Semicontinuum models

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. 

In the continuum and semicontinuum models of es, long-range forces due to distant solvent molecules are usually represented by the optical and static dielectric constants. In a true continuum model, the continuity is extended to the origin or to the surface of the cavity. In some sense, the continuum and semicontinuum models both contain both short- and long-ranged interactions. The main difference is that in the semicontinuum model, the molecules in the first shell(s) are structured. 

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... 

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. 

Kestner (1976) has analyzed the results of various semicontinuum models by comparing their features and reviewing experimental results. Some of his points are summarized in the following subsections. 

In general, semicontinuum models explain the band maximum position rather well. GJ calculate the energy at maximum absorption as 0.9 and 2.0 eV respectively for eam and eh, which compare reasonably well with the experimental values, 0.8 and 1.7 eV respectively. 

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. 

Experimental mobility values, 1.2 X 10-2 cm2/v.s. for eam and 1.9 x 10-3 cm2/v.s. for eh, indicate a localized electron with a low-density first solvation layer. This, together with the temperature coefficient, is consistent with the semicontinuum models. Considering an effective radius given by the ground state wave-function, the absolute mobility calculated in a brownian motion model comes close to the experimental value. The activation energy for mobility, attributed to that of viscosity in this model, also is in fair agreement with experiment, although a little lower. 

TABLE 6.5 Results of Calculations Using the FFK Semicontinuum Model"... 

Kevan (1974) and Tachiya (1972) point out that CKJ use an SCF approximation to calculate the medium polarization energy, but in everything else they use the adiabatic approximation. This somewhat inconsistent procedure, which may be called the modified adiabatic approximation, gives results similar to those obtained by FFK. Varying the dipole moment and the polarizability in the semicontinuum models varies the result qualitatively in the same direction. It increases the electron-solvent attraction in the first shell and also increases the dipole-dipole repulsion. Both hv and I increase with the dipole moment, but not proportionately. 

This model accounts only partially for the specific structure of liquid water, and to refine it, calculations within supermolecular and semicontinuum models were also performed. In these cases, the properties were computed for a cluster of five water molecules, simulating the inclusion of a first solvation shell. In the semicontinuum model, the cluster was immersed in the dielectric continuum. Because of the (prohibitive for the times) size of the cluster, it was possible to obtain only an uncorrelated result. On the other hand, a nonequilibrium solvation model was used in computing the orientational contribution of Equation (2.218). Finally, to determine mC(o>, T), an extensive property, a differential shell method was employed. 

In a later paper [204] the same group attempted a different approach, i.e. a semicontinuum model of ion hydration at supercritical conditions, whereby MD simulation is used both as a source of data for the model and as a test of the results obtained. 

Das and Dudis have found that the second-order transition moments (5 ) of the PNA molecule are strongly influenced by the presence of the solvent (Scheme 5) [110], It has been also demonstrated that the diagonal polarizability components a j = a, Uyy, are weakly affected by the solvents in comparison with S j. In that work, and have been evaluated by using the modified sum-over-states (MSOS) approach combined with the semicontinuum model for the solvent. 

Martinez JM, Pappalardo RR, Marcos ES (1997) Study of the Ag+ hydration by means of a semicontinuum quantum-chemical solvation model. JPhys Chem A 101 4444-4448 Matsuoka O, dementi E, Yoshimine M (1976) Cl study of the water dimer potential surface. J Chem Phys... 

The effect of the solvent (acetone) on the first hyperpolarizability of p-nitroaniline has been investigated using supermolecule and semicontinuum approaches.Employing the time-dependent Hartree-Fock method, the projection of the first hyperpolarizability on the dipole moment increases by 18 and 37% when considering one or two acetone molecules forming H-bonds with the amino group, respectively while the use of a continuum model leads to an enhancement by more than a factor of 3. 

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