Title: transition state theory
Long Title: IUPAC Gold Book - transition state theory
DOI: 10.1351/goldbook.T06470
Status: current

Definition
A theory of the rates of elementary reactions which assumes a special type of equilibrium, having an equilibrium constant \(K^{\ddagger }\), to exist between reactants and activated complexes. According to this theory the rate constant is given by: \[k=\frac{k_{\rm{B}}\ T}{h}\ K^{\ddagger }\] where \(k_{B}\) is the Boltzmann constant and \(h\) is the Planck constant. The rate constant can also be expressed as: \[k=\frac{k_{\rm{B}}\ T}{h}\ \exp (\frac{\Delta ^{\ddagger }S^{\,\unicode{x26ac}}}{R})\ \exp (- \frac{\Delta ^{\ddagger }H^{\,\unicode{x26ac}}}{R\ T})\] where \(\Delta ^{\ddagger}S^{\,\unicode{x26ac}}\), the entropy of activation, is the standard molar change of entropy when the activated complex is formed from reactants and \(\Delta ^{\ddagger}H^{\,\unicode{x26ac}}\), the enthalpy of activation, is the corresponding standard molar change of enthalpy. The quantities \(E_{a}\) (the energy of activation) and \(\Delta ^{\ddagger}H^{\,\unicode{x26ac}}\) are not quite the same, the relationship between them depending on the type of reaction. Also: \[k=\frac{k_{\rm{B}}\ T}{h}\ \exp (- \frac{\Delta ^{\ddagger }G^{\,\unicode{x26ac}}}{R\ T})\] where \(\Delta ^{\ddagger}G^{\,\unicode{x26ac}}\), 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, \(\kappa \), 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 \(\Delta ^{\ddagger}S^{\,\unicode{x26ac}}\), \(\Delta ^{\ddagger}H^{\,\unicode{x26ac}}\) and \(\Delta ^{\ddagger}G^{\,\unicode{x26ac}}\) occurring in the former three equations are not ordinary thermodynamic quantities, since one degree of freedom in the 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.

Related Terms
- Boltzmann constant: https://goldbook.iupac.org//terms/view/B00695
- Gibbs energy of activation: https://goldbook.iupac.org//terms/view/G02631
- Planck constant: https://goldbook.iupac.org//terms/view/P04685
- activated complex: https://goldbook.iupac.org//terms/view/A00092
- elementary reactions: https://goldbook.iupac.org//terms/view/E02035
- energy of activation: https://goldbook.iupac.org//terms/view/E02108
- energy profile: https://goldbook.iupac.org//terms/view/E02112
- enthalpy: https://goldbook.iupac.org//terms/view/E02141
- enthalpy of activation: https://goldbook.iupac.org//terms/view/E02142
- entropy: https://goldbook.iupac.org//terms/view/E02149
- entropy of activation: https://goldbook.iupac.org//terms/view/E02150
- equilibrium constant: https://goldbook.iupac.org//terms/view/E02177
- potential-energy profiles: https://goldbook.iupac.org//terms/view/P04779
- probability: https://goldbook.iupac.org//terms/view/P04855
- rate constant: https://goldbook.iupac.org//terms/view/O04322
- reaction coordinate: https://goldbook.iupac.org//terms/view/R05168
- transmission coefficient: https://goldbook.iupac.org//terms/view/T06479

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)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/T06470/html
- json: https://goldbook.iupac.org/terms/view/T06470/json
- xml: https://goldbook.iupac.org/terms/view/T06470/xml

Citation: Citation: 'transition state theory' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.T06470
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Accessed: 2026-04-19T00:15:24+00:00