Bridge-mediated long-range electron transfer

Note that is the donor ionization potential in the polar solvent that may be different from the vacuum value. 

Note that this tunneling factor is not the only term in the nonadiabatic electron transfer rate expression (16.96) that depends on the donor-acceptor distance. The reorganization energy E-c also depends on this distance as seen, for example, in Eq. (16.48). Still, the exponential form of the tuimeling factor dominates the distance dependence at large separations. We finally get rate exp(—or 

12 Bridge-mediated long-range electron transfer 

The appearance of the ionization potential in (16.101) reflects the understanding that for transfer to take place over large distances the electron has to traverse the space between the donor/acceptor centers, that is, to move in free space outside these centers. If we use a vacuum-based estimate /p 5 eV we find (2.3 A) . This implies that the coupling effectively vanishes for distances larger than just a few angstroms. Experiments show, however, that in suitable environments electron transfer can take place over considerably longer distances. 

It is not difficult to point out a plausible reason for this observation when we realize that in order to move an electron out of any of the wells in Fig. 16.6 it is not necessary to move it energetically up to the vacuum levels. In fact any unoccupied molecular levels of the solvent can supply the needed transient residence at a lower cost of energy. An example is shown in Fig. 16.7(a). D and A represent the electronic potential wells on the donor and acceptor centers, while Bi, i = 1,2. represent 

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