Approximate forms of the macroscopic rate coefficient

This rate kernel may now be incorporated into the Noyes expression for the rate coefficient [see eqn. (191)], where ft[( ) = h(f), providing that the rate kernel varies much more rapidly than does the concentration 8nA change with time. The rate coefficient is 

When oAB = R and ftf° = ftact, this rate coefficient is identical to the Collins and Kimball rate coefficient [eqn. (27)] under conditions where the reaction of encounter pairs is slow (fef0 47roABD) and over long times [4]. 

To consider the effect of an improved description of motion of the reactants in the solvent, Kapral used the Gaussian approximation for the propagator, which has been deduced from inelastic neutron scattering studies to be a reasonable description [543], The variance of a displacement by the reactant A is 

1 and Chap. 11, Sect. 2.4, where the rate coefficient is singular (infinite) at short times. Introduction of the partially reflecting boundary condition or use of telegrapher s equations are not entirely successful methods of remedying this situation. Here, the kinetic theory and modified Gaussian approximation has a clear advantage over the usual diffusion equation approach [37]. 

As a final point, Kapral has discussed the higher collision events where multiple collisions between A and B occur and a near equilibrium spatial distribution is not maintained. He found that the rate kernel was of the form 

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