Perturbation method bimolecular reactions

Study of Bimolecular Reactions Using Perturbation Methods... 

The FO method is also unable to treat unimolecular reactions except in a purely intuitive way. During a unimolecular reaction, the perturbations involve changes in Coulomb and resonance integrals of atoms and bonds in the reactant molecule. These lead to first-ovdQV perturbations which affect all the MOs in the system. The FO method can be applied only by the artificial and unsatisfactory expedient of treating such processes as bimolecular reactions between different parts of a single molecule. 

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. 

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

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