Gibbs energy of activation (standard free energy of activation), \(\Delta ^{\ddagger}G^{\,\unicode{x26ac}}\)

https://doi.org/10.1351/goldbook.G02631
The standard Gibbs energy difference between the transition state of a reaction (either an elementary reaction or a stepwise reaction) and the ground state of the reactants. It is calculated from the experimental rate constant \(k\) via the conventional form of the absolute rate equation: \[\Delta ^{\ddagger}G = R\ T\ \left[\ln (\frac{k_{\text{B}}}{h}) - \ln (\frac{k}{T})\right]\] where \(k_{\text{B}}\) is the Boltzmann constant and \(h\) the Planck constant (\(\frac{k_{\text{B}}}{h} = 2.083\ 58\times 10^{10}\ \text{K}^{-1}\ \text{s}^{-1}\)). The values of the rate constants, and hence Gibbs energies of activation, depend upon the choice of concentration units (or of the thermodynamic standard state).
See also: enthalpy of activation, entropy of activation
Sources:
PAC, 1994, 66, 1077. (Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)) on page 1118 [Terms] [Paper]
PAC, 1996, 68, 149. (A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)) on page 166 [Terms] [Paper]