Electronic Factors Nonadiabaticity

The heavy-atom effect of substituents introduced in a porphyrin will depend on the substitution pattern and may be different for Si Ti and Ti So transitions. Thus, it should be possible to control the electronic factor to increase the triplet quantum yield without compromising its lifetime. This hypothesis was investigated in detail using various meso- and beta-substituted free-base and Mg, Zn, or Cd metalloporphyrins (53). It was considered that the spin-orbit coupling of atoms in identical substitution patterns gives additive contributions to the nonadiabatic factor... 

The electron-transfer reactions that occur within and between proteins typically involve prosthetic groups separated by distances that are often greater than 10 A. When we consider these distant electron transfers, an explicit expression for the electronic factor is required. In the nonadiabatic limit, the rate constant for reaction between a donor and acceptor held at fixed distance and orientation is ... 

Gosavi S, Qin Gao Y, Marcus RA (2001) Temperature dependtmee of the electronic factor in the nonadiabatic electron transfer at metal and semiconductra- electrodes. J Electroanal Chem 500 71-77... 

The factor k takes into acount the effects of nonadiabatic transition and tunneling properly. Also note that the electronic coupling //ad is assumed to be constant in the Marcus formula, but this is not necessary in the present formulation. The coupling Had cancels out in k of Eq. (126) and the ZN probability can be calculated from the information of adiabatic potentials. 

The exact form of the pre-exponential factor A (see Chapter 5) is still being debated from the preceding considerations it is apparent that we must distinguish two cases If the reaction is adiabatic, the pre-exponential factor will be determined solely by the dynamics of the inner and outer sphere if it is nonadiabatic, it will depend on the electronic overlap between the initial and final state, which determines the probability with which the reaction proceeds once the system is on the reaction hypersurface. 

So far, only the nuclear reorganization energy attending electron transfer has been discussed, yielding the expressions above of the free energy of activation in the framework of classical transition state theory. A second series of important factors are those that govern the preexponential factor, k, raising in particular the question of the adiabaticity or nonadiabaticity of electron transfer between a molecule and the electronic states in the electrode. 

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. 

On the question of obtaining estimates of the electronic nonadiabaticity factor, you hinted at, but I don t think explicitly mentioned, one approximate approach. That is the method used by Dogonadze and German [German, E. D. Dogonadze, R. R. Izv. Akad. Nauk SSSR, Ser. Khim. 1973, 2155 Chem.Abstr. 1974, 80, 30998a], who compared the entropies of activation... 

That effective hamiltonian according to formula 29, with neglect of W"(R), appears to be the most comprehensive and practical currently available for spectral reduction when one seeks to take into account all three principal extramechanical terms, namely radial functions for rotational and vibrational g factors and adiabatic corrections. The form of this effective hamiltonian differs slightly from that used by van Vleck [9], who failed to recognise a connection between the electronic contribution to the rotational g factor and rotational nonadiabatic terms [150,56]. There exists nevertheless a clear evolution from the advance in van Vleck s [9] elaboration of Dunham s [5] innovative derivation of vibration-rotational energies into the present effective hamiltonian in formula 29 through the work of Herman [60,66]. The notation g for two radial functions pertaining to extra-mechanical effects in formula 29 alludes to that connection between... 

Fiereby, Vq refers to the maximal electronic coupling element and p is the decay coefficient factor (damping factor), which depends primarily on the nature of the bridging molecule. From the linear plot of In ETmax versus R the p value is obtained as 0.60 A [47]. This p value is located within the boundaries of nonadiabatic ET reactions for saturated hydrocarbon bridges (0.8-1.0 A ) and unsaturated phenylene bridges (0.4 A ) [1-4,54,55]. 

In a semiclassical picture, the rate kda of nonadiabatic charge transfer between a donor d and an acceptor a is determined by the electronic coupling matrix element Vda and the thermally weighted Franck-Condon factor (f C) [25, 26] ... 

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