redox chemistry of water is in fact complicated because transformations between stable forms (H20 - H2 + 1/2 02) involve multielectron steps. On the other hand, the one-electron reduction of H+ to H and the one-electron oxidation of H20 to H+ + OH require much more energy than that available to the excited complex103). In order to circumvent these difficulties, one can devise cycles in which the excited state undergoes a simple electron transfer reaction to yield a reduced or oxidized quencher which is able to react with water. For example, one could take into con-... 

Equation (7) expresses an important distinction between the activation free energy for the overall electrochemical reaction in the absence of a net driving force, AG 0, and the intrinsic barrier for the electron-transfer step, AG, t. The former is most directly related to the experimental standard rate constant, whereas the latter is of more fundamental significance from a theoretical standpoint (vide infra). It is therefore desirable to provide reasonable estimates of wp and ws so that the experimental kinetics can be related directly to the energetics of the electron-transfer step. 

The systems of the first class afford the closest approach to a simple barrier penetration process, and perhaps they more readily respond to a theoretical analysis. It can reasonably be supposed that for these systems orbital overlap for the two ions is small, so that the frequency of the electronic transition is small, and there is no substantial binding between the two exchanging centers. A model of this kind presumably corresponds to the weak overlap cases as defined and discussed by Marcus (8 ). In attempting to calculate the rates of these reactions, besides the problem of the shape and height of the barrier for the electron transfer, electrostatic interaction of the reactants must be dealt with and the energy necessary to distort the solvent and ionic atmosphere about each ion to make the enei of the electron equal at the two sites. Different workers have emphasized different ones of these factors, and serious differences of opinion are recorded. 

The intersection of the reactant and product surfaces (point S) represents the transition state (or activated complex ), and is characterized by a loss of one degree of freedom relative to the reactants or products. The actual electron-transfer event occurs when the reactants reach the transition-state geometry. For bimolecular reactions, the reactants must diffuse through the solvent, collide, and form a precursor complex prior to electron transfer. Hence, disentangling the effects of precursor complex formation from the observed reaction rate can pose a serious challenge to the experimentalist unless this is done, the factors that determine the kinetic activation barrier for the electron-transfer step cannot be identified with certainty. 

In the Marcus formula, reorganization energy plays an important role. This energy is the main reason for the electron-transfer reaction barrier. 

The theory for this intermolecular electron transfer reaction can be approached on a microscopic quantum mechanical level, as suggested above, based on a molecular orbital (filled and virtual) approach for both donor (solute) and acceptor (solvent) molecules. If the two sets of molecular orbitals can be in resonance and can physically overlap for a given cluster geometry, then the electron transfer is relatively efficient. In the cases discussed above, a barrier to electron transfer clearly exists, but the overall reaction in certainly exothermic. The barrier must be coupled to a nuclear motion and, thus, Franck-Condon factors for the electron transfer process must be small. This interaction should be modeled by Marcus inverted region electron transfer theory and is well described in the literature (Closs and Miller 1988 Kang et al. 1990 Kim and Hynes 1990a,b Marcus and Sutin 1985 McLendon 1988 Minaga et al. 1991 Sutin 1986). 

Figure 1. Potential energy as a function of reaction coordinate for a self-exchange reaction. AE, energy barrier for thermal electron transfer (weak coupling) AE2, energy of an intervalence transition which is possible for the system.

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