Electron transfer semiclassical model

There is one experimental parameter that does serve to distinguish between the semiclassical model and the quantum model for nonadiabatic proton transfer. In the semiclassical model, if one assumes that the magnitude of the electronic barrier directly correlates with the thermodynamic driving force, a statement of the Hammond postulate, then as the driving force increases the rate of reaction increases, eventually reaching a maximum rate. The quantum model has a... 

A recently proposed semiclassical model, in which an electronic transmission coefficient and a nuclear tunneling factor are introduced as corrections to the classical activated-complex expression, is described. The nuclear tunneling corrections are shown to be important only at low temperatures or when the electron transfer is very exothermic. By contrast, corrections for nonadiabaticity may be significant for most outer-sphere reactions of metal complexes. The rate constants for the Fe(H20)6 +-Fe(H20)6 +> Ru(NH3)62+-Ru(NH3)63+ and Ru(bpy)32+-Ru(bpy)33+ electron exchange reactions predicted by the semiclassical model are in very good agreement with the observed values. The implications of the model for optically-induced electron transfer in mixed-valence systems are noted. 

In the classical activated-complex formalism nuclear tunneling effects are neglected. In addition, the electron transfer is assumed to be adiabatic. These assumptions are relaxed in the semiclassical model. 

Classically, the rate of electron transfer is determined by the rate of passage of the system over the barrier defined by the surfaces. In the semiclassical model (13) a nuclear tunneling factor that measures the increase in rate arising from... 

To summarize, in this article we have discussed some aspects of a semiclassical electron-transfer model (13) in which quantum-mechanical effects associated with the inner-sphere are allowed for through a nuclear tunneling factor, and electronic factors are incorporated through an electronic transmission coefficient or adiabaticity factor. We focussed on the various time scales that characterize the electron transfer process and we presented one example to indicate how considerations of the time scales can be used in understanding nonequilibrium phenomena. 

The semiclassical mapping approach outlined above, as well as the equivalent formulation that is obtained by requantizing the classical electron-analog model of Meyer and Miller [112], has been successfully applied to various examples of nonadiabatic dynamics including bound-state dynamics of several spin-boson-type electron-transfer models with up to three vibrational modes [99, 100], a series of scattering-type test problems [112, 118, 120], a model for laser-driven... 

Figure 2 Plots of the logarithm of electron transfer rate vs. the negative of the free energy of the reaction for three ET models and six rate measurements. The data are from Refs. 54, 55, 57, 59, 60 for a Zn-substituted Candida krusei cytochrome c that was also successively substituted at histidine 33 by three Ru(NH3)4L(His 33)3+ derivatives with L = NH3, pyridine, or isonicotinamide. The shortest direct distance between the porphyrin and imidazole carbon atoms was 13 A corresponding to the 10-A edge-to-edge D/A distance. Table 1 presents a summary of the parameters used in the three calculations plotted in this figure. For a (3 of 1.2 A-1, Eq. (5) yields HAB values ( 10 cm-1) of 80 cm-1,50 cm-1, and 75 cm-1, respectively, for Eq. (1), the semiclassical model [Eq. (4)], and the Miller-Closs model at the above D/A separation distance. The s values were calculated using Eq. (6) with the following parameters aD = 10 A, aA = 6 A, and r = 13 A. The kj and H°B parameters were varied independently to produce the plotted curves.

Theoretical efforts beginning in the late 1950s and continuing to the present day have provided a remarkably detailed description of ET reactions [3]. The semiclassical model (Eq. 1) describes the first-order rate constant for electron transfer from a donor... 

In these sections the classical, semiclassical, and quantum-mechanical models of electron transfer are outlined. In all three treatments the nuclear factors determining the rate are calculated using the zero-order or diabatic-energy surfaces. Interaction of these surfaces is necessary for the electronic factor to be nonzero. This interaction is introduced as a correction to the zero-order surfaces and determines the degree of adiabaticity of the reaction. 

The adiabatic redox reactions at electrodes were first considered by MARCUS /40a,145/ in a classical (semiclassical) framework. lEVICH, DOGONADZE and KUSNETSOV /146,147/, SGHMICKLER and VIELSTICH /169/ a.o. have developed a quantum theory for non-adiabatic electron transfer electrode reactions based on the oscillator-model. The complete quantum-mechanical treatment of the same model by CHRISTOV /37d,e/ comprises adiabatic and non-adiabatic redox reactions at electrodes. 

The clear dependence of spectral coalescence on solvent dynamics implies that the origin of the coalescence is itself dynamic. In a semiclassical electron transfer theoretical framework (Equation (2)), this could be explained in terms of electron transfers with essentially zero activation energy. The rates would then converge to the nuclear frequency factor, Vn, which in this case would appear to be dominated by solvent dipolar relaxation frequencies. In more recent solvent dynamical models, the observed effects could be considered to result from solvent friction limiting the rate of exploration of the electron transfer reaction coordinate. 

---