Collision complexes, statistical lifetimes

The mean squared energies (A ( o)) are of course also determined by the intermolecular potentials. The duration of the collision or the lifetime of the collision complex will be of primary importance. The statistical collision model assumes a statistical distribution of the energies of all oscillators in A and M during collision. If before collision A is highly excited but M is not excited, this results in very effective energy transfer. With the statistical theory of reaction rates as discussed in section 1.8 one can easily calculate for this model values of (AE ( o)>. see e.g. ref. 97. One finds in general V kT, and so = 1 in equation (1.55). Details of (AE (Eg)) for this model are... 

The most general approach towards quantum lifetimes of collision complexes starts from the energy dependence of the statistical S-matrix. Following Smith, one can show that equation (37) holds ... 

The reason for this enliancement is intuitively obvious once the two reactants have met, they temporarily are trapped in a connnon solvent shell and fomi a short-lived so-called encounter complex. During the lifetime of the encounter complex they can undergo multiple collisions, which give them a much bigger chance to react before they separate again, than in the gas phase. So this effect is due to the microscopic solvent structure in the vicinity of the reactant pair. Its description in the framework of equilibrium statistical mechanics requires the specification of an appropriate interaction potential. 

Although radiative association has been occasionally studied in the laboratory (e.g., in ion traps ), most experiments are imdertaken at densities high enough that ternary association, in which collision with the background gas stabihses the complex, dominates. A variety of statistical treatments, such as the phase-space theory, have been used to study both radiative and ternary association. These approximate theories are often quite reliable in their estimation of the rate coefficients of association reactions. In the more detailed treatments, microscopic reversibility has been applied to the formation and re-dissociation of the complex. Enough experimental and theoretical studies have been undertaken on radiative association reactions to know that rate coefficients range downward from a collisional value to one lower than lO cm s and depend strongly on the lifetime of the complex and the frequency of photon emitted. The... 

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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