Solvated electron models

The configurational model was used for the calculation of the elementary act in the reactions of solvated electrons21 and in the electrochemical generation of solvated electrons.22 The results for the activation free energy of the process of electrochemical generation of solvated electrons as a function of the reaction free energy... 

Although various structural models (Raff and Pohl, 1965 Natori and Watanabe, 1966 Newton, 1973) and semicontinuum models (Copeland et aL, 1970 Kestner and Jortner, 1973 Fueki et al, 1973) have been proposed for the solvated electron, the basis of the agreement or disagreement between theory and experiment is not well established. Another complication with the continuum or the semicontinuum models is the fact that in a number of polar systems the spectrum is fully developed in a time far shorter than the dielectric relaxation times (see, e.g., Bronskill et al, 1970 Baxendale and Wardman, 1973 Rentzepis et al, 1973). 

Theories of solvated electrons may be divided as follows (Jortner, 1970 Webster and Howat, 1972 Kevan, 1974 Kestner, 1976) (1) molecular orbital models, (2) structural models, (3) continuum models, and (4) semicontinuum models. We will consider these models a little in detail. 

FIGURE 6.5 Schematic of the structural model of the solvated electron. The electron is considered trapped at the center of the tetrahedron, whereas for the hydrated electron, the vertices are occupied by O atoms. Arrows indicate the direction of molecular dipoles that may differ from cell to cell. 

The optical absorption of the solvated electron, in the continuum and semicontinuum models, is interpreted as a Is—-2p transition. Because of the Franck-Condon principle, the orientational polarization in the 2p state is given... 

Much worse than the oscillator strength is the line shape. The calculated absorption spectra has no similarity with what is experimentally seen. The calculated half-width is always smaller, typically by a factor of 2 the exact reasons for this are only speculated. It is common knowledge that a photodetachment process is capable of giving a very broad absorption spectrum, but a satisfactory method has not been developed to adopt this with the bound-bound transition of the semicontinuum models. Higher excited states (3p, 4p, etc.) have been proposed for the solvated electron, but they have never been identified in the absorption spectrum. 

The model of metal-ammonia solutions that has emerged is based on ionization of the metal atoms to produce metal ions and electrons that are both solvated. The solvated electron is believed to reside in a cavity in ammonia, and thus it may behave as a particle in a three-dimensional box with quantized energy levels. Transitions between the energy levels may give rise to absorption of light and thereby cause the solutions to be colored. The dissolution process can be represented as... 

Mott transition, 25 170-172 paramagnetic states, 25 148-161, 165-169 continuum model, 25 159-161 ESR. studies, 25 152-157 multistate model, 25 159 optical spectra, 25 157-159 and solvated electrons, 25 138-142 quantitative theory, 25 138-142 spin-equilibria complexes, 32 2-3, see also specific complex four-coordinated d type, 32 2 implications, 32 43-44 excited states, 32 47-48 porphyrins and heme proteins, 32 48-49 electron transfer, 32 45-46 race-mization and isomerization, 32 44—45 substitution, 32 46 in solid state, 32 36-39 lifetime limits, 32 37-38 measured rates, 32 38-39 in solution, 32 22-36 static properties electronic spectra, 32 12-13 geometric structure, 32 6-11 magnetic susceptibility, 32 4-6 vibrational spectra, 32 13 summary and interpretation... 

An almost complete description of both OH radical-mediated and one-electron oxidation reactions of the thymine moiety (3) of DNA and related model compounds is now possible on the basis of detailed studies of the final oxidation products and their radical precursors. Relevant information on the structure and redox properties of transient pyrimidine radicals is available from pulse radiolysis measurements that in most cases have involved the use of the redox titration technique. It may be noted that most of the rate constants implicating the formation and the fate of the latter radicals have been also assessed. This has been completed by the isolation and characterization of the main thymine and thymidine hydroperoxides that arise from the fate of the pyrimidine radicals in aerated aqueous solutions. Information is also available on the formation of thymine hydroperoxides as the result of initial addition of radiation-induced reductive species including H" atom and solvated electron. 

As demonstrated below, a primary charge viewed as a solvated electron or the molecular ion residing in an inert liquid does not account for experimental observations in many, if not in most, of the systems. While we cannot offer a specific, general model of these exceptional ions, we provide a general introduction to the known properties of such species. Furthermore, we argue that these species comprise the rule rather than the exception. The reader is invited to reach his or her own conclusions. 

In the previous four sections, several solvent radical ions that cannot be classified as molecular ions ( a charge on a solvent molecule ) were examined. These delocalized, multimer radical ions are intermediate between the molecular ions and cavity electrons, thereby bridging the two extremes of electron (or hole) localization in a molecular liquid. While solvated electrons appear only in negative-EAg liquids, delocalized solvent anions appear both in positive and negative-EAg liquids. Actually, from the structural standpoint, trapped electrons in low-temperature alkane and ether glasses [2] are closer to the multimer anions because their stabilization requires a degree of polarization in the molecules that is incompatible with the premises of one-electron models. 

Finally, a striking property of metal-ammonia solutions is the large expansion of the liquid due to the solvated electrons. The apparent volume of the solvated electron remains roughly constant up to the metallic range, then shows a slight increase. It is about 100 cm3 mol. It is this effect that has led to the hypothesis that the electron forms a cavity for itself a cavity of radius 3.2 A accounts quantitatively for the excess volume. A model in which the electron moves in a cavity, and the surrounding liquid is polarized or solvated as it is round a cation, was first put forward by Jortner (1959), who showed that it was able to account for the absorption spectrum. Jortner s model, as modified by Mott (1967), Cohen and Thompson (1968) and Catterall and Mott (1969), will now be described. 

Fig. 10.16 Potential seen by a solvated electron according to the model of Jortner (1959). The wave function r of the electron is also shown. The optical absorption is due to the ls-2p transition. The radius R of the cavity is approximately 3.2 A. From Cohen and...

From the steady state fluorescence spectrum of indole in water a fluorescence quantum yield of about 0.09 is determined. Since the cation appears in less than 80 fs a branching of the excited state population has to occur immediately after photo excitation. We propose the model shown in Fig. 3a). A fraction of 45 % experiences photoionization, whereas the rest of the population relaxes to a fluorescing state, which can not ionize any more. A charge transfer to solvent state (CITS), that was also introduced by other authors [4,7], is created within 80 fs. The presolvated electrons, also known as wet or hot electrons, form solvated electrons with a time constant of 350 fs. Afterwards the solvated electrons show no recombination within the next 160 ps contrary to solvated electrons in pure water as is shown in Fig. 3b). 

Simple cavity models have been used to study solvated electrons in liquid ammonia. In that case the dominant interactions arise from long range polarization effects, so that the energy of the localized state is not very sensitive to the fluid deformation in the vicinity of the localized charge. In the case of an excess electron in liquid helium, however, the electron-fluid interaction arises mainly from short range electron-atom interactions, and we shall show that the localized excess electron in a cavity in liquid helium lies lower in energy than the quasi-free electron. 

It would appear at this stage that a good deal of useful information has yet to be obtained by the pulse radiolysis method concerning the absorption spectra of the solvated electron in various organic liquids. Such data would help to remove uncertainties regarding the assignment of bands and would serve as criteria for the validity of developing models. 

The metallic nature of concentrated metal-ammonia solutions is usually called "well known." However, few detailed studies of this system have been aimed at correlating the properties of the solution with theories of the liquid metallic state. The role of the solvated electron in the metallic conduction processes is not yet established. Recent measurements of optical reflectivity and Hall coefficient provide direct determinations of electron density and mobility. Electronic properties of the solution, including electrical and thermal conductivities, Hall effect, thermoelectric power, and magnetic susceptibility, can be compared with recent models of the metallic state. 

The unique properties of dilute metal-ammonia solutions depend not upon the nature of the metal species, but upon the solvated electron common to all these solutions. Thus, the electron-in-a-cavity model (17, 19, 21) seems best suited to describe the species present in these solutions since the model is independent of the type of cation present. Jortner and his associates (15, 16) have extended this model by assuming that the cavity arises from polarization of the medium by the electron. The energy levels of the bound electrons are obtained by using a potential function containing the static and optical dielectric constants of the bulk medium as parameters. Using one-parameter hydrogen-like wave functions for the first two bound states of the electron, the total energy of the ith state is expressed as... 

The value for X2 is the same as that for this same reactant in an ordinary homogeneous or electrochemical electron transfer occurring at the same R and can be estimated from them, as described later (6). AF0/int is known for many reactions of the solvated electron, and w can be estimated approximately. Accordingly, a theoretical value of AF can be calculated from Equation 7 once X/ is known. Either X/ can be calculated from other sources (it depends on the model of the solvated electron) or a value can be used which best fits data on k t for several reactions, or both. In making such calculations it should be noted that AF is not highly accurately given by Equation 7, because of the various... 

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