Theoretical Models of the Solvated Electron

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. 

A molecular orbital model (MO) treats all electrons belonging to a fixed number of solvent molecules plus an excess electron in the resultant field of the nuclei of the molecules as being in a fixed configuration. The nuclei belonging to a particular molecule normally keep the ground state structure of that molecule. The relative distances and orientations of these molecules are varied until energetic, and if possible configurational, stability is obtained. In some cases, molecular distortions have been considered. 

The various MO calculations use different basis sets and have different ways of calculating multicenter coulomb and exchange integrals. The current trend in MO is to expand as a linear combination of atomic orbitals (LCAO). The atomic orbitals are represented by Slater functions with expansion in gaussian functions, taking advantage of the additive rule. When the calculation is performed in this 

The excited state is formed out of a combination of 2p orbitals, and the absorption spectrum is seen as a Is-1 2p transition. The excited state is weakly bound in this model, by 0.9 eV. The calculated oscillator strength is too low, which seems to be a feature of all structural models. There is no configurational 

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. 

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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... 

The reader is also referred to the innovative nonphotochemical electron transfer studies of Weaver et al. [147], These authors have been exploring dynamical solvent effects on ground state self-exchange kinetics for or-ganometallic compounds. This work has explored many aspects of solvent control on intermediate barrier electron transfer reactions, including the effect on a distribution of solvation times. The experimental C(t) data on various solvents have been incorporated into the theoretical modeling of the ground state electron transfer reactions studied by Weaver et al. [147]. 

B) Theoretical values of mp and Xg°° would depend on the model of a solvated electron. The value of mp used in the text is at best rough (8), but AF °trans is relatively insensitive to it in the region of interest. 

The solvated electron is a transient chemical species which exists in many solvents. The domain of existence of the solvated electron starts with the solvation time of the precursor and ends with the time required to complete reactions with other molecules or ions present in the medium. Due to the importance of water in physics, chemistry and biochemistry, the solvated electron in water has attracted much interest in order to determine its structure and excited states. The solvated electrons in other solvents are less quantitatively known, and much remains to be done, particularly with the theory. Likewise, although ultrafast dynamics of the excess electron in liquid water and in a few alcohols have been extensively studied over the past two decades, many questions concerning the mechanisms of localization, thermalization, and solvation of the electron still remain. Indeed, most interpretations of those dynamics correspond to phenomenological and macroscopic approaches leading to many kinetic schemes but providing little insight into microscopic and structural aspects of the electron dynamics. Such information can only be obtained by comparisons between experiments and theoretical models. For that, developments of quantum and molecular dynamics simulations are necessary to get a more detailed picture of the electron solvation process and to unravel the structure of the solvated electron in many solvents. 

The theoretical modeling of electron transfer reactions at the solution/metal interface is challenging because, in addition to the difficulties associated with the quantitative treatment of the water/metal surface and of the electric double layer discussed earlier, one now needs to consider the interactions of the electron with the metal surface and the solvated ions. Most theoretical treatments have focused on electron-metal coupling, while representing the solvent using the continuum dielectric media. In keeping with the scope of this review, we limit our discussion to subjects that have been adi essed in recent years using molecular dynamics computer simulations. 

Given tlie disparate nature of the physical interactions between die different electronic states and the solvent, and the non-equilibrium nature of the solvation of at least one state in die vertical process, theoretical models require a fairly high degree of sophistication in their construction to be applicable to predicting spectroscopic properties in solution. This requirement, coupled with the rather poor utility of available experimental data (most solution spectra show very broad absorption peaks, making it difficult to assign vertical transitions accurately in the absence of a very complex dynamical analysis), has kept most theory in this area at the developers level. A full discussion is beyond the scope of an introductory text, but we will briefly touch on a few of die key issues. 

In the first contribution, Huxter Scholes present a review of the recent evolution of theory of EET in condensed phase from their earliest and simple formulation, based on the Forster theory to the most recent advances of theoretical and computational methods based on continuum solvation models. In the second contribution, Curutchet reviews the recent developments of PCM towards accurate theoretical investigations of EET in solution. In particular, the modelization of the various contributions of solvent effects in the chromophore-chromophore electronic coupling is presented using quantum-mechanical approaches. 

Developments in experimental and computational science have shed light on phenomena in bioenvironments and condensed phases that pose significant challenges for theoretical models of solvation [27]. Tapia [22] raises the important distinction between solvation theory and solvent effects theory. Solvation theory is concerned with direct evaluation of solvation free energies this is extensively covered by recent reviews [16,17]. Solvent-effect theory concerns changes induced by the medium onto electronic structure and molecular properties of the solute. Solvent-effect theory is concerned with molecular properties of the solvated molecule relative to the properties in vacuo as such it focuses on chemical features suitable for studying systems at the microscopic level [23]. Extensive reviews of different computational methods are given in a book by Warshel [24]. 

This narrative echoes the themes addressed in our recent review on the properties of uncommon solvent anions. We do not pretend to be comprehensive or inclusive, as the literature on electron solvation is vast and rapidly expanding. This increase is cnrrently driven by ultrafast laser spectroscopy studies of electron injection and relaxation dynamics (see Chap. 2), and by gas phase studies of anion clusters by photoelectron and IR spectroscopy. Despite the great importance of the solvated/ hydrated electron for radiation chemistry (as this species is a common reducing agent in radiolysis of liquids and solids), pulse radiolysis studies of solvated electrons are becoming less frequent perhaps due to the insufficient time resolution of the method (picoseconds) as compared to state-of-the-art laser studies (time resolution to 5 fs ). The welcome exceptions are the recent spectroscopic and kinetic studies of hydrated electrons in supercriticaF and supercooled water. As the theoretical models for high-temperature hydrated electrons and the reaction mechanisms for these species are still rmder debate, we will exclude such extreme conditions from this review. 

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