Transition State Theory

Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.

The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their potential energy increases due to repulsive interactions and structural distortions. This increase continues until a maximum is reached along the reaction coordinate, producing the highest-energy configuration known as the transition state. The energy difference between the reactants and this maximum corresponds to the activation energy barrier that must be overcome for the reaction to proceed.

The transition state corresponds to the single highest-energy configuration within this region. Once this configuration is reached, the system may either revert to the reactants or proceed forward to form products. The activated complex, therefore, represents a transient equilibrium with the reactants, which is often expressed as

\begin{equation*}{\text A} + {\text B} \rightleftharpoons {\text C}^{\ddagger}\end{equation*}

where C^‡ denotes the activated complex.

Transition-state theory provides an expression for the rate constant of bimolecular reactions through the Eyring equation. In this formulation, the rate constant depends on temperature, fundamental constants, and the equilibrium constant for the formation of the activated complex.

\begin{equation*}k_r = \kappa \frac{k T}{h c\degree} \overline {K}_c^{\ddagger}\end{equation*}

Because ̅K_c^‡ is related to the Gibbs free energy of activation, the equation can also be written as

\begin{equation*}k_r = \kappa \frac{k T}{h c\degree} e^{- \Delta G^{\ddagger} / RT}\end{equation*}

where ΔG^‡ represents the activation Gibbs free energy. This formulation connects reaction kinetics with thermodynamic quantities and provides a theoretical basis for understanding how temperature, entropy, and enthalpy influence reaction rates.