We address the question that every chemist asks: given thermal reactants, how do you compute the rate of crossing the barrier toward the products? We seek to cast the answer using traditional tools and, specifically, the structure of the system at the barrier. Using just one, physically realistic, approximation, transition state theory enables us to do that. The theory identifies a bottleneck for the reaction and computes the rate of passage through it.

The success of transition state theory inspires us to do more. We shall, but we require additional assumptions to be made at each point where we seek a generalization. The most pressing reasons for doing this are that there may be more than one barrier separating the reactants and products and that there can be multiple reaction paths. The case of the O2 + C2H5 reaction, shown in Figure 5.6, represents the norm rather than the exception. Transition state theory allows us to compute the rate of barrier crossing, but to get to the products we may need to cross several barriers and/or take different paths. It is for this reason that quantum chemists have grown proficient in computing the structures at each barrier (and each hollow). But we still need to know how to compound the effects of multiple bottlenecks to obtain the overall reaction rate – and this task calls for either dynamical computations as in Chapter 5 or for an additional assumption as introduced in Section 6.2.