Marcus region

The origin of Groups I and II is otherwise rationalized in terms of the Marcus formalism (54) as in the case of HRP-catalyzed oxidation of phenols (125,126). The data in Fig. 11 are plotted to highlight the inverted Marcus region in reaction (37). The following standard assumptions have been made in the calculations (53,54) ... 

This distribution duplicates the shape of the ionization rate in the normal Marcus region it is quasiexponential, while in the inverted region it is bell-shaped and shifted from the contact as in Figure 3.5 at large X. 

When diffusion slows down, starting to control the ionization, the shape of the distribution gradually transforms from kinetic to static. This transformation is especially dramatic in the normal Marcus region. This is illustrated by the example of the exponential transfer rate (Fig. 3.31). Being exponential at the fastest diffusion, the distribution /o(r, c) shifts to higher distances, acquiring a bell shape at slower one. Finally it acquires a static shape monotonously decreasing with r. 

Figure 3.41. The diffusional dependence of the recombination efficiency Z in the contact approximation (dotted line) at starting distance ro — 1.124 a and the same for the remote recombination in a normal (solid line) and inverted (dashed line) Marcus region, in highly polar solvents. The horizontal dashed-dotted line represents the exponential model result, Z — z — const. (From Ref. 152.)...

The simplest solution of the problem can be obtained if both the ionization and recombination rates, W/(r) and WR(r), are assumed to be contact as in Eq. (3.368). According to the analysis presented in Section VILA, this is possible only in case (a) of Figure 3.36, within the NN subregion, where both the forward and backward electron transfers occur in the normal Marcus regions. For the sake of simplicity, we also neglect the force interaction between reactants and assume diffusion to be the same in all pairs as in Eq. (3.479) ... 

The Marcus theory also predicts the Bronsted slope magnitude in the normal Marcus region ... 

The second property expected for non-equilibrium processes is the lack of dependence (Fig. 2.6, curve 1) or weak dependence (curve 2) of the experimental rate constant of ET in both Marcus regions (inverted and non-inverted), compared to that predicted by the classic Marcus expression (curve 3). 

Figure 2.5. Schematic representation of electronic potential energy surfaces 1, consecutive conformational and solvatational equilibrium processes with the essential change in the nuclear coordinates Q and the standard Gibbs energy AG0 2, consecutive non-equilibrium processes with small changes in Q and AG0 3, 4, equilibrium (full line) and non-equilibrium (broken line) processes in the normal and inverted Marcus regions respectively. (Likhtenshtein, 1996) Reproduced in permission.

If correct, this may be instructive in the discussions about the inverted Marcus region. In these freely diffusing systems, the exothermicity needed to demonstrate the inverted area is much more difficult to reach than previously expected. When this region is approached, some new efficient acceptors or donors are needed. Generally, this will introduce new uncertainties as far as the... 

The back reaction M+-A" M-A, which regenerates the initial state, often occurs in the inverted Marcus region, which makes it much slower than the forward electron transfer. In this situation, the charge-separated state can be utilized in follow-up reactions (energy conversion, catalysis) or as a bit of chemical information. A long-lived, long-distance charge separation can be produced in molecular triads in which an electron donor and acceptor are attached simultaneously to the photoactive center ... 

The data in Figures 23 and 24 clearly show that the efficiency of the BP-TAA as a polymerization initiator couple depends on both the benzophenone structure and the structure of the tertiary amine. Since the trend observed in Figure 24 is characteristic for kinetic phenomena in what is known as the inverted Marcus region [12-14, 110, 111], and since benzophenone triplet quenching cannot display this specific kinetic phenomena, one concludes that the rate of polymerization photoinitiated by... 

The data in Figures 33 and 34 show typical thermodynamic properties (normal Marcus region) for the electron transfer reaction. In these examples, the rate of the process increases as the driving force of the reation (—AGet) increases. The properties observed in Figures 33 and 34 also predict the type of radical formed after electron transfer. From studies of sulfur-containing amino acids and sulfur-containing carboxylic acids [170-175] it is known that decarboxylation occurs only if the carbox-... 

While electron injection is kinetically near optimum, the high exoergicity of the back electron transfer can make the system lie deep in the inverted Marcus region, where the rate of the charge transfer process is expected to decease with increasing driving force. 

Radiative Electron Transfer in the Inverted Marcus Region. 11... 

For many reasons it is convenient to distinguish between two cases. The first is called the normal free-energy region (or the normal Marcus region) and is defined by —A < AG12 < A (Fig. 1) with the reaction rate expressed as follows ... 

Fig. 1. Electron transfer in the normal Marcus region. Potential energies of the reactant and product as a function of the nuclear (reaction) coordinate the zero-order (left) and first-order (right) representations.

Fig. 3. Schematic illustration of non-radiative election transfer (horizontal arrows) in the normal (left) and inverted (right) Marcus regions. Associated with each vibronic state is a stack of sublevels representing low-frequency (mainly) solvent modes. In the initial state only one vibrational mode, with j = 0, is mainly occupied, whereas in the final state various vibrational modes, with y = 0,1,2..., may be accessible. Diagonal arrows (in the inverted Marcus region) correspond to radiative electron transfer (charge-transfer fluorescence). Adapted from [55].

Fig. S. Radiative transition in the inverted Marcus region charge-transfer absorption (arrow up) and charge-transfer emission (arrow down).

Equations (22) and (23), similarly to Eq. (9), are applicable to the electron transfer reactions in the normal Marcus region. In the inverted Marcus region, possible vibrational excitation of the reaction products should again be taken into account. Depending on the values of S and V12, some of the accessible reaction channels may be affected by the solvent molecular dynamics. This problem has been discussed in [89], with the main conclusion that the overall reaction rate may be expressed as follows ... 

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