Bimolecular reactions, collision model transition state theory

Flere, we shall concentrate on basic approaches which lie at the foundations of the most widely used models. Simplified collision theories for bimolecular reactions are frequently used for the interpretation of experimental gas-phase kinetic data. The general transition state theory of elementary reactions fomis the starting point of many more elaborate versions of quasi-equilibrium theories of chemical reaction kinetics [27, M, 37 and 38]. 

A transition-state theory (Safron et al, 1972) has been developed within the context of scattering theory, to provide suitable models for crossed molecular beam processes. As in the case of RRKM theory, it is based on the premise that the probability of complex decomposition is a product of a probability of break-up and a probability Of departure from the collision region. But it adds restrictions peculiar to bimolecular reactions, such as a limit on the maximum angular momentum that allows formation of the complex from reactants. Let p(E t) indicate the probability density for finding a product pair with kinetic energy E. This may be written as... 

Solvent effects enter through the potential of mean force and the activation energy they may cancel or nearly cancel in the expression for kj (cf. Northrup and Hynes ). The collision frequency per unit density of B, ab(8 b /Mab) 1 expression for k° for a bimolecular reaction, takes the place of the frequency Wq in (3.23) for an isomerization reaction. This analysis shows that the transition state expression for the rate coefficient appears in this theory as a singular contribution to the rate kernel for the hard-sphere model of the reaction. 

The statistical adiabatic channel model (SACM) " is one realization of the laiger class of statistical theories of chemical reactions. Its goal is to describe, with feasible computational implementation, average reaction rate constants, cross sections, and transition probabilities and lifetimes at a detailed level, to a substantial extent with state selection , for bimolecular reactive or inelastic collisions with intermediate complex formation (symbolic sets of quantum numbers v, j, E,J. ..)... 

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