Bimolecular Collision dynamics

In SCT the thermal rate coefficient is the product of the cross-section and average speed, kscr =, where the reactive cross-section is 

Similarly, the rate coefficient for a thermal reaction occurring with the influence of a spherically symmetric potential V(r) can be calculated from equation (63) by relating the cross-section to the potential. A useful relationship from classical scattering dynamics [16] is found in terms of the impact parameter, b. The impact parameter is the distance of closest approach between two particles in the absence of an interparticle force. At large separation, the collision trajectories of two particles will be parallel straight lines, and the impact parameter is the perpendicular distance between the trajectories. The cross-section is given by equation (64), 

---

Early attempts to describe bimolecular gas phase ion-molecule reactions were based on the classical collision dynamics of a point charge and a structureless polarizable neutral molecule. The collision process is dominated by the long range attractive ion-induced dipole potential V(r) given by (16),... 

We consider the dynamics of bimolecular collisions within the framework of... 

In the previous chapter, we have discussed the reaction dynamics of bimolecular collisions and its relation to the most detailed experimental quantities, the cross-sections obtained in molecular-beam experiments, as well as the relation to the well-known rate constants, measured in traditional bulk experiments. Indeed, in most chemical applications one needs only the rate constant—which represents a tremendous reduction in the detailed state-to-state information. 

The harmonic approximation is unrealistic in a dynamical description of the dissociation dynamics, because anharmonic potential energy terms will play an important role in the large amplitude motion associated with dissociation. An accurate potential energy surface must be used in order to obtain a realistic dynamical description of the dissociation process and, as in the quasi-classical approach for bimolecular collisions, a numerical solution of the classical equations of motion is required [2]. 

As will be shown throughout this book, quantum control of molecular dynamics has been applied to a wide variety of processes. Within the framework of chemical applications, control over reactive scattering has dominated. In particular, the two primary chemical processes focused upon are photodissociation, in which a molecule is irradiated and dissociates into various products, and bimolecular reactions, in which two molecules collide to produce new products. In this chapter we formulate fie quantum theory of photodissociation, that is, the light-induced breaking of a chemical bond. In doing so we provide an introduction to concepts essential for the 1 remainder of this book. The quantum theory of bimolecular collisions is also briefly ydiscussed. 

One useful approach to examining the dynamics of reactive bimolecular collisions involves analysis of the unimolecular dissociation of species that correspond to a reaction intermediate. This criterion was applied to the S 2 reaction in three independent investigations which made use of different experimental techniques and conditions to study the decomposition to products of specific ion-dipole complexes, the presumed intermediates of these nucleophilic displacement reactions239-241. 

The detailed analysis of the dynamics of bimolecular collisions leads to the result that the number of collisions s-1 cm-3 between molecules A and B, when the relative kinetic energy E along the line of centres is greater than the threshold energy, is given by... 

Consideration of bound-state dynamics affords one advantage not shared by systems undergoing reaction or decay. Specifically, since formal ergodic conditions require a compact phase space, ideal chaotic systems exist for bound systems but not for bimolecular collisions or unimolecular decay. Studies of these ideal bound systems therefore provide a route for analyzing statistical behavior in circumstances where the system is fully characterized. Furthermore, these ideal system results can be compared with the behavior of model molecular systems to assess the degree to which realistic systems display chaotic relaxation. 

---