transition state theory

https://doi.org/10.1351/goldbook.T06470
A theory of the rates of @E02035@ which assumes a special type of equilibrium, having an @E02177@ \(K^{\ddagger }\), to exist between reactants and activated complexes. According to this theory the @O04322@ is given by: \[k=\frac{k_{\text{B}}\ T}{h}\ K^{\ddagger }\] where \(k_{B}\) is the @B00695@ and \(h\) is the @P04685@. The @O04322@ 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 \(\Delta ^{\ddagger}S^{\,\unicode{x26ac}}\), the @E02150@, is the standard molar change of @E02149@ when the @A00092@ is formed from reactants and \(\Delta ^{\ddagger}H^{\,\unicode{x26ac}}\), the @E02142@, is the corresponding standard molar change of @E02141@. The quantities \(E_{a}\) (the @E02108@) and \(\Delta ^{\ddagger}H^{\,\unicode{x26ac}}\) 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 \(\Delta ^{\ddagger}G^{\,\unicode{x26ac}}\), known as the @G02631@, is the standard molar Gibbs energy change for the conversion of reactants into @A00092@. A plot of standard molar Gibbs energy against a @R05168@ is known as a Gibbs-@E02112@; such plots, unlike @P04779@, are temperature-dependent. In principle the equations above must be multiplied by a @T06479@, \(\kappa \), which is the @P04855@ that an @A00092@ forms a particular set of products rather than reverting to reactants or forming alternative products. It is to be emphasized that \(\Delta ^{\ddagger}S^{\,\unicode{x26ac}}\), \(\Delta ^{\ddagger}H^{\,\unicode{x26ac}}\) and \(\Delta ^{\ddagger}G^{\,\unicode{x26ac}}\) occurring in the former three equations are not ordinary thermodynamic quantities, since one degree of freedom in the @A00092@ 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 [Terms] [Paper]