## transition state theory

https://doi.org/10.1351/goldbook.T06470
A theory of the rates of elementary reactions which assumes a special type of equilibrium, having an equilibrium constant K‡, to exist between reactants and activated complexes. According to this theory the rate constant is given by: $k=\frac{k_{\text{B}}\ T}{h}\ K^{\ddagger }$ where kB is the Boltzmann constant and h is the Planck constant. The rate constant can also be expressed as: $k=\frac{k_{\text{B}}\ T}{h}\ \exp (\frac{\Delta ^{\ddagger }S^{\,\unicode{x26ac}}}{R})\ \exp (- \frac{\Delta ^{\ddagger }H^{\,\unicode{x26ac}}}{R\ T})$ where Δ‡S°, the entropy of activation, is the standard molar change of entropy when the activated complex is formed from reactants and Δ‡H°, the enthalpy of activation, is the corresponding standard molar change of enthalpy. The quantities Ea (the energy of activation) and Δ‡H° are not quite the same, the relationship between them depending on the type of reaction. Also: $k=\frac{k_{\text{B}}\ T}{h}\ \exp (- \frac{\Delta ^{\ddagger }G^{\,\unicode{x26ac}}}{R\ T})$ where Δ‡G°, known as the Gibbs energy of activation, is the standard molar Gibbs energy change for the conversion of reactants into activated complex. A plot of standard molar Gibbs energy against a reaction coordinate is known as a Gibbs-energy profile; such plots, unlike potential-energy profiles, are temperature-dependent. In principle the equations above must be multiplied by a transmission coefficient, κ, which is the probability that an activated complex forms a particular set of products rather than reverting to reactants or forming alternative products. It is to be emphasized that Δ‡S°, Δ‡H° and Δ‡G° occurring in the former three equations are not ordinary thermodynamic quantities, since one degree of freedom in the activated complex is ignored. Transition-state theory has also been known as absolute rate theory, and as activated-complex theory, but these terms are no longer recommended.
Source:
PAC, 1996, 68, 149. 'A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)' on page 190 (https://doi.org/10.1351/pac199668010149)