Homogeneous electron exchange

In alkaline 252 is formed in the first reduction and can be isolated when working at low temperature. Further reaction involves loss of water and fast homogeneous electron exchange between 253 and 252 with formation of 251 and product 254 [Eq. (135)]. 

In homogeneous electron exchange reactions between two species differing only in their valence states, AF is given by Equation 10 with X equal to 2X2 and (AF0,int — w) replaced by AFot — uf + wp (5). (uf... 

Additional experiments related to the influence of the composition of the surface layer in mixed solvents on electrode kinetics were carried out [281] with the V(III)/V(II) system. The electrode kinetics of this system in water-f-butanol mixtures were studied in parallel with the kinetics of the homogeneous electron exchange... 

Figure 2. (A) Dependence on A of the logarithm of the rate constants of reoxidation of the following radical anions (with increasing A ) biphenyl, 1-methylnaphthalene, naphthalene, 2-methylphenanthrene, phenanthrene, / -etrphenyl, and benzonitrile in the presence of chlorobenzene. From Ref. [7]. (B) Rate constants of the homogeneous electron exchange between chlorobenzene and redox catalysis as functions of the half-wave potential difference and of the standard potential difference (at room temperature in the considered solvent =). With increasing AE biphenyl, naphthalene, dibenzothiophene, phenanthrene, / -toluonitrile, m-toluonitrile, /7-terphenyl, and benzonitrile. From Refs 1 and 2.

The electrogenerated chemiluminescence (eel) is therefore specific of the triplet-triplet annihilation for A-type compounds. In such processes, the triplet formation, on which the eel phenomenon is based is in competition with the expected reactions already established for redox catalysis, namely homogeneous electron exchange reactions (SET and then disproportionation reactions) ... 

This Hamiltonian, which was introduced by Schmickier [12], is equivalent to earher formulations by Levich and Dogo-nadze in terms of wave mechanics [5] it is also related to the spin-boson model for homogeneous electron exchange [13] and to the Anderson—Newns model for specific adsorption [14]. 

Inserting equation (6-14) into equation (6-12) retrieves the p4/3 dependence of the exchange energy indicated in equation (3-5). This exchange functional is frequently called Slater exchange and is abbreviated by S. No such explicit expression is known for the correlation part, ec. However, highly accurate numerical quantum Monte-Carlo simulations of the homogeneous electron gas are available from the work of Ceperly and Alder, 1980. 

One obvious drawback of the LDA is that, when we replace unknown exchange-correlation energy by the known form of the exchange-correlation for a homogeneous electron gas in Equation (17), we have a problem in that cancelation of self-Coulomb... 

Here, i is the faradaic current, n is the number of electrons transferred per molecule, F is the Faraday constant, A is the electrode surface area, k is the rate constant, and Cr is the bulk concentration of the reactant in units of mol cm-3. In general, the rate constant depends on the applied potential, and an important parameter is ke, the standard rate constant (more typically designated as k°), which is the forward rate constant when the applied potential equals the formal potential. Since there is zero driving force at the formal potential, the standard rate constant is analogous to the self-exchange rate constant of a homogeneous electron-transfer reaction. 

In Eq. [47], epc ( ) and exc (n) are the exchange-correlation energy densities for the nonpolarized (paramagnetic) and fully polarized (ferromagnetic) homogeneous electron gas. The form of both exc(n) and exc(n) has been conveniently parameterized by von Barth and Hedin. Other interpolations have also been proposed24,33 for eKC(n, J ). The results for the homogeneous electron gas can be used to construct an LSDA... 

The theory of homogeneous electron transfer processes, as well as of the closely-related electron exchanges with metallic electrodes, has been the subject of considerable study. The proposal by Hush and by Marcus that these processes are, for simple systems, either usually electronically adiabatic or... 

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