Inverted regions

Guldi D M and Asmus K-D 1997 Electron transfer from Cjg D2) and Cjg C2 ) to radical cations of various arenes evidence for the Marcus inverted region J. Am. Chem. See. 119 5744-5... 

Gould I R, Ege D, Mattes S L and Farid S 1987 Return electron transfer with geminate radical ion pairs - observation of the Marcus inverted region J. Am. Chem. Soc. 109 3794-6... 

The reaction exothermicities ( —AG°) for forward and back ET in polar media were approximately estimated to be 1.39 and 2.18 eV, respectively [120], Since the back ET is highly exothermic, the relatively small kb-1 values for the compartmentalized system may be ascribed to the combined effect of the inverted region [97-99] and the loose ion-pair state. 

To examine the shape that this equation enables us to predict for log k or AG as a function of AG, we substitute the parameter for a specific case. The value of kfc will be taken as 7.4 x 109 L mol-1 s l, that being the value in water at 298 K. Values of k calculated from Eq. (10-66) are shown in Fig. 10-10 as a function of AG. Values of AG are also depicted. The value A = 80 kJ mor1 was used and Z was taken from TST as 6.21 x 1012 s l at 298 K. The effect of introducing the diffusion-controlled limit is that the plot is shaped like a truncated parabola. This figure was drawn with K = k /k-Ac = 0.2 L mol-1. The left side of each of the diagrams shows the inverted region where k decreases and AG increases as AG becomes more negative. 

Electron transfer corresponds to the transition from U, to at the transitional confignration P. AF is the free-energy of the transition. The lower free-energy snrface of the final state corresponds to the inverted region. 

Equation (34.32) is remarkable in the relation that it shows that (1) the observable symmetry factor is determined by occupation of the electron energy level in the metal, giving the major contribution to the current, and (2) that the observable symmetry factor does not leave the interval of values between 0 and 1. The latter means that one cannot observe the inverted region in a traditional electrochemical experiment. Equation (34.32) shows that in the normal region (where a bs is close to ) the energy levels near the Fermi level provide the main contribution to the current, whereas in the activationless (a bs 0) and barrierless (a bs 1) regions, the energy levels below and above the Fermi level, respectively, play the major role. 

The physical mechanism described allows one to answer two basic questions (1) Why does the electrochemical process usually require activation and (2) Why is there no inverted region in the current-overpotential dependence ... 

FIGURE 34.5 Scheme explaining the absence of the inverted region in the electrochemical processes. The position of the free-energy surfaces 7 and U corresponds to the inverted region. However, the major contribution to the current is due to the transition from to U(, which are in activationless configuration. 

The relationship between electron transfer in the normal and inverted regions is illustrated in Figure 3 for the case of quenching of Ru(bpy) + by a nitroaromatic quencher. Excitation... 

One striking prediction of the energy gap law and eq. 11 and 14 is that in the inverted region, the electron transfer rate constant (kjjj. = ket) should decrease as the reaction becomes more favorable (lnknr -AE). Some evidence has been obtained for a fall-off in rate constants with increasing -AE (or -AG) for intermolecular reactions (21). Perhaps most notable is the pulse radiolysis data of Beitz and Miller (22). Nonetheless, the applicability of the energy gap law to intermolecular electron transfer in a detailed way has yet to be proven. 

Schmickler W, Tao N (1997) Measuring the inverted region of an electron transfer reaction with a scanning tunneling microscope. Electrochim Acta 42 2809-2815... 

Most photoinduced CS processes take place within the Marcus normal region. However, chaige recombination processes take place within the inverted region. Thus, the small reorganization eneigy of CHI will slow down CR processes. 

One of the most important consequences of taking all electrode electronic states into account is the disappearance of the inverted region that is predicted by the simplified treatment. Equation (1.32) indeed entails that the forward rate constant should increase as E = EP becomes more and more negative, reach its maximal value for E — E° = —1, and decrease further on (Figure 1.16a). Similarly, the backward rate constant should increase as = ° becomes more and more positive, reach its maximal value for E — = 1, and decrease... 

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