Essentials of Computational Chemistry

524 15 ADIABATIC REACTION DYNAMICS
TS structures must proceed more slowly than reactions with low-energy TS structures, but a
more quantitative analysis requires that we invoke more sophisticated models describing the
relationship between the properties of the activated complex and kinetics. Of such models,
the most versatile is transition-state theory (TST).
15.3 Transition-state Theory
15.3.1 Canonical Equation
The fundamental equations of transition-state theory may be derived in a number of different
ways. Presented here is a somewhat less rigorous derivation that has the benefit of being
pleasantly intuitive. Other derivations may be found in the sources listed in the bibliography
at the end of the chapter, or in references therein.
Consider the simple unimolecular reaction of Eq. (15.3), where the objective is to compute
the forward rate constant k1. Transition-state theory supposes that the nature of the activated
complex, A ‡ , is such that it represents a population of molecules in equilibrium with one
another, and also in equilibrium with the reactant, A. That population partitions between
an irreversible forward reaction to produce B, with an associated rate constant k‡, and
deactivation back to A, with a (reverse) rate constant of kdeact. The rate at which molecules
of A are activated to A ‡ is kact. This situation is illustrated schematically in Figure 15.1.
Using the usual first-order kinetic equations for the rate at which B is produced, we see that
E
k1[A] = k‡[A ‡ ] (15.14)
kact k ‡
A A B
‡
kdeact Reaction coordinate
Figure 15.1 The nature of a unimolecular reaction within the framework of transition-state theory