Solvated electron continuum

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. 

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... 

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... 

Transient spectra of solvated indole are measured in a 120 Jim liquid jet with a crosscorrelation of 80 fs by means of a white light continuum (450 - 740 nm) generated in a sapphire disc. The molecules are excited at 270 nm with pump pulses generated by frequency doubling the output of a noncollinearly phase matched optical parametric amplifier [2], Due to the short pump pulses there is a small yet finite probability for two-photon ionization in pure solvents. This allows us to study the spectral properties of the generated solvated electrons by measurements in pure solvents. The transient spectra of the indole solution are corrected for these solvent contributions. 

We have presented and compared different solvation models (continuum, discrete, continuum + discrete) to study solvent effects on molecular properties. In particular, the nitrogen nuclear shielding, which is known to be very sensitive to even small modifications of electronic and/or nuclear charge distributions, has been analyzed. Such alternation/combination of different models has been required to study the complex nature of solute-solvent interactions when both long-range polar and shorter-range specific H-bond effects are active. 

Fueki K, Feng D-F, Kevan L. (1974) Application of the semi-continuum model to temperature effects on solvated electron spectra and relaxation rates of dipole orientation around an excess electron in liquid alcohols. J Phys Chem 78 393-398. 

The computed value of is much more than that estimated by experiment it exceeds even the upper limit of this estimate (0.85 eV). This discrepancy cannot be removed by varying the parameters in reasonable limits. It is much easier, one would think, to attribute this difference to insufficient accuracy of the continuum model. But it is known that for reactions of complex ions whose dimensions are close to those of solvated electron this model usually provides a better agreement between the values discussed... 

Many of the available computations on radicals are strictly applicable only to the gas phase they do not account for any medium effects on the molecules being studied. However, in many cases, medium effects cannot be ignored. The solvated electron, for instance, is all medium effect. The principal frameworks for incorporating the molecular environment into quantum chemistry either place the molecule of interest within a small cluster of substrate molecules and compute the entire cluster quantum mechanically, or describe the central molecule quantum mechanically but add to the Hamiltonian a potential that provides a semiclassical description of the effects of the environment. The 1975 study by Newton (28) of the hydrated and ammoniated electron is the classic example of merging these two frameworks Hartree-Fock wavefunctions were used to describe the solvated electron together with all the electrons of the first solvent shell, while more distant solvent molecules were represented by a dielectric continuum. The intervening quarter century has seen considerable refinement in both quantum chemical techniques and dielectric continuum methods relative to Newton s seminal work, but many of his basic conclusions... 

This equation contains the basic model used by M. Newton in his pioneering calculations of the solvated electron [7]. If the charge density is replaced by a classical unit charge at the origin of the sphere, the RF potential obtained after integration of Eq. (26) corresponds to Born s model for a metalized sphere immersed in an isotropic continuum. 

The model using spherical harmonics expansions for the RF potential can be derived from Eq. (26) by introducing spherical boundary conditions. The procedure has already been outlined by this author [6] and will not be repeated here. Semi-continuum models. In this type of approach, the first solvation shell is represented in the supermolecule and, consequently, enters into the quantum chemical description. Basically, the radius of the sphere embedded in the continuum dielectric is much larger than for the desolvated solute. This model has been used in several occasions, e.g. solvated electron, electron transfer in solution. 

Although continuum solvation models do appear to reproduce the structural and spectroscopic properties of many molecules in solution, parameterization remains an issue in studies involving solvents other than water. In addition, the extension of these approaches to study proteins embedded in anisotropic environments, such as cell membranes, is clearly a difficult undertaking96. As a result, several theoretical studies have been undertaken to develop semi-empirical methods that can calculate the electronic properties of very large systems, such as proteins28,97 98. The principal problem in describing systems comprised of many basis functions is the method for solving the semi-empirical SCF equations ... 

There are basically two semicontinuum models one owing to Copeland, Kestner, andjortner (1970) (CKJ) and another to Fueki, Feng, and Kevan (1970, 1973 Fueki et al, 1971) (FFK). The calculations were designed for eh and eam,but have been extended to other polar media (Fueki et al., 1973 Jou and Dorfman, 1973). In these four or six solvent molecules form the first solvation layer in definite arrangement. Beyond that, the medium is taken as a continuum with two dielectric constants and a value of VQ, the lowest electron energy in the conduction state. 

There is greatly renewed interest in electron solvation, due to improved laser technology. However it is apparent that a simple theoretical description such as implied by Eq. (9.15) would be inadequate. That equation assumes a continuum dielectric with a unique relaxation mechanism, such as molecular dipole rotation. There is evidence that structural effects are important, and there could be different mechanisms of relaxation operating simultaneously (Bagchi, 1989). Despite a great deal of theoretical work, there is as yet no good understanding of the evolution of free-ion yield in polar media. 

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