Weak overlap electron transfer

Some time ago it was predicted (1, 2) that, in a series of weak-overlap electron transfer reactions, the rate would first... 

The specific interaction between the electrode material and some of reacting species has to be defined formally by the overlap of the electronic states of the reactant and the electrode material at the transition state. A weak overlap electron-transfer reaction is defined as that in which the energy of the transition state is not affected by the proximity of the reacting species to the electrode. Conversely, in strong overlap... 

In systems such as [A... A ]+ where an electron (or a hole) hesitates or oscillates between two equivalent positions on subsystems A or A, symme breakings may occur when the effective transfer integral between the two sites is weak. Hiis will be the case when A and A are far apart, when they are bridged by an "insulating" ligand, or when the two localized MOs concerned by the electron transfer have a very we spatial overlap. 

Consider the case where the interaction between the molecules A and B is not yet very strong. The magnitude of Hq>P is almost linear with So,p, so that the second-order term in Eq. (3.9) is proportional to the square of So,p. The order of magnitude of So,p is equal to the rth power of an overlap integral s of an MO a of the molecule A and an MO b of the molecule B, where y is the minimum number of electron transfers between A and B required to shift the electron configuration from 0 to p. Therefore, the terms from monotransferred configurations in Eq. (3.9) have magnitudes of the order of Sab, while the monoex. and the ditr. terms are of Sob, and the monoex.-monotr. term s , the diex. term s , and so on. If the interaction is weak and s0 is small, the mono-transferred terms are important in comparison with the others. 

This expression constitutes the basis of current interpretations of electron transfer processes in biological systems. From Eq. (9), the functions Hg, (Q) and Hbb (Q) represent potential energy surfaces for the nuclear motion described by Xav and Xbw respectively, if the weak diagonal corrections Taa and T b are neglected. Then, the region Q Q where Xav and Xbw overlap significantly corresponds to the minimum of the intersection hypersurface between Hga (Q) and Hbb (Q)- Referring to definition (5), this implies ... 

Distance The affects of electron donor-acceptor distance on reaction rate arises because electron transfer, like any reaction, requires the wavefunctions of the reactants to mix (i.e. orbital overlap must occur). Unlike atom transfer, the relatively weak overlap which can occur at long distances (> 10 A) may still be sufficient to allow reaction at significant rates. On the basis of work with both proteins and models, it is now generally accepted that donor-acceptor electronic coupling, and thus electron transfer rates, decrease exponentially with distance kji Ve, exp . FCF where v i is the frequency of the mode which promotes reaction (previously estimated between 10 -10 s )FCF is a Franck Condon Factor explained below, and p is empirically estimated to range from 0.8-1.2 with a value of p 0.9 A most common for proteins. 

On the other hand, complexes with weak Jt interaction between the metal and the carbene will have an energetically low-lying K orbital. In addition to this, electron-transfer from the metal to C will be less efficient, thus leading to a more positively charged carbene fragment. Hence, carbene complexes with a large energy gap and poor orbital overlap between the metal d orbital and the carbene 2 p orbital will be prone to react with nucleophiles. 

Similarly, the fluorescence intensity of the 1,4-disubstituted azine with ferrocene and pyrene units (17) can be reversibly modulated by sequential redox reactions of ferrocene moiety. In the neutral state, compound 17 displays weak fluorescence owing to the electron transfer from the ferrocenyl group to the excited pyrene unit or by energy transfer from the excited pyrene unit to the ferrocenyl unit. Oxidation of the ferrocenyl unit, however, leads to remarkable fluorescence enhancement. This is because the ferrocenium cation shows weak electron donating ability and also the corresponding spectral overlap becomes small.27... 

Further work by Flowers examined the role of solvent polarity in the electron transfer process.30 Inner-sphere electron transfer kinetics show a weak dependence on solvent polarity due to the considerable orbital overlap of the donor-acceptor pair in the transition state. In an outer-sphere process, changes in solvent polarity alter the energetics of electron transfer. The addition of excess HMPA, beyond that required to saturate Sml2, resulted in a linear correlation to the rate of reduction for alkyl iodides, whereas no impact was observed on the rate of ketone reduction.30 Thus the experiments showed a striking difference in the electron transfer mechanism for the substrate classes, which is consistent with the operation of an outer-sphere-type process for the reduction of alkyl iodides and an inner-sphere-type mechanism for the reduction of ketones.30 These findings are consistent with the observations of Daasbjerg and Skrydstrup.28,29... 

Both these processes can be considered to occur in several distinct stages as follows (i) formation of precursor state where the reacting centers are geometrically positioned for electron transfer, (ii) activation of nuclear reaction coordinates to form the transition state, (iii) electron tunneling, (iv) nuclear deactivation to form a successor state, and (v) dissociation of successor state to form the eventual products. At least for weak-overlap reactions, step (iii) will occur sufficiently rapidly (< 10 16s) so that the nuclear coordinates remain essentially fixed. The "elementary electron-transfer step associated with the unimolecular rate constant kel [eqn. (10)] comprises stages (ii)—(iv). 

The foregoing theoretical treatment implicitly assumes that the interaction between the reacting species and the electrode is sufficiently weak and non-specific so that the energetics of the elementary electron-transfer step are determined by the properties of the isolated reactant and the surrounding solvent ("weak-overlap pathway, Sect. 2.2). However, as noted in Sect. 2.2, the occurrence of inner-sphere pathways may not only alter the overall reaction energentics via stabilization of the precursor and successor states, but also via alterations in the shape of the electron-transfer barrier itself ("strong-overlap pathway). 

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