Marcus theory adiabatic processes

See -> charge transfer reaction, -> electron transfer at liquid-liquid interfaces, - Marcus theory, -> adiabatic process, -> non-adiabatic process... 

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... 

The Marcus theory of adiabatic electron-transfer processes. 95... 

Thus, the model incorporating the direct hole trapping by adsorbed dichloroacetate molecules, which has been proposed by Bahnemann and co-workers, appears to be probable [7]. Moreover, calculations using the Marcus electron transfer theory for adiabatic processes which result in a reorientation energy of 0.64 eV suggest that also in the case of SCN- the hole transfer occurs in the adsorbed state [7]. 

See - nonadiabatic (diabatic) process, -> Marcus theory, - Randles, and - Gurney, - adiabatic process (thermodynamics). 

The Marcus theory, as described above, is a transition state theory (TST, see Section 14.3) by which the rate of an electron transfer process (in both the adiabatic and nonadiabatic limits) is assumed to be determined by the probability to reach a subset of solvent configurations defined by a certain value of the reaction coordinate. The rate expressions (16.50) for adiabatic, and (16.59) or (16.51) for nonadiabatic electron transfer were obtained by making the TST assumptions that (1) the probability to reach transition state configuration(s) is thermal, and (2) once the reaction coordinate reaches its transition state value, the electron transfer reaction proceeds to completion. Both assumptions rely on the supposition that the overall reaction is slow relative to the thermal relaxation of the nuclear environment. We have seen in Sections 14.4.2 and 14.4.4 that the breakdown of this picture leads to dynamic solvent effects, that in the Markovian limit can be characterized by a friction coefficient y The rate is proportional to y in the low friction, y 0, limit where assumption (1) breaks down, and varies like y when y oo and assumption (2) does. What stands in common to these situations is that in these opposing limits the solvent affects dynamically the reaction rate. Solvent effects in TST appear only through its effect on the free energy surface of the reactant subspace. 

As already mentioned above, the derivation of the Butler-Volmer equation, especially the introduction of the transfer factor a, is mostly based on an empirical approach. On the other hand, the model of a transition state (Figs. 7.1 and 7.2) looks similar to the free energy profile derived for adiabatic reactions, i.e. for processes where a strong interaction between electrode and redox species exists (compare with Section 6.3.3). However, it should also be possible to apply the basic Marcus theory (Section 6.1) or the quantum mechanical theory for weak interactions (see Section 6.3.2) to the derivation of a current-potential. According to these models the activation energy is given by (see Eq. 6.10)... 

The adiabatic inner-sphere redox reactions were first treated by MARCUS /145/, who made use of the classical and semiclassical statistical theory A quantum-mechanical treatment of the two-frequency oscillator model by DOGONADZE and KUSNETSOV /147/ provides tractable rate expressions for non-adiabatic processes in both high and low temperature ranges. Similar results were obtained by KESTNER, LOGAN and JORTNER /148/. 

Within the framework of Marcus theory of electron tfansfer, the activation energy for a non-adiabatic electron transfer process is given by. ... 

See also adiabatic process, Marcus theory, -> Randles, and Gurney. 

The Marcus classical free energy of activation is AG , the adiabatic preexponential factor A may be taken from Eyring s Transition State Theory as (kg T /h), and Kel is a dimensionless transmission coefficient (0 < k l < 1) which includes the entire efiFect of electronic interactions between the donor and acceptor, and which becomes crucial at long range. With Kel set to unity the rate expression has only nuclear factors and in particular the inner sphere and outer sphere reorganization energies mentioned in the introduction are dominant parameters controlling AG and hence the rate. It is assumed here that the rate constant may be taken as a unimolecular rate constant, and if needed the associated bimolecular rate constant may be constructed by incorporation of diffusional processes as ... 

Our application of this approach to the benzene ion dissociation in collaboration with Klippenstein was noted in Section II. When it can be carried out, this is by far the most satisfactory way currently available for extrapolation to E. The necessary VTST calculations, whether by way of the Marcus variational RRKM approach or other approaches (e.g., statistical adiabatic channel theory ) are laborious, involving the quantum chemical construction of large potential maps for the interaction of the separating fragments and extensive statistical calculations for the dissociation process. Application of this approach to a variety of interesting systems is one of the outstanding opportunities for future work. 

Excited State Charge Transfer. Our goal here is to discuss aspects of ET theory that are most relevant to the charge transfer processes of excited molecules. One important point is that often the solvent relaxation is not well modeled with a single t, but rather a distribution of times apply. This subject has been treated by Hynes [63], Nadler and Marcus [65], Rips and Jortner [66], Mukamel [67], Newton and Friedman [68], Zusman [62], Warshel [71], and Fonseca [139], We also would like to study ET in the strongly adiabatic regime since experimental results on BA indicate this is the correct limit. Finally, we would like to treat the special case of three-well ET, which is the case for BA. 

---