## Wikipedia - Activation energy enthalpy of activation, $$\Delta ^{\ddagger}H^{\,\unicode{x26ac}}$$

https://doi.org/10.1351/goldbook.E02142
The standard @E02141@ of @A00093@ $$\Delta ^{\ddagger}H^{\,\unicode{x26ac}}$$ is the @E02141@ change that appears in the thermodynamic form of the rate equation obtained from conventional @T06470@. This equation is only correct for a first order reaction, for which the @R05138@ has the dimension reciprocal time. For a second order reaction, for which the @R05138@ has the dimension (reciprocal time) × (reciprocal concentration), the left hand side should be read as $$k\ c^{\,\unicode{x26ac}}$$, where $$c^{\,\unicode{x26ac}}$$ denotes the @S05909@ (usually $$1\ \text{mol dm}^{-3}$$). $k = \frac{k_{\text{B}}\ T}{h}\ \text{e}^{\frac{\Delta ^{\ddagger }S^{\,\unicode{x26ac}}}{R}}\ \mathrm{e}^{\frac{-\Delta ^{\ddagger }H^{\,\unicode{x26ac}}}{R\ T}}$ The quantity $$\Delta ^{\ddagger}S^{\,\unicode{x26ac}}$$ is the standard @E02150@, and care must be taken with standard states. In this equation $$k_{\text{B}}$$ is the @B00695@, $$T$$ the absolute temperature, $$h$$ the @P04685@, and $$R$$ the @G02579@. The @E02141@ of @A00093@ is approximately equal to the @A00102@; the conversion of one into the other depends on the @M03989@. The @E02141@ of @A00093@ is always the standard quantity, although the word standard and the superscript $$^{\unicode{x26ac}}$$ on the symbol are often omitted. The symbol is frequently (but incorrectly) written $$\Delta H^{\ddagger }$$, where the standard symbol is omitted and the $$\ddagger$$ is placed after the $$H$$.
Sources:
Green Book, 2nd ed., p. 56 [Terms] [Book]
PAC, 1993, 65, 2291. (Nomenclature of kinetic methods of analysis (IUPAC Recommendations 1993)) on page 2294 [Terms] [Paper]
PAC, 1994, 66, 1077. (Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)) on page 1113 [Terms] [Paper]
PAC, 1996, 68, 149. (A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)) on page 164 [Terms] [Paper]