Probability of charge transfer

Once the fj(t) have been obtained - either approximately or numerically -the function P,(t), required to evaluate the probability of charge transfer through (17a) or (17b), can be found. Since <0 i/ > = vjfj(t), it follows from (16) that... 

Equation (43) assumes a specific value for Sq- A more general result follows from the fact that the Fourier transforms in (41) will be small, except for small values of o)p so that, as expected, to obtain high probabilities of charge transfer, Eq should either be in the solid band or, at least, not lie very far from the band. An interesting result, showing the dependence of P, on Eq, can be obtained for the one-dimensional model of section 3.3 with a half-filled band, V(t) of exponential form, P — co) = 0 and V% XB. This is... 

From this equation we can see that, in the problem considered, the characteristic size (in atomic units) is of the order of yfz consequently, the time of collision has the order of y/z/v, where v is the relative velocity of the colliding particles. The probability of charge transfer during the collision with the impact parameter p can be estimated if we multiply the probability of tunneling per unit time by the time of collision... 

Fig. 7. Interactions of electronically excited adsorbate with adsorbent, (a) Spectroscopic evidence from absorption spectra of Rose Bengale (i) in 0.5 M KN03 aqueous solution (ii) adsorbed on glass (iii) adsorbed on transparent gold film, (b) Charge-transfer possibilities at illuminated interfaces (i) Reversible for adsorbate /metal (ii) nett electron donation from adsorbate for adsorbate/semiconductor I (iii) nett electron acceptance by adsorbate for adsorbate/semiconductor II (iv) low probability of charge transfer from bulk energy bands of adsorbate/insulator interfaces. Reproduced with permission and with minor adaptation from ref. 100.

It is thought that the spacial constraint placed upon the electron donor and electron acceptor functions enhances the probability of charge transfer interaction. In addition, certain conformational and steric requirements must also be satisfied in order to facilitate efficient overlap of donor and acceptor electron orbitals required of this type of charge transfer interaction. 

To show more clearly the difference between this new approach and that used earlier, we will briefly summarize the model which was widely used for the calculation of the probability of the elementary act of charge transfer processes in polar media. 

Generally, it is the interaction of a donor (D) and an acceptor (A) involving the transfer of one electron. The probability of one-electron transfer is determined by thermodynamics namely, by the positive difference between the acceptor electron affinity and donor IP. The electron transfer is accompanied by a change in the solvate surroundings—charged particles are formed, and the solvent molecules (the solvent is usually polar) create a sphere around the particles thereby promoting their formation. Elevated temperatures destroy the solvate shell and hinder the conversion. Besides, electron transfer is often preceded by the formation of charge-transfer complexes by the sequence D A D A (D +, A -) (D+, A ) D+ A . ... 

Influence of Charge-transfer and 4/ i5d States on Energy Transfer Probabilities 68... 

The basic theory of the kinetics of charge-transfer reactions is that the electron transfer is most probable when the energy levels of the initial and final states of the system coincide [5] following the Franck-Condon principle. Thus, the efficiency of the redox reaction processes is primarily controlled by the energy overlap between the quantum states in the energy bands of the semiconductor and the donor and acceptor levels of the reactants in the electrolyte (Fig. 1). In the ideal case, the anodic current density is given by the... 

As mentioned in Section 3.4, clusters of metal atoms of varying sizes can be prepared. The presence of alkali atom clusters in the vapour phase is well documented. Such clusters have a much lower ionization energy than that of an isolated atom and also have a high electron affinity. The probability of electron transfer is therefore considerably greater in a metal cluster. It is indeed known in the case of caesium that as the density of caesium increases (from isolated atoms in a low-density gas to a liquid), larger clusters form and charge-transfer becomes increasingly favoured as the density... 

The positive S.P. observed when gases are adsorbed on a metal surface has been atrributed to (a) polarization of the adsorbate by the electron field of the metal double layer 73) and (6) charge-transfer effects 103). The importance of charge-transfer forces has been stressed by Mulliken 87) in his general theory of donor-acceptor interaction. If, as suggested, these charge-transfer forces contribute to the van der Waals attraction, then they probably take part in the physical adsorption process. The complex M X resulting from the adsorption of an inert gas on a metal surface M has been described as essentially no-bond with a small contribution from the structure As seen in Table VI, the S.P., and hence... 

The phenomenon of charge transfer in the gas phase has been discussed above. It was pointed out that such processes are quite probable when energetically allowed and commonly transfer vibrational... 

The quantity 17(f) is the time-dependent friction kernel. It characterizes the dissipation effects of the solvent motion along the reaction coordinate. The dynamic solute-solvent interactions in the case of charge transfer are analogous to the transient solvation effects manifested in C(t) (see Section II). We assume that the underlying dynamics of the dielectric function for BA and other molecules are similar to the dynamics for the coumarins. Thus we quantify t](t) from the experimental C(t) values using the relationship discussed elsewhere [139], The solution to the GLE is in the form of p(z, t), the probability distribution function. 

The cross-section of electron transfer to a multiply charged ion can be calculated by solving a set of coupled equations which take into account the probability of electron transfer on to different levels. Such calculations are extremely tedious (for a review, see ref. 21). At the same time, the presence of transitions into a large number of states makes it possible to describe the charge transfer in terms of the formalism, based on the idea of electron tunneling from one potential well to another. Using such an approach, Chibisov [22] has obtained an analytical expression for the charge transfer cross-section. 

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