Two-electron exchange

Mossin S, Weihe H (2003) Average One-Center Two-Electron Exchange Integrals and Exchange Interactions 106 173-180 Murakami S, see Morita M (2004) 107 115-144 Muller E, see Roewer G (2002) 101 59-136... 

A simple chemical example of a photodriven one-to-two electron exchange was encountered earlier in the excited state chemistry of cyclooctatetraenyl dianion, eq. 98 (243-246) ... 

The two-electron exchange between the principal oxidation states of thallium,... 

S is the overlap integral between the magnetic orbitals, and j is the two-electron exchange integral. 

This is a sum of diagonal terms, one for each orbital. The potential operator V is given by (7.35) and includes direct terms and one- and two-electron exchange terms. 

In the exchange mechanism (Figure 56b), the two electrons exchange orbitals and so the EET dynamics now depend on inter-orbital overlap and therefore should display an exponential decay with distance. In fact, the exchange mechanism may... 

Thus three pyrylium molecules are consumed for only two electrons exchanged, resulting in n p = 2/3. 

Assuming that only the redox steps from Ir(II) to Ir(IV) (i.e., two electron exchanges) are involved in the charging process, the theoretical voltammetric charge can be estimated from Faraday s law (3.2 x 10 mC per Ir02 molecule). 

Figure 4-7. (A) Voltammogram of a film of/f coli fumarate reductase (FrdAB) adsorbed on a PGE electrode. This is a non-turnover experiment (no fumarate is present) and the voltammogram reveals discrete signals due to the redox active sites these signals are deconvolved to show the components due to the three Fe-S clusters and the FAD (prominent because it undergoes a cooperative two-electron exchange). (B) Catalytic voltammogram measured in the presence of 0.2 mM fumarate, rotation rate varied from 100 to 3000 rpm, 20 °C. The catalytic activity is boosted at potentials below that of the [4Fe-4S] cluster. Reproduced from ref. 7 and 49 with permission.

From the slope of a potentiometric titration curve or of a polaro-graphic step and, in favorable cases, from elemental analysis of the products, we know whether we are dealing with a one- or two-electron exchange. With very few exceptions metalloporphyrins are oxidized or reduced in well-defined, one-electron steps separated by more than 100 mV. 

The accuracy of this procedure depends on the thresholds set to form Z. Kashiwaga establishes two the overlap should be below a given threshold, and the two-electron exchange integral must also be below a set threshold. In practice, both these thresholds are set quite small, and the calculations closely resemble their ab initio counterpart. No empirical parameters are introduced. 

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