Solvated electron electronic wave function

The electronic wave function of a solvated electron, spread over several solvent molecules, should be very sensitive to orientation fluctuations of these molecules, unlike that of an ordinary reactant. 

In the usual quantum-mechanical implementation of the continuum solvation model, the electronic wave function and electronic probability density of the solute molecule M are allowed to change on going firom the gas phase to the solution phase, so as to achieve self-consistency between the M charge distribution and the solvent s reaction field. Any treatment in which such self-consistency is achieved is called a self-consistent reaction-field (SCRF) model. Many versions of SCRF models exist. These differ in how they choose the size and shape of the cavity that contains the solute molecule M and in how they calculate t nf... 

The polaron model is properly an extension of the primitive cavity model. In both, the electron is considered to be solvated by a number of ammonia molecules. However, in the cavity model one considers the localization or solvation of the electron as described by a cavity of some shape whose boundaries act as limiting points for the potential or the electronic wave function. In the polaron model, on the other hand, the electron is considered to polarize the surrounding ammonia molecules in such a way as to provide a trapping potential for itself. The potential is derived from the laws of electrostatics adapted to the quantum mechanical description of the electron density in terms of the electronic wave function. In the final development of the theory one would of course, require self-consistency between the wave function of the electron and the potential in which it moves. It is possible that the end result may indicate that the electronic wave function is in fact almost localised within a definite volume of certain shape. However, no such assumption is made a priori as in the cavity model. 

As discussed by Travers [102], this can be due to either (1) an increase in the intrachain diffusion rate or (2) a decrease in the electron-proton coupling constants. In case 1, hydration has an effect on the polaron mobility, i.e., the latter is enhanced in case 2, hydration modifies the polaron electronic wave function. In addition, T p shows that the low frequency contribution to the proton relaxation is not affected, which is not consistent with a change in the coupling constant. It can be concluded that the increase in the macroscopic conductivity observed on hydration is related to an increase of the on-chain polaron mobility. A possible explanation can be proposed in terms of a solvation effect of the counterions resulting in a depinning of the polarons. 

This is the most sophisticated (and computationally demanding) approach and involves the explicit determination of the electronic wavefunctions for both the solvent and solute. At present serious approximations relating to the size of samples studied and/or the liquid structure, and/or the electronic wavefunctions are necessary. A very successful scheme is the local-density-functional molecular-dynamics approach of Car and Parrinello that treats the electronic wave functions and liquid structure in a rigorous and sophisticated manner but is at present limited to sample sizes of the order of 32 molecules per unit cell to represent liquid water, for example. Clusters at low temperatures are well suited to supermolecular approaches as they are intrinsically small in size and could be characterized on the basis of a relatively small number of cluster geometries. Often, however, liquids are approximated by low temperature clusters in supermolecular calculations with the aim of qualitatively describing the processes involved in a particular solvation process. Alternatively, semiempirical or empirical electronic structure methods can be used in supermolecular calculations, allowing for more realistic sample sizes and solvent structures. Care must be taken, however, to ensure that the method chosen is capable of adequately describing the intermolecular interactions. 

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. 

More recently, electrostatic theory has been revived due to the concept of molecular electrostatic potentials. The potential of the solute molecule or ion was used successfully to discuss preferred orientations of solvent molecules or solvation sites 50—54). Electrostatic potentials can be calculated without further difficulty provided the nuclear geometry (Rk) and the electron density function q(R) or the molecular wave function W rxc, [Pg.14]

Bernhardsson and coworkers have recently used CASPT2 calculations (electron-correlation correction to the CAS wave function) to model carbonyl oxides in solution. Solvation effects in acetonitrile solvent also suggest that the zwitterionic form would be favored with an elongation of the 0—0 bond length and a decrease in the C—O bond. Ab initio calculations have been recently reported for monofluorocarbonyl oxide , diflu-orocarbonyl oxide , methylcarbonyl oxide and cyclopropenone carbonyl oxide. In the recent literature the idea that carbonyl oxide can be an important source of OH radicals has also been presented. ... 

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...

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... 

Following a variational solution of the ground (Is) and first excited state (2p) of the electron in this potential well, various other polarization terms are added and a variety of characteristics for the solvated electron (optical transition energy, heat of solution, etc.) can be calculated (101,105). For illustrative purposes, we shall utilize this simple model because of its obvious transparency in relating certain (macroscopic) features of solvent properties to the energy levels and wave functions for the solvated electron in polar solvents. 

Fig. 2. Wave functions and energy levels for the solvated electron in (a) methylamine (MeA) and (b) hexamethylphosphoramide (HMPA). The potential V(r) and wavefunction are based upon the model of Jortner (101) and computed using values of the optical and static dielectric constants of the two solvents. The optical absorption responsible for the characteristic blue color is marked by h v and represents transitions between the Is and 2p states. The radius of the cavity is 3 A in MeA, and —4.5 A in HMPA. 

Considerably more elaborate treatments (1, 40,105) for calculating the electronic energy levels and wave functions for the excess electron have since been developed and attempt to introduce certain microscopic features of the local molecular environment. Such calculations for electrons in ammonia were first reported by Copeland, Kestner, and Jortner (40). The reader is referred to the paper by Baneijee and Simons (1) and the recent review by Brodsky and Tkarevsky (9) for comprehensive discussions of the current theoretical descriptions for solvated electrons in disordered condensed media (see also Ref. 171). 

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