Weak overlap limit

Providing that the interactions between the reactant and the electrode in the electrochemical transition state, and between the two reactants in the homogeneous transition state, are negligible ("weak overlap" limit), the activation barriers for reactions 10 and 11 will be closely related. 

Given that inner-sphere pathways are commonly encountered at metal-solution interfaces, as between reactants in homogeneous solution, a key question concerns the manner and extent to which the reactant-electrode interactions associated with such pathways lead to reactivity enhancements compared with weak-overlap pathways (Sect. 3.5.2). A useful tactic involves the comparison between the kinetics of structurally related reactions that occur via inner- and outer-sphere pathways. This presumes that the outer-sphere route yields kinetics which approximate that for the weak-overlap limit. For this purpose, it is desirable to estimate the work-corrected uni-molecular rate constant for the outer-sphere pathway at a particular electrode potential, k° , from the corresponding work-corrected measured value, kCOTr, using [cf. eqns. (10) and (13)]. 

The sharp separation of CT solids in Fig. 2 into neutral (...DADA...) and ionic (...D A"D A"...) is not satisfied by several phenazine-TCNQ complexes whose ground states are best characterized as partly-ionic, with fractional q in mixed stacks. Partial ionicity raises both theoretical and experimental questions. The main theoretical problem for weakly-overlapping sites is that any one-electron treatment, even in the Hartree-Fock limit, yields a minimum energy for integral, rather than fractional q. Perturbing the individual molecular sites is not an attractive solution for small overlap. 

The line width of the resonance-broadened adsorbate level is proportional to the square of the overlap energy and varies inversely as the bandwidth of the surface valence electron levels. The general form of the LDOS in the weak-adsorption limit... 

Figure 2.42. Bond-order overlap population density between adatom and endatom, one-dimensional chain (schematic), a weak adsorption limit b surface molecule limit.

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