Chemical kinetics: Transition state theory

Transition state theory (TST) is one of most successful theories in theoretical chemistry [202]. It gives the framework of chemical reaction rate theory and today it is the general name for many theories based in whole or in part on the fundamental assumption of the existence of a hypersurface (transition state) in the phase space^2.13 that divides reactants and products. Three properties are assumed:

i) Reactant states are in local equilibrium along a progress coordinate, which is the reaction coordinate.
ii) Trajectories that cross the transition state hypersurface do not recross it before becoming thermalized on the reactant or product side
iii) The reaction coordinate degree of freedom can be separated from the rest and it is treated by classical mechanics.

The rate constant at a given temperature T is

$$k(T)=\gamma (T)\frac{1}{\beta h}e^{-\beta \Delta G^{\neq}(T)}$$ (2.129)

The magnitude $\Delta G^{\neq}(T)$ is the free energy difference between the reactants and the transition state. The transmission coefficient $\gamma (T)$ is a correction term that stands for all the approximations assumed in the TST.

$$\gamma (T) = g(T)\kappa (T)\Gamma (T)$$ (2.130)

Given in the same order as the approximations these three correction terms are:
i) $g(T)$ accounts for the deviations from equilibrium distribution in phase space. It can be either less than or greater than 1.
ii) $\Gamma (T)$ arises from dynamical recrossing. It will be 1 or less than 1.
iii) $\kappa (T)$ is the contribution from quantum mechanical tunneling therefore almost always this correction is greater or equals to 1.

For a review of the current status of the TST theory see reference [203], and [62] for TST applied to enzymatic systems.

However, the most expensive and problematic task is the computation of the free energy difference $\Delta G^{\neq}(T)$, which must be calculated along a predefined reaction coordinate. In some condensed phase reactions the mechanism should be intuitively predicted, such as proton transfers, and therefore the reaction coordinate is adequately chosen. On the other hand, many other reactions have a complicated or unpredictable mechanism and therefore the choice of a predefined reaction coordinate is difficult. A paradigmatic example is the reaction of autoionization of water [204]. In this sense there has been recent improvements in the computation of reaction rates without the knowledge of the reaction mechanism through transition path sampling method [137], but the computational cost is still too high and some alternatives are needed to model enzymatic reactions adequately.