Classical transition state theory transfer

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. 

We start from classical transition state theory which provides the basic factorization of the electron transfer rate constant ... 

Another model that treats the ion transfer across ITIES as an activated transport process by applying classical transition state theory has been suggested by Girault and SchifFrin [55]. Also in this case the equation describing the ion flux across the interface is similar to that obtained by the Butler-Volmer approach. Naturally, the interpretation of the a values and k° is somewhat different in that case. Experimentally [85] and theoretically [79], the effect of solvent viscosity on the ion-transfer process has been confirmed indicating the importance of this parameter. 

The analysis presented in this review appears to show that while classical transition state theory provides a good account for experimental observation concerning ET kinetics, the picture is less clear for ion-transfer processes. Our understanding remains hindered by the primitive knowledge of the ITIES structure at a microscopic level, despite current efforts based on computer modeling (41, 51, 66, 87]. The potential distribution across the interface is also an essential piece of information that is yet to be clarified in the liquidjliquid context. Furthermore, these analyses have excluded any specific interaction of ions at the interface, which can also exert a profound effect on the reactivity of the system. In order to address all these aspects, it is crucial to develop novel spectroscopic techniques coupled to electrochemical systems. 

Transition state theory has been useful in providing a rationale for the so-called kinetic isotope effect. The kinetic isotope effect is used by enzy-mologists to probe various aspects of mechanism. Importantly, measured kinetic isotope effects have also been used to monitor if non-classical behaviour is a feature of enzyme-catalysed hydrogen transfer reactions. The kinetic isotope effect arises because of the differential reactivity of, for example, a C-H (protium), a C-D (deuterium) and a C-T (tritium) bond. 

The interpretation of phenomenological electron-transfer kinetics in terms of fundamental models based on transition state theory [1,3-6,10] has been hindered by our primitive understanding of the interfacial structure and potential distribution across ITIES. The structure of ITIES was initially studied by electrochemical and thermodynamic analyses, and more recently by computer simulations and interfacial spectroscopy. Classical electrochemical analysis based on differential capacitance and surface tension measurements has been extensively discussed in the literature [11-18]. The picture that emerged from... 

The rate of hydrogen transfer can be calculated using the direct dynamics approach of Truhlar and co-workers which combines canonical variational transition state theory (CVT) [82, 83] with semi-classical multidimensional tunnelling corrections [84], The rate constant is calculated using [83] ... 

A well defined theory of chemical reactions is required before analyzing solvent effects on this special type of solute. The transition state theory has had an enormous influence in the development of modern chemistry [32-37]. Quantum mechanical theories that go beyond the classical statistical mechanics theory of absolute rate have been developed by several authors [36,38,39], However, there are still compelling motivations to formulate an alternate approach to the quantum theory that goes beyond a theory of reaction rates. In this paper, a particular theory of chemical reactions is elaborated. In this theoretical scheme, solvent effects at the thermodynamic and quantum mechanical level can be treated with a fair degree of generality. The theory can be related to modern versions of the Marcus theory of electron transfer [19,40,41] but there is no... 

There have been numerous kinetic studies of the deuterium isotope effect for proton and hydrogen atom transfer where values for EH — Ev greatly exceed 1.4kcal/mol and the ratio of A factors, AD/AH, are significantly >1.4 values >10 are very common [4]. These observations directly challenge the classical model for proton transfer based upon transition state theory that neglects contributions from k. 

Figure 11. The solid line depicts the quantum adiabatic free energy curve for the Fe /Fe electron transfer at the water/Pt(lll) interface (obtained by using the Anderson-Newns model, path integral quantum transition state theory, and the umbrella sampling of molecular dynamics. The dashed line shows the curve from the classical calculation as given in Fig. 5. (Reprinted from Ref 14.)...

Experimental data on primary and secondary kinetic isotope effects in the hydride-transfer step in liver alcohol dehydrogenase, LADH, were analyzed using canonical variational transition theory (CVT) for overbarrier dynamics and the optimized multidimentional path (OMT) for the nuclear tunneling (Alhambra et al., 2000 and references therein). This work demonstrates somewhat better agreement of theoretical values of primary and secondary Schaad- Swein exponents calculated by combining CVT/OMT methods with the experimental values instead of CVT and classical transition states (TST). 

The transition state theory assumes that as the reacting species proceeds over the energy barrier, the medium adjusts rapidly enough to stay in equihbrium. Classical electron-transfer theory takes the first step away from this idea by distingnishing rapid and slow polarization dne to electronic and atomic motion, respectively. More recently, as faster reactions have been studied, interest has turned to the effects of rates of motion of solvent molecules. It is stiff possible to retain the notion of the solvent as a continnum, by introdncing polarizations that respond at... 

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