Electron transfer model approximation

The third term, Uqt, in Eq. (27) is due to the partial electron transfer between an ion and solvents in its immediate vicinity. The model Hamiltonian approach [33], described in Section V, has shown that Uqt (= AW in Ref. 33) per primary solvent molecule, for an ion such as the polyanion, can also be expressed as a function of E, approximately a quadratic equation ... 

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

He solved this equation, using three different boundary conditions, two of which are also used in the field of particle deposition on collectors the Perfect Sink (SINK) model, the Surface Force Boundary Layer Approximation (SFBLA) and the Electrode-Ion-Particle-Electron Transfer (EIPET) model. 

FIGURE 1.13. Free-energy profiles in outer-sphere electron transfer according to the Butler-Volmer approximation (a) and to the Marcus-Hush model (b). 

When conformational change and electron transfer are concerted, the structural change may be treated as an internal reorganization factor in the electron transfer dynamics. This is the A, term of the Marcus-Hush model (Section 1.4.2 see also Section 1.4.4 for experimental examples). The model is applicable as long as the conformational changes are not so strong as to invalidate the harmonic approximation. 

One may wonder whether a purely harmonic model is always realistic in biological systems, since strongly unharmonic motions are expected at room temperature in proteins [30,31,32] and in the solvent. Marcus has demonstrated that it is possible to go beyond the harmonic approximation for the nuclear motions if the temperature is high enough so that they can be treated classically. More specifically, he has examined the situation in which the motions coupled to the electron transfer process include quantum modes, as well as classical modes which describe the reorientations of the medium dipoles. Marcus has shown that the rate expression is then identical to that obtained when these reorientations are represented by harmonic oscillators in the high temperature limit, provided that AU° is replaced by the free energy variation AG [33]. In practice, tractable expressions can be derived only in special cases, and we will summarize below the formulae that are more commonly used in the applications. 

The TMCs electronic wave function formalizing the CFT ionic model is one with a fixed number of electrons in the d-shell. In the EHCF method it is used as a zero approximation. The interactions responsible for electron transfers between the d-shell and the ligands are treated as perturbations. Following the standards semiempirical setting we restrict the AO basis for all atoms of the TMC by the valence orbitals. All the AOs of the TMC are... 

In order to treat solid DNA systems, Cai et al. propose a three-dimensional tunneling model that assumes electron transfer both along a primary DNA duplex and between neighboring duplexes [7b], as shown in Fig. 8. The apparent transfer distance (Da) can be approximately related to the transfer distance along the primary DNA ds (Di) via Eq. 10 ... 

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