Electron Transfer in Polar Medium

For the closed description of the electron transfer in polar medium, it is necessary to express the reorganization energy in the formula (27) via the characteristics of polar media (it is assumed that the high-temperature approach can be always applied to the outer-sphere degrees of freedom). It was done in the works [12, 19, 23], and most consistently in the work of Ovchinnikov and Ovchinnikova [24] where the frequency dependence of the medium dielectric permittivity e(co) is taken into account exactly, but the spatial dispersion was neglected. 

At high temperatures, hm/kT 1 it is valid to approximate equality coth(hm/2kT) 2kT/hm, and the resulting expression for the rate constant of electron transfer in polar medium will be the expression (29), where Er is given by the expressions (50) and (48). 

Much fundamental work, concerned mostly with the mechanism and kinetics of photoinduced electron transfer in polar medium, has been reported that helps in the design of new solar energy storage systems. General treatments of electron transfer... 

The electron transfer in polar media is described by the general theory where the reorganization energy is expressed via dielectric characteristics of the medium. The strong interaction between the terms results in the transition of the adiabatic one over the activation barrier. 

Condition (16) enables one to consider such transitions in harmonic approximation. It is shown elsewhere [25] that the description of the polar medium by the set of classical harmonic oscillators is equivalent to the supposition of linear polarizability, that is, the applicability of Maxwell equations. Arrhenius temperature dependence is typical of the overwhelming majority of the outer-spheric reactions of electron transfer in polar liquids [27, 28]. 

We present a derivation of the broadening due to the solvent according to a system/ bath quantum approach, originally worked out in the field of solid-state physics to treat the effect of electron/phonon couplings in the electronic transitions of electron traps in crystals [67, 68]. This approach has the advantage to treat all the nuclear degrees of freedom of the system solute/medium on the same foot, namely as coupled oscillators. The same type of approach has been adopted by Jortner and co-workers [69] to derive a quantum theory of thermal electron transfer in polar solvents. In that case, the solvent outside the first solvation shell was treated as a dielectric continuum and, in the frame of the polaron theory, the vibrational modes of the outer medium, that is, the polar modes, play the same role as the lattice optical modes of the crystal investigated elsewhere [67,68]. The total Hamiltonian of the solute (5) and the medium (m) can be formally written as... 

The brief review of the newest results in the theory of elementary chemical processes in the condensed phase given in this chapter shows that great progress has been achieved in this field during recent years, concerning the description of both the interaction of electrons with the polar medium and with the intramolecular vibrations and the interaction of the intramolecular vibrations and other reactive modes with each other and with the dissipative subsystem (thermal bath). The rapid development of the theory of the adiabatic reactions of the transfer of heavy particles with due account of the fluctuational character of the motion of the medium in the framework of both dynamic and stochastic approaches should be mentioned. The stochastic approach is described only briefly in this chapter. The number of papers in this field is so great that their detailed review would require a separate article. 

The solid-state structure of the photosynthetic reaction centre complexes has inspired several studies of light-induced electron transfer in solid media. A particularly useful medium is provided by porous glass which facilitates rapid electron-transfer reactions without the involvement of polar solvents. Solid matrices suitable for light-induced electron-transfer processes are also provided by silica, zeolites, and clays. A theoretical description has been reported for dealing with the distribution of separation distances between donor and acceptor that is often found in the solid state. ... 

For unsubstituted stilbene, azastilbenes, and naphthylethylenes the CT interaction involves only singlet states as initial species. Introduction of a nitro group makes triplet states accessible for electron transfer [513], Because of the larger value of tt as compared to rs, smaller donor concentrations are required for electron transfer in the triplet state. The same Stern-Volmer constants for quenching of 4>, c and 1/tt (or l() indicate that trans - cis photoisomerization and electron transfer compete. This was also found when a positive charge was introduced by quaternization of 4-R-azastilbenes (A+, R = nitro or cyano) [170,489], but not for compounds with R = dimethylamino [171]. Under certain conditions (e.g., in a solvent of medium polarity such as dichloromethane and for X- = I"), a radical pair (A. . X ) is produced by excitation of the ion pair (Figure 20b) [172,489]. The same (neutral) radical can be formed by electron transfer from the amine, (e.g., DABCO) to the cation of a quarternary salt of 4-R-azastilbene in the case R = nitro the electron is transferred to the triplet state, in competition with trans- cis photoisomerization (Figure 21). 

By a detailed CIDNP investigation [117a] of the Patemo-Biichi reactions of anetholes 31 with quinones 30 in polar medium earlier mechanistic hypotheses were disproved. Stationary and time-resolved experiments showed the mechanism to have the following novel features (cf. Chart XIV) Spin-correlated radical ion pairs (i.e., 30 31,+) are key intermediates for cycloadduct formation free radical ions do not play a significant role. In the singlet state, these pairs undergo back electron transfer geminate reaction of triplet pairs leads to triplet biradicals, which are the precursors to the photoproducts. 

The synergic effects which are generally invoked to account for the specific features of a system of two ketones used as polymerization photoinitiators are reconsidered. The increase of reactivity observed when mixing these two Initiators is reinterpreted in terms of a simultaneous energy and electron transfer in the pair. The relative efficiencies of these processes depends on the energy gap between the triplet states involved, which is known to be influenced by the polarity of the medium. A general discussian on the efficiency of various couples photoinitiator/photosensitizers is presented. 

The one-electron transfer to free CO2 affords CO2, as seen in Chap. 1. Table 8.1 shows that it requires much more energy than multielectron transfers. Moreover, the potential is dependent on the medium in which the electron transfer occurs polar media (—1.9 V) or apolar media ( 2.21 V). The one-electron transfer generates the CO2 species which can evolve according to two different routes (Scheme 8.3). 

The microscopic mechanism of these reactions is closely related to interaction of the reactants with the medium. When the medium is polar (e.g., water), this interaction is primarily of electrostatic nature. The ionic cores of the donor and acceptor located at fixed spatial points in the medium produce an average equilibrium polarization of the medium, which remains unchanged in the course of the reaction and does not affect the process of electron transfer itself. The presence of the transferable electron in the donor induces additional polarization of the solvent around the donor that is, however, different from polarization in the final state where the electron is located in the acceptor. 

Therefore, the electronic polarization induced by the transferable electron in the medium can follow any instant position of the electron without delay. This means that at any position of the transferable electron between the donor and acceptor, the electronic polarization of the medium induced by this electron is practically the same, and therefore the energy of the interaction of the electron with this polarization is... 

First, we shall discuss reaction (5.7.1), which is more involved than simple electron transfer. While the frequency of polarization vibration of the media where electron transfer occurs lies in the range 3 x 1010 to 3 x 1011 Hz, the frequency of the vibrations of proton-containing groups in proton donors (e.g. in the oxonium ion or in the molecules of weak acids) is of the order of 3 x 1012 to 3 x 1013 Hz. Then for the transfer proper of the proton from the proton donor to the electrode the classical approximation cannot be employed without modification. This step has indeed a quantum mechanical character, but, in simple cases, proton transfer can be described in terms of concepts of reorganization of the medium and thus of the exponential relationship in Eq. (5.3.14). The quantum character of proton transfer occurring through the tunnel mechanism is expressed in terms of the... 

The effects of the modulation of electron density by local vibrations and polarization fluctuations are most pronounced for reactions involving transfer of weakly bound electrons. These effects were investigated in Ref. 16 for the transfer of weakly bound electrons from a donor Az to an acceptor BZ2 in a polar medium. 

Based on the results obtained in the investigation of the effects of modulation of the electron density by the nuclear vibrations, a lability principle in chemical kinetics and catalysis (electrocatalysis) has been formulated in Ref. 26. This principle is formulated as follows the greater the lability of the electron, transferable atoms or atomic groups with respect to the action of external fields, local vibrations, or fluctuations of the medium polarization, the higher, as a rule, is the transition probability, all other conditions being unchanged. Note that the concept lability is more general than... 

The effects of charge variation may also play a certain role in other processes involving adsorbed atoms, in particular, in electron transfer processes.59 The physical nature of these effects is to some extent similar to that of the effects of polarization of the electron plasma of the metal by vibrations in a polar medium considered in Ref. 60. 

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