Reaction rate prediction hard-sphere theory

To a first approximation, the activation energy can be obtained by subtracting the energies of the reactants and transition structure. The hard-sphere theory gives an intuitive description of reaction mechanisms however, the predicted rate constants are quite poor for many reactions. 

By contrast, when both the reactive solute molecules are of a size similar to or smaller than the solvent molecules, reaction cannot be described satisfactorily by Langevin, Fokker—Planck or diffusion equation analysis. Recently, theories of chemical reaction in solution have been developed by several groups. Those of Kapral and co-workers [37, 285, 286] use the kinetic theory of liquids to treat solute and solvent molecules as hard spheres, but on an equal basis (see Chap. 12). While this approach in its simplest approximation leads to an identical result to that of Smoluchowski, it is relatively straightforward to include more details of molecular motion. Furthermore, re-encounter events can be discussed very much more satisfactorily because the motion of both reactants and also the surrounding solvent is followed. An unreactive collision between reactant molecules necessarily leads to a correlation in the motion of both reactants. Even after collision with solvent molecules, some correlation of motion between reactants remains. Subsequent encounters between reactants are more or less probable than predicted by a random walk model (loss of correlation on each jump) and so reaction rates may be expected to depart from those predicted by the Smoluchowski analysis. Furthermore, such analysis based on the kinetic theory of liquids leads to both an easy incorporation of competitive effects (see Sect. 2.3 and Chap. 9, Sect. 5) and back reaction (see Sect. 3.3). Cukier et al. have found that to include hydrodynamic repulsion in a kinetic theory analysis is a much more difficult task [454]. 

A basic goal of the theory of chemical kinetics is to predict the magnitude of the reaction rate coefficient and its temperature dependence. We focus first on bimolecular reactions. The most elementary approach to bimolecular reactions is based on the collision of hard, structureless spheres. This approach is called collision theory. 

I) the reactant particles behave as hard spheres, (ii) there is no interaction between the reactant particles until they collide, and (iii) only collisions with a combined minimum kinetic energy greater than the activation energy, f, will lead to reaction. The collision theory is usually able to predict, satisfactorily, the rate of reaction involving simple molecules. However, difficulties arise with reactions that involve complicated molecules. The observed rates tend to be lower than what the collision theory predicts, sometimes by a factor of 10 or more. Therefore, another factor, called the steric factor, has to be introduced this may be interpreted as a preference for a particular orientation (e g. direction, angle of approach) of the reacting molecules. 

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