Lifetimes of collision complexes

Many trajectories were calculated to investigate the numbers of reflections which would occur and thus to obtain estimates of the lifetimes of collision complexes. Summaries of the parameters of the three systems used are given in Table III. Summaries of the results of the calculated trajectories are shown in Table IV. ... 

The densities of states q(E, J) of the collision complex are not needed explicitly anywhere in these expressions, although they arise implicitly in the conditions of validity, equations (10) and (11). The densities are needed, however, for calculating lifetimes of collision complexes, and for specific rate constants of unimolecular decay. 

Lifetimes of Collision Complexes, Specific Rate Constants k(E,J) for Unimolecular Decay, and Transmission Coefficients... 

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 ... 

To obtain additional information about the lifetimes of collision complexes in the reactions studied here, we computed two other measures, the delay time (DT) and the time spent in a "tight complex" (TC), for each trajectory in selected runs. We defined the delay time as the actual time for the trajectory minus an approximate zero-interaction time. The zero-interaction time was taken to be the time required for reactants to approach to the distance b, the initial impact parameter, at the initial relative velocity, v j plus the time for the products to separate from the distance b , the final impact parameter, to the final separation at the final relative... 

Comparison of lifetimes of collision complexes in reactions of atoms with simple diatomic molecules. ... 

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 decrease In reaction rate with Increase In Internal energy can be rationalized In terms of the lifetime of the collision complex. Rearrangements such as those Involved In reaction 13 may be expected to Increase In probability when the collision partners remain together for a longer period of time. Because the lifetime of the complex will be shortened by Increased Internal or translational energy the rate coefficient of such an exothermic reaction will also be reduced. 

Lifetimes for collision complexes and specific rate coefficients for unimolecular decay of metastable states can be derived in several ways in the framework of the adiabatic channel model, resulting in similar fundamental expressions. The major differences between the various derivations of lifetimes are connected to the physical interpretation. 

One system is 0( D) with the (v=0,j=l) state of H2, HD, or D2 at a collision energy of 2 kcal/mol. Most reactions proceed via an intermediate complex. An analysis of the differential cross sections by the osculating complex model indicates that the average lifetime of the complex is less than or on the order of a rotational period. 

The introductory remarks about unimolecular reactions apply equivalently to bunolecular reactions in condensed phase. An essential additional phenomenon is the effect the solvent has on the rate of approach of reactants and the lifetime of the collision complex. In a dense fluid the rate of approach evidently is detennined by the mutual difhision coefficient of reactants under the given physical conditions. Once reactants have met, they are temporarily trapped in a solvent cage until they either difhisively separate again or react. It is conmron to refer to the pair of reactants trapped in the solvent cage as an encounter complex. If the unimolecular reaction of this encounter complex is much faster than diffiisive separation i.e., if the effective reaction barrier is sufficiently small or negligible, tlie rate of the overall bimolecular reaction is difhision controlled. 

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. 

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