Dissociation rate constant transition frequency

There are two classes of reactions for which Eq. (10) is not suitable. Recombination reactions and low activation energy free-radical reactions in which the temperature dependence in the pre-exponential term assumes more importance. In this low-activation, free-radical case the approach known as absolute or transition state theory of reaction rates gives a more appropriate correlation of reaction rate data with temperature. In this theory the reactants are assumed to be in equilibrium with an activated complex. One of the vibrational modes in the complex is considered loose and permits the complex to dissociate to products. Figure 1 is again an appropriate representation, where the reactants are in equilibrium with an activated complex, which is shown by the curve peak along the extent of the reaction coordinate. When the equilibrium constant for this situation is written in terms of partition functions and if the frequency of the loose vibration is allowed to approach zero, a rate constant can be derived in the following fashion. 

Radiationless transitions occur in complexes formed with a rate constant ki, which equals the collision rate constant, 10 M s for intermolecular processes or the rotational frequency, 10 s" , for intramolecular processes. Assuming the complex dissociates with a rate constant fc-j s v k , the TET rate constant is given by... 

E = total energy h = Planck constant kg = Boltzmeinn constant k(B) = unimolecular micro canonical rate constant k(7) = canonical rate con stant Nq = initial number of ions formed M E - E< = number of states of the transition state up to - Elj above the critical energy E P E) = distribution of internal energies R(E,tj = rate of dissociation T = temperature Af = activation enthalpy A5 = activation entropy A5j = microcanonical entropy of activation Vr = reaction coordinate frequency p E) = density of states of the parent ion at internal energy E o= degeneracy of reaction path. 

The transition-state moment of inertia can only be calculated with the transition-state bond lengths. This is not a problem because the transition-state bond order, , obtained with eq. (6.68), can be employed in eq. (6.57) to yield the transition-state bond extensions. In summary, classical rate constants can be calculated with eqs. (6.57), (6.68), (6.76), (6.77) and (6.78), that only require bond dissociation energies, vibrational frequencies and bond lengths of the reactive bonds, ionization energies and electron affinities of the relevant radicals, and the masses of the atoms involved in the reaction coordinate. A few examples can make these calculations more clear. 

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