Equations Rehm-Weller

The system consists of donor D and acceptor A. To obtain charge separation, the energy of the D A state should be higher than that of the D+A state. The energy of the excited state D A is the excitation energy between the two lowest vibration levels, Eqo. In the gas phase, the energy of the charge-separated state is 1(D) - A(A), since the process means that one electron is transferred from D to A. In a solution phase, we have to use the oxidation potential for D and the reduction potential for A in the relevant solvent. 

In the gas phase, the free energy of the charge separation process is 

We have assumed that the charge of one electron is moving and we use atomic units. The term -1/R represents the lowering of the final energy due to the attraction between the separated charges at a distance R. 

In the solvent with dielectric constant equal to e, we have to use instead 

We see that the larger the distance for ET, R, the less negative is the free energy. The larger the distance R, the higher in energy is the CT state compared with the locally excited states. 

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Rehm-Weller equation Reichert cone Reich process Reichstein approach... 

This considerable enhancement in redox properties may however remain chemically hidden. Several causes may converge to mask these properties. First of all electron transfer is an intermolecular act of reactivity even when thermodynamically feasible it may have to compete with very rapid intramolecular acts of deactivation (fluorescence, phosphorescence, internal conversion) . The rate of electron transfer is given by the Rehm-Weller equation ... 

The facility of PET can be confirmed by a thermodynamic approach. For weakly interacting PET process, the associated free energy driving force of reaction (AG) can be estimated by the Rehm-Weller equation [20], expressed as... 

Figure 13. Test for the consistency of AG evaluated from the intrinsic rate constant (log kj using Marcus Equation 4 (a), Rehm-Weller Equation 17 (b), and Marcus-Levine-A gmon Equation 18 (c) at various potentials.

Regulatory systems, environmental impact assessment, 10 232-233 Rehalogenating bleaches, 19 261 Reheat blow-molding process, 20 47 Rehm-Weller equation, 19 112 Rehydration bonded alumina, 2 395, 396-397... 

These equations are called Rehm-Weller equations. If the redox potentials are expressed in volts, AG° is then given in volts. Conversion into J mol-1 requires multiplication by the Faraday constant (F = 96500 C mol-1). 

The free-enthalpy change AG of a PET process can be described by the simplified Rehm-Weller equation [5] ... 

Similar results were obtained [139] with the three dimethoxybenzenes and acrylonitrile, methacrylonitrile, and crotonitrile. The amounts of substitution products decrease in the order acrylonitrile (49%) > methacrylonitrile (45%) > crotonitrile (6%), which agrees with the electron affinities of these compounds. Simultaneously, the amount of addition product increases acrylonitrile, 0% methacrylonitrile, 38% crotonitrile, 67%. In the series of anisole and the dimethoxybenzenes with crotonitrile, the amount of substitution products decrease in the order ortho- and para-dim ethoxy benzene > meta-dimethoxyben-zene > anisole, which is just the reverse of the order of their oxidation potentials. Ohashi et al. [139] have attempted to relate the photochemical behavior of these systems to the free enthalpy of electron transfer in the excited state as calculated with the Rehm-Weller equation, AG = E(D/D+) - E(A /A) - el/eR - AE00. 

In view of the occurrence of electron transfer and also in view of the observations made by Bryce-Smith and Gilbert (on which the ionization potential rule is based), Mattay et al. [15,143,144] have proposed a relationship between the mode of reaction (ortho addition, meta addition, substitution) and the free enthalpy of electron transfer between the reaction partners. The free enthalpy was calculated using the Rehm-Weller equation... 

Use of the Rehm-Weller equation made it possible to predict the direction of charge transfer in a given system and to establish empirical correlations between the AG value for electron transfer and the mode of the photoreaction (meta addition, ortho addition, and/or substitution). 

Radical ion species (D+, A ) are usually produced by one-electron transfer from D to A or D to A in polar solvents. The calculated values for the free-energy change using the Rehm-Weller equation (Eq. 1) predict a photoinduced electron-transfer process between D and A [38]... 

In the above sections, nothing was said about the type of reaction between M and Q. This is because the Stem-Volmer equation is model independent, as explained above and also because eqs. (20)-(22) are for a diffusion-controlled reaction. Some information can be obtained regarding an electron transfer from various quenchers of similar chemical structures towards M. In this case, one may derive a relationship between ksv (as obtained from eq. (17)) and the ionization potential of these inhibitors. This is the Rehm-Weller equation, which is schematically depicted in fig. 4. In this plot, the plateau value corresponds to fcdin. For a general overview of problems related to electron transfers, see Pouliquen and Wintgens (1988) (in French). 

The fact is that the reaction free energies are hardly ever determined experimentally, but are simply calculated from the Rehm-Weller equation which will be discussed in detail in the next section [26]. There are still considerable technical problems in direct experimental measurements, because standard methods of calorimetry cannot cope with reactions in time scales of ns or ps but this is slowly changing with the advent of fast calorimetric techniques such as time-resolved photoacoustic spectroscopy [27] and thermal lensing [28] these are considered in the following section. Nevertheless, it appears that all the data currently used in the rate constant-energy plots simply use the Rehm-Weller equation (sometimes with various corrections) and it is obviously important to consider the assumptions built into this equation, its limitations, and possible improvements. 

The Rehm-Weller equation which is based on electrochemical and spectroscopic data is used almost universally for the calculation of reaction free energies of e.t. It relates the oxidation potential of the donor D and the reduction potential of... 

At the singlet excited state, ortho and meta photocycloadditions are often competitive processes and physicochemical investigations were carried out to rationalize the modes of cycloaddition of arenes with alkenes. In the context of the study of photochemical electron transfer reactions, it has been proposed that the difference of the redox potentials of the reaction partners might play an important role in this competition [10]. Such a discussion involves the intervention of an exciplex as intermediate. The Rehm-Weller equation [11] was used to quantify the relationship. When an electron transfer process is strongly endergonic (AG>1.5eV), the meta cycloaddition should be favored. When such a process is less endergonic (1 < AG< 1.5 eY), the ortho addition dominate [12]. This means that the... 

Figure 9 shows the log k/AG° plot based on the data given by Rehm and Weller (1970) for more than 60 systems. The solid line is calculated using (73) and (74), the former one being the so-called Rehm-Weller equation, whereas the broken line is based on (56) and (74), i.e. the Marcus model in both cases a AG (0) of 2.4 kcal mol-1 (A = 9.6 kcal mol-1) is used. The dotted line is again based on the Marcus equation (56) but with a large value of AG (0), 9.6 kcal mol-1 (A = 38.4 kcal mol-1). It is immediately noticeable that the Marcus... 

For AG° > 4 AG (0), the Rehm-Weller equation approximates a straight line with slope 1/2.303 RT= —0.74 mol kcal-1, whereas the parabolic Marcus plot over narrow intervals, if approximated as a straight line, gives slopes < —0.74 mol kcal-1. No distinction between the two equations can be made on the basis of the data of Fig. 9. 

Fig. 3. Bimolecular electron transfer of photoexcited donors and acceptors. The parabolas (a) and (i>) represent Eq. 1 with l = 0.42 eV. Curve (a) is flattened at the top due to the diffusional limit [27]. The Rehm-Weller equations (Eq. 6) with identical A is presented by lines (e) and (/), where the former includes a diffusional limit of kd = 2 x 1010 M 1 s"The filled circles represent the Rehm-Weller data for neutral aromatic donors and acceptors in acetonitrile [25]. The squares denote similar data for inorganic (charged) acceptors and organic (neutral) donors also in acetonitrile [28], The data are fitted into Eq. 6 with X = 0.69 eV and kd = 9 x 109 M 1 s "1 (line d). The open squares represent the forward ET to the excited inorganic complexes the filled squares depict the bimolecular BET within the photogenerated ion pairs of the same systems [28], The triangles represent forward electron transfer between organic borates [29] and cyanines (filled triangles) or pyrylium cations (open triangles) within contact ion pairs in benzene. Even in this case, without diffusional interference, the data seem to fit better the Rehm-Weller equation (g) than the Marcus equation (c)...

Various compounds were shown to sensitize the photochemical decomposition of pyridinium salts. Photolysis of pyridinium salts in the presence of sensitizers such as anthracene, perylene and phenothiazine proceeds by an electron transfer from the excited state sensitizer to the pyridinium salt. Thus, a sensitizer radical cation and pyridinyl radical are formed as shown for the case of anthracene in Scheme 15. The latter rapidly decomposes to give pyridine and an ethoxy radical. Evidence for the proposed mechanism was obtained by observation of the absorption spectra of relevant radical cations upon laser flash photolysis of methylene chloride solutions containing sensitizers and pyridinium salt [64]. Moreover, estimates of the free energy change by the Rehm-Weller equation [65] give highly favorable values for anthracene, perylene, phenothiazine and thioxanthone sensitized systems, whilst benzophenone and acetophenone seemed not to be suitable sensitizers (Table 5). The failure of the polymerization experiments sensitized by benzophenone and acetophenone in the absence of a hydrogen donor is consistent with the proposed electron transfer mechanism. 

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