Vibrational trapping electron transfer

The expression for Ke includes a rather elaborate correction for reversibility. It takes into account the fact that in the intersection region, there is no vibrational trapping. Electron transfer can occur back and forth between redox sites until vibrational redistribution removes the system from the intersection region. 

In the classical limit where the condition << kgT is met for the trapping vibrations, the rate constant for electron transfer is given by eq. 6. In eq. 6, x/4 is the classical vibrational trapping energy which includes contributions from both intramolecular (X ) and solvent (XQ) vibrations (eq. 5). In eq. 6 AE is the internal energy difference in the reaction, vn is the frequen-... 

The origin of the barrier to electron transfer is vibrational in nature. The electron becomes trapped at one site as a consequence of changes in molecular and medium structure and/ or vibrations with changes in the electron position. As an ex-... 

The Fe111/11 case is particularly simple. For electron transfer reactions in general, several normal modes may contribute to the trapping of the exchanging electron at a particular site. In addition, intramolecular vibrational modes are of relatively high frequency, 200-4000 cm-1, and at room temperature the classical approximation is not valid since only the v = 0 level is appreciably populated. In order to treat the problem more generally, it is necessary to turn to the quantum mechanical results in a later section. 

Marcus attempted to calculate the minimum energy reaction coordinate or reaction trajectory needed for electron transfer to occur. The reaction coordinate includes contributions from all of the trapping vibrations of the system including the solvent and is not simply the normal coordinate illustrated in Figure 1. In general, the reaction coordinate is a complex function of the coordinates of the series of normal modes that are involved in electron trapping. In this approach to the theory of electron transfer the rate constant for outer-sphere electron transfer is given by equation (18). 

The expressions for ket in equations (29) and (30) are the products of two factors (1) an exponential term which, assuming a common force constant, gives the fractional population of reactants at temperature T with vibrational distributions at the intersection regions for each of the trapping vibrations, and (2) a pre-exponential term ve, the electron transfer frequency ve is defined in equation (31). 

Equation (36), which attempts to include both t and re, has been proposed as a more general expression for et.48 Note that in the limit, when Te -4 t , the expression for the electron transfer rate constant (equation 37) no longer depends on the extent of electronic coupling since vel > vn. In this limit the rate constant for electron transfer for a vibrational distribution near the intersection region is dictated by rates of repopulation of those intramolecular and/or solvent modes which cause the trapping of the exchanging electron. 

The most striking application of electron transfer theory has been to the direct calculation of electron transfer rate constants for a series of metal complex couples.36 37 46 The results of several such calculations taken from ref. 37b are summarized in Table 2. The calculations were made based on intemuclear separations appropriate to the reactants in close contact except for the second entry for Fe(H20)j3+/2+, where at r = 5.25 A there is significant interpenetratidn of the inner coordination spheres. The Ke values are based on ab initio calculations of the extent of electronic coupling. k includes the total contributions to electron transfer from solvent and the trapping vibrations using the dielectric continuum result for A0. the quantum mechanical result for intramolecular vibrations, and known bond distance changes from measurements in the solid state or in solution. 

The absorption band shape is necessarily dictated by those same intramolecular trapping and solvent vibrations which determine the rate of thermal electron transfer since the change in electronic distribution is the same for the two processes. The band shape depends on the product of two terms. The first is the transition moment M = the square of which determines the... 

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