The tight-binding bridge model

As a last example consider a model of molecular bridge similar to that used in the electron transfer problem in Section 16.12. We consider the model of Fig. 17.6(a) 

Note that in writing Eqs (17.44) we have invoked the wide band approximation (Section 9.1). The bridge Green s function, Eq. (17.23), then satisfies 

The inequality (17.43) suggests that the needed Green function matrix element can be evaluated to lowest order in Fs/( s - f)I using the Dyson expansion (compare Eq. (16.115)) 

It is instructive to compare this result for the conduction through an TV + 2 level bridge to the parallel expression for the bridge-assisted electron transfer rate (cf. Eqs (16.114) and (16.113) 

The main difference between these expressions lies in the factors / ofEq. (17.49) and F of Eq. (17.50), that express the different ways by which the processes are terminated. The word termination is used here to express the relaxation mechanism that makes the transition a b between two stable species a and b different from the two-state dynamics of Section 2.2. In the latter case, starting from state a, the system oscillates coherently and forever between states a and b. In contrast, the present case corresponds to a process where the a b transition is followed by a fast stabilization (or tennination ) that establishes b as a distinct species and makes the reverse transition b - a an independent rate process. 

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