Coulombic wells

Here D is the coefficient of the encounter diffusion of the ions and rc = e1 /cT is the Onsager radius of the Coulomb well in solvent with dielectric constant e. By... 

In the contact approximation (CA) the electron transfer proceeds in the thin reaction layer adjacent to the nontransparent sphere of radius a [Fig. 3.22(a)], However, the ions do not necessarily start from there as in EM. When their initial separation exceeds a, the ions do not recombine until they are delivered to the contact by encounter diffusion. Their distribution obeys the diffusional equation similar to (3.19) but for ions in the Coulomb well ... 

First, the kinetics of charge recombination/separation fl(t) is never exponential as in EM. In solvents of low polarity it is quasiexponential at the very beginning until the Coulomb well is devastated. The end of the process is universal and nonexponential at any polarity [19] ... 

The calculated kinetics of charge and radical accumulation was in qualitative agreement with what was expected. However, the theory does not fit the experimental data obtained by Beckert et al. [183,184]. The reaction time reported there is 0.8 ns, while the calculated buildup time of radical accumulation varies from 60 to 560 ns. The alcohols used by Dinse et al. can be scarcely considered as nonpolar solvents. Their polarity is so high as to render the Coulomb well insignificant and facilitates evacuation of products. The accumulation of radicals must end in a few nanoseconds, but in fact it lasts about 100 ns. This is actually an indication that there is some binding potential for ions or radicals that is deeper than that originating from the Coulomb attraction. There is room for the exciplex formation discussed in a recent review in 2000 [32]. 

These or similar sets were sometimes used for the rough interpretation of the experimental data [109,187], but in principle EM is much worse than other approximations. The escape from the reaction zone and even more so from the Coulomb well does not proceed by a single jump described as an exponential (rate) process even if /tsep is given a reasonable estimate as in Eq. (3.91). This simplification ignores all subsequent re-contacts and an essential nonexponen-tiality of the whole geminate process [20]. 

Coulombic well may change the function (213) to include an additional probability factor (.P) allowing for the carrier to reach the potential maximum [257,361]... 

The ionic charge carriers in ionic crystals are the point defects.1 2 23,24 They represent the ionic excitations in the same way as H30+ and OH-ions are the ionic excitations in water (see Fig. 1). They represent the chemical excitation upon the perfect crystallographic structure in the same way as conduction electrons and holes represent electronic excitations upon the perfect valence situation. The fact that the perfect structure, i.e., ground structure, of ionic solids is composed of charged ions, does not mean that it is ionically conductive. In AgCl regular silver and chloride ions sit in deep Coulomb wells and are hence immobile. The occurrence of ionic conductivity requires ions in interstitial sites, which are mobile, or vacant sites in which neighbors can hop. Hence a superionic dissociation is necessary, as, e.g. established by the Frenkel reaction ... 

In all cases, however, a pronounced increase in the rate of recombination occurs with increasing pressure, corresponding to a three-body process of rate coefficient a,. As opposed to the close similarity of the (Xj values, the values of a, were found to increase by two orders of magnitude in going from iso pentane to water vapor. The magnitude of a, could in fact be directly related to the efficiency of the different molecules at exchanging energy with electrons while within the coulomb well, which results in closed rather than open orbits. 

Figure 3. The Onsager model with an insert showing an electron in the coulomb well of a hole. (Reprinted with permission from Ref. [18d].)...

The fact that the stability rules of negative ions differ so much from those for neutral atoms is, again, a consequence of their radial properties. Binding by a polarisation potential is completely different from binding by a Coulomb well, even if the angular equations are identical. 

We turn now to the mechanism of orbital collapse, which is not immediately obvious from the numerical calculations of the various authors quoted above. It has been explained by Connerade [210, 211] using analytic potentials and elementary quantum theory. The key feature to note is the difference in nature between different kinds of potential in quantum mechanics. This is illustrated in fig. 5.9(a). First, we have the familiar Coulomb well or long range potential. This, as we have seen in chapter 2, gives rise to Rydberg series containing an infinite number of... 

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