Free-energy-gap law

Figure 3.2. The free-energy-gap law for single-channel (thin line) and multichannel (thick line) electron transfer, decomposed into vibronic components (dashed lines).

The argument AG, = AG/(c>) is the contact value of the ionization free energy AGj(r) inherent in the reactions (3.52). Since the reaction volume v 271 (u2l + a/2 + l3/2) does not depend on the free energy, it was expected from the very beginning that the ko(AGi) dependence reproduces that of Wc(AGi), which is the Marcus free-energy-gap law (3.50) for W(a). The same is true for the Stern-Volmer constant Kq = ko in the kinetic control limit (D > oo) as follows from Eq. (3.27). 

Initially, I t) increases due to ionization but begins to decrease as soon as recombination starts to prevail, and eventually comes down to a constant value that determines the photoseparation quantum yield, /(oo) = 0. It is cj) that is usually measured experimentally. Since cf) depends on the parameters of both forward and backward ET reactions in a rather complicated way, one generally cannot expect to observe the usual Marcus-type free energy gap law by plotting cj) (or any other characteristic of geminate recombina-... 

The fonn of the classical (equation C3.2.11) or semiclassical (equation C3.2.11) rate equations are energy gap laws . That is, the equations reflect a free energy dependent rate. In contrast with many physical organic reactivity indices, these rates are predicted to increase as -AG grows, and then to drop when -AG exceeds a critical value. In the classical limit, log(/cg.j.) has a parabolic dependence on -AG. Wlren high-frequency chemical bond vibrations couple to the ET process, the dependence on -AG becomes asymmetrical, as mentioned above. 

It has in fact been anticipated for many years that the CT free energy surfaces may deviate from parabolas. A part of this interest is provoked by experimental evidence from kinetics and spectroscopy. Eirst, the dependence of the activation free energy, Ff , for the forward (/ = 1 ) and backward i = 2) reactions on the equilibrium free energy gap AFq (ET energy gap law) is rarely a symmetric parabola as is suggested by the Marcus equation,Eq. [9]. Second, optical spectra are asymmetric in most cases and in some cases do not show the mirror symmetry between absorption and emission.In both types of experiments, however, the observed effect is an ill-defined mixture of the intramolecular vibrational excitations of the solute and thermal fluctuations of the solvent. The band shape analysis of optical lines does not currently allow an unambiguous separation of these two effects, and there is insufficient information about the solvent-induced free energy profiles of ET. 

Equation [79] produces the MH quadratic energy gap law at small AEo l i il and yields a linear dependence of the activation energy on the equilibrium free energy gap at AFq - k a lai >... 

Both reactions are exothermic. Transfer from bipy to Oj is more favorable than transfer from to O2 and the rate is faster for the former reaction (18) which is in agreement with the energy gap law of electron transfer. Also the free energy does not change with pressure for these two reactions, which implies that there are no overall volume changes in the reactions. This is as expected since clustering around the products should be very similar to that around the reactants. 

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