Charge-hopping bridges

If, on the other hand, the LUMO of the bridge is energetically accessible from the donor orbitals, electron injection from the donor is promoted and the bridge acts as a real intermediate in transferring the electron to the acceptor. This situation is then termed as charge hopping. 

Fig. 3.6 Charge hopping in a donor-bridge-acceptor system involving a modular bridge...

Assuming, that charge hopping involving different bridge units is a diffusive process a simple treatment leads to the overall rate constant [33]... 

In summary, the distance dependence of electron transport dynamics varies as r p, where r is the bridge length (or the number of bridge units in the case of a charge hopping process) and p is less than 2. Consequently, electron transport rates display a very weak dependence on bridge length. 

Figure 41. Two charge-hopping mechanisms. The donor injects an electron (or hole) into the bridge which consists of discrete redox units, (a) The bridge units are nearly degenerate. Consequently, the injected electron (or hole) moves randomly and reversibly up and down the bridge, finally becoming irreversibly trapped by the acceptor, (b) The bridge units constitute an ordered redox cascade the electron or hole moves essentially irreversibly along the bridge towards the acceptor.

When the frontier orbitals of the bridge are not much higher in energy than those of D (for ET) or A (for HT), the dominant mechanism becomes incoherent charge hopping. Figure 4.16b shows ET by this mechanism. The electron hops in a thermally activated step from D onto the bridge frontier orbital(s) before it comes to rest on A. The intermediate state D B A is populated and the electron phase coherence is lost. The... 

Because it is affected by the interaction of a redox molecule and a matrix, charge transfer can involve both physical diffusion and charge hopping. A typical example is an oxo-bridged trinuclear ammine ruthenium complex called Ru-red 6. 

Hopping among (ideally) isoenergetic charge-transfer states of adjacent bridge... 

The general concepts as they were derived in the previous section apply only to theoretical models and/or idealized systems. In real systems, both superexchange and hopping mechanisms through modular bridges require a more sophisticated treatment. In fact, both mechanisms are omnipresent in charge-transfer reactions and interplay with each other. 

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