Reaction mechanisms adiabatic processes

Figure 2. Interconversion coordinate used in generic group exchange reactions. In this case a Sjq2 model is described. The donor and acceptor in the scheme above would correspond for instance to an halide ion Y- entering from the right in the APC and the leaving group is the halide ion Y-. The central carbon is shetched by the dark circle. The distance R is determined by the SPi-1, and the quantum states to the left and the right of the plane formed by the 3-substituents linked to the C-atom being different, they cannot physically be reached by an adiabatic process as implied in the BO-scheme if quantum mechanics must prevail (two different quantum states cannot be linked adiabatically ).

An important factor is the electron coupling between the electrode metal and the redox species or between the two members of the redox couple. If this coupling is strong the reaction is called adiabatic, i.e., no thermal activation is involved. For instance, electrons are already delocalized between the metal and the redox molecule before the electron transfer therefore, in this case no discrete electron transfer occurs [see also -> adiabatic process (quantum mechanics), - nonadiabatic (diabatic) process]. 

Chapter 3 is an overview of chemical and biological nonlinear dynamics. The kinetics of several types of reactions -first order, binary, catalytic, oscillatory, etc - and of ecological interactions -predation, competition, birth and death, etc - is described, nearly always within the framework of differential equations. The aim of this Chapter is to show that, despite the great variety of mechanisms and processes occurring, a few mathematical structures appear recurrently, and archetypical simplified models can be analyzed to understand whole classes of chemical or biological phenomena. The presence of very different timescales and the associated methodology of adiabatic elimination is instrumental in recognizing that. 

The condition (75.Ill) for a reactive collision is well known from the simple kinetic collision theory in which it is postulated without any justification. It is evident only in the special case of a completely separable reaction coordinate in which the motion along it does not influence the non-reactive modes. In general, however, the condition (75 111) requires a justification which is given by the above considerations based on the classical mechanics of non-adiabatic processes. 

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/. 

The kinetic parameters of a chemical reaction can be obtained from isothermal or adiabatic reaction calorimeters, although this is normally done as a way of elucidating a reaction mechanism rather than for reasons of process safety. 

The static theory of atomic forces, which has been considered almost exclusively up to now with the methods of quantum mechanics, needs the addition of a dynamics of a chemical reaction. The collision methods, used by several groups, do not appear to be a useful method for the treatment of chemical processes (Section 1). In what follows, a dynamical theory for the simplest cases of bimolecular reactions is developed (Sections 2 and 3), in which the problem of chemistry is expressed immediately, and clearly discussed with the help of elementary examples (Section 4). Sections 5 and 6 contain a perturbation approach, whic converges for small and large collision velocities and allows for a relatively simple sqiproximation method for the reaction velocity of non-adiabatic processes. On the other hand the theory contains a quantitative description of the connection to the adiabatic reaction process in the limit of low velocities or separated characteristics of the potential. In this way it yields a conditional justification for the application of potential theoretical representations to chemical processes and at the same time a fixation of the limits of such idealisations. 

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