Backward Electron Transfer

In spite of those difficulties, generalizations can be easily made. The onset of the inverted region starts around 1.5-2 eV of driving force (corresponds to 2j + As). The value of V is small (10-20 cm-1), and the solvent reorganization energy is the dominant component of the total reorganization energy. An increase in size of the aromatic system leads to a decrease in V and 2S, but the 

The data in Fig. 5 are a little more scattered, but they involve donors and acceptors of various sizes that are quite distinct electronically [64], Taking into account the uncertainties in the determination of the driving force for BET from (sometimes irreversible) cyclic voltammetry experiments, the data of Figs. 4 and 5 are an excellent starting point for semi-quantitative predictions of BET rates within photoinduced ion pairs, and may be used to estimate efficiencies of follow up reactions, including fragmentation reactions. 

Most of the studies of BET within geminate ion pairs have been carried out in acetonitrile. As discussed in Sect. 2.1, change of solvent may simultaneously 

---

Three-pulse ESEEM spectrum of perdeuterated P-carotene imbedded in Cu-MCM-41 exhibits an echo decay with an echo modulation due to deuterons. The three-pulse ESEEM is plotted as a function of time, and curves are drawn through the maximum and minima. From ratio analysis of these curves, a best nonlinear least-squares lit determines the number of interacting deuterons, the distance (3.3 0.2A), and the isotopic coupling (0.06 0.2MHz). This analysis made it possible to explain the observed reversible forward and backward electron transfer between the carotenoid and Cu2+ as the temperature was cycled (77-300 K). 

Insofar as the intermediate B obeys the steady-state approximation, as is usually the case in practice, there are two limiting situations as to the nature of the rate-limiting step according to the value of the parameter A e/lc = k-rCp/kc, which measures the competition between the followup reaction and the backward electron transfer (see Section 6.2.7). 

Most of the work published to date on molecular dynamic studies of interfacial electron transfer involves the simplified assumption of a two-state model for the electronic degrees of freedom. Consider an ion of charge qj near a solution/metal interface. As a result of electron transfer between the ion and the metal surface, the charge of the ion changes to qj. We will consider both forward and backward electron transfer and assume that = <7 - = -1, so that the forward reaction corresponds to a single electron transfer from the metal to the ion, for example + e ... 

If the electron donor is so efficient a reductant as to react with the acceptor with a rate constant equal to the diffusion limit, then not much information can be derived from the experiments, except the knowledge of the diffusion limit itself. The opposite situation, where an endergonic electron transfer is followed by a fast bond-breaking step, is of more interest. There is then competition between the follow-up reaction and the backward electron-transfer step. If the latter is faster than the former, kinetic control is by the bond-breaking step, the electron-transfer step acting as a preequilibrium. Under these conditions, there is no difficulty to conclude from the adherence to the rate law (61) that the overall reaction is stepwise rather than concerted, since, in the concerted case, the rate law would be (62). If, in... 

Substituent effects on the electron-transfer processes between pyrrolidinofullerenes and tetrakis(dimethylamino)ethylene (TDAE) were studied in both the ground state and excited triplet state. ° Equilibrium constants and rate constants for forward and backward electron-transfer processes in the ground state, in addition to rate constants of the forward electron transfer in the excited triplet state were measured. 

The process is induced photochemically and involves the single-electron transfer oxidation of cubane then completed with a backward electron transfer to the transient radical cations. A Li+ salt with a weakly coordinating anion is able to induce pericyclic transformations, including the rearrangement of cubane to cuneane, quadricyclane to norbomadiene, and basketene to Nenitzescu s hydrocarbon 392... 

The theory of geminate recombination experienced a similar evolution from primitive exponential model and contact approximation [19,20], to distant recombination carried out by backward electron transfer [21], However, all these theories have an arbitrary parameter initial separation of reactants in a pair, / o. This uncertainty was eliminated by unified theory (UT) proposed in two articles published almost simultaneously [22,23], UT considers jointly the forward bimolecular electron transfer and subsequent geminate recombination of charged products carried out by backward electron or proton transfer. The forward transfer creates the initial condition for the backward one. This is the distribution of initial separations in the geminate ion pair/(ro), closely analyzed theoretically [24,25] and inspected experimentally [26,27], It was used to specify the geminate recombination kinetics accompanied by spin conversion and exciplex formation [28-31], These and other applications of UT have been covered in a review published in 2000 [32],... 

The one most known is the extra large width of the diffusional plateau seen in Figure 3.14. The plateau is much longer than a single FEG parabola could be, as is obvious when comparing it with the rate of the backward electron transfer, which is never as wide. A number of causes were offered to explain why the ionization is so strong (and therefore controlled by diffusion) in such a wide region. 

The most primitive but popular exponential model (EM) implies that the recombination occurs within the transparent reaction sphere where the ions are born [Fig. 3.22(a)]. The backward electron transfer to the ground state proceeds there with the uniform rate k et, but some ions escape recombination leaving the sphere, due to encounter diffusion that finally separate them. EM ascribes to this process the rate... 

Since ionization was assumed irreversible, the elements containing the backward electron transfer rate WB(r) are zero. The assumption is actually acceptable for exclusively exergonic ionization... 

It does not always happen that the ion recombination proceeds through the backward electron transfer. Sometimes the ions are discharged because of proton transfer between them, resulting in their transformation to free radicals D and A ... 

The Marcus rates are essentially better than their exponential models because they include the space-dependent Arrhenius factor, which causes them to differ for ionization and recombination. However, the position of the maximum on the curve Zip ) and its inherent existence depends on the relationship between the free energies of forward and backward electron transfers. As a rule, the situation is favorable for the emergence of a maximum because the backward transfer is usually more exergonic than the forward one. Nonetheless, so far the extremum has been obtained in only one system, and we have to ascertain why it is so exceptional. 

The Coulomb interactions affect both forward and backward electron transfers, changing their free energies... 

Although this equation involves the rate Wb of backward electron transfer, it treats this transfer as the irreversible recombination of ions through an additional... 

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) ... 

Instead of the universal recombination rate Wr there is a sequence of two vertical transitions. The triplet-singlet conversion precedes the backward electron transfer from the singlet RIP to the ground state. Symbolizing Ru2+ by D and MV2+ by A, we can formalize this reaction scheme in the following way ... 

The mechanism of chemically initiated electron exchange luminescence (CIEEL) has been specified and studied in solvents of different viscosities [226-230]. The intramolecular electron transfer in the oxyaryl-substituted adamantyldioxetane anion D [2 (the boldfaced numbers refer to the numbered structures 1-5 in Fig. 3.77)], followed by decomposition of the latter into two radicals A and M (5), allows them to diffuse freely in and out of the cage until the backward electron transfer (BET) excites the methyl-m-oxybenzoate anion M (4), as shown in Figure 3.77. In general, the intermolecular BET mechanism of excitation (right branch) competes with a direct chemiexcitation in the course... 

The shape of the kernels (3.651) is rather obvious from the physical point of view. The kernels R and R are exactly the same as in Eq. (3.369) of the spinless theory. When spin conversion during encounter is negligible, the backward electron transfer to the ground state remains the single channel of geminate ion recombination. Therefore, the kernel R is 4 times smaller than... 

Figure 3.97. The Stern-Volmer constant of biexcitonic quenching at xD = 0.5 ns, D — 10 5 cm2s 1, ct = 5 A, rc = 10A, No = 0.2M, and the exponential rates of the forward and backward electron transfer with W/(a) = 500ns, W/ (cf) = 500ns and L= 1A. The dashed line shows the Markovian result, = 4.84M/ns. (From Ref. 199.)...

For the correct description of electron transfer processes (forward and backward electron transfers) and also relaxation from conduction to valence bands in a semiconductor, we include e-ph interaction into a semiconductor Hamiltonian ... 

Electron-phonon interaction in a semiconductor is the main factor for relaxation of a transferred electron. There are two different relaxation processes that decrease the efficiency of light conversion in a solar system (1) relaxation of an electron from a semiconductor conduction band to a valence band and (2) a backward electron transfer reaction. The forward and backward electron transfer processes have been already included in the tunneling interaction, HSm-qd, described by Eq. (108). However, the effect of SM e-ph interaction is important for the correct description of electron transfer in the SM-QD solar cell system. In the previous section, we have gradually considered different types of interactions in the quantum dot and obtained the exact expression for the photocurrent (128) where the exact nonequilibrium QD Green s functions determined from Eq. (127) have been used. However, in... 

Conversely, when the proton transfer rate is considerably faster than the backward electron transfer, the RDS is the forward electron transfer and the observed rate constant is then kf, as given in Eq. (46) ... 

When, although vis-a-vis the mass transfer rate, the chemical reaction is slow compared with the backward electron transfer, the reduction or oxidation in Eq. (120) remains at equilibrium. The electrode potential is then given by the Nernst law in Eq. (122) ... 

A. I. Burshtein. Diffusional and spin-dependent theory of chemiluminescence resulting from backward electron transfer. Chem. Phys., 289(2-3) 251-261, 2003. 

---