Bond electrons, current density

At the platinum electrode the individual steps of the four-electron reaction cannot be studied separately. Slope b has its usual value of about 0.12 V, but in contrast to what is seen at the mercury electrode, the polarization is practically independent of solution pH (i.e., the potential at a given current density shifts by 0.06 V in the negative direction when the pH is raised by a unit). It follows that the reaction rate depends on hydrogen ion concentration. The step in which an electron and a proton are transferred while the 0-0 bond is broken is probably the ratedetermining step. 

Electrochemical reductions of CO2 at a number of metal electrodes have been reported [12, 65, 66]. CO has been identified as the principal product for Ag and Au electrodes in aqueous bicarbonate solutions at current densities of 5.5 mA cm [67]. Different mechanisms for the formation of CO on metal electrodes have been proposed. It has been demonstrated for Au electrodes that the rate of CO production is proportional to the partial pressure of CO2. This is similar to the results observed for the formation of CO2 adducts of homogeneous catalysts discussed earlier. There are also a number of spectroscopic studies of CO2 bound to metal surfaces [68-70], and the formation of strongly bound CO from CO2 on Pt electrodes [71]. These results are consistent with the mechanism proposed for the reduction of CO2 to CO by homogeneous complexes described earlier and shown in Sch. 2. Alternative mechanistic pathways for the formation of CO on metal electrodes have proposed the formation of M—COOH species by (1) insertion of CO2 into M—H bonds on the surface or (2) by outer-sphere electron transfer to CO2 followed by protonation to form a COOH radical and then adsorption of the neutral radical [12]. Certainly, protonation of adsorbed CO2 by a proton on the surface or in solution would be reasonable. However, insertion of CO2 into a surface hydride would seem unlikely based on precedents in homogeneous catalysis. CO2 insertion into transition metal hydrides complexes invariably leads to formation of formate complexes in which C—H bonds rather than O—H bonds have been formed, as discussed in the next section. 

Mapping of the current densities in these and a wide range of hypothetical clamped systems gives a surprising result [14a,b]. Substantial bond alternation can coexist with the characteristic 4-electron diatropic ring current of benzene, but systems with similar alternation can also be found where the current is quenched. 

The reduction of benzene itself may then be achieved either in LiBr + HMPA solution (water as proton donor) [313] or in ethanol-HMPA (66.6 mol% ethanol) at an aluminum catghode [311] this gives a mixture of 22% cyclohexadiene, 10% cyclohexene, and 67% cyclohexane with an overall current efficiency of 95% [311]. The electrolysis must be carried out with a large excess of benzene. However, product distribution may depend on both the concentration of ethanol and the current density. As previously studied under chemical conditions (lithium metal added to ethanol in ammonia [314]), the product distribution would depend on the rates of reduction of benzene (/cb) and of cyclohexene (kc) by the reducing species (here the solvated electron), the nature of the solvent, and efficiency of the proton donor in the considered solvent. In ethylenediamine, the ratio /kc was found to be equal to 200, and this value explains why reduction stops when an isolated double bond has been formed. In contrast, in HMPA-ethanol mixtures, the ratio k[)/kc is only 1.4 this may explain the lack of selectivity and high yield of cyclohexane when a large excess of proton donor is used. 

Let us consider the current density j r) of bond electrons. It is zero, when the molecular structure is isolated in free space... 

The bond electrons at position r are described by a real wave function x) with momentum p. The coordinate vector r is the distance between the nucleus position and the electron location r = ro — Rn- If the system is located in a homogenous magnetic field Sz along the z-direction with Bz = rot Az and. (/ I 2/L X r, then the current density becomes non-zero... 

---