heat capacity of activation, \(\Delta ^{\ddagger}C_{p}^{\,\unicode{x26ac}}\)

https://doi.org/10.1351/goldbook.H02754
A quantity related to the temperature @C01124@ of \(\Delta ^{\ddagger}H\) (@E02142@) and \(\Delta ^{\ddagger}S\) (@E02150@) according to the equations: \[\Delta ^{\ddagger}C_{p} = (\frac{\partial \Delta ^{\ddagger }H}{\partial T})_{p}=T\ (\frac{\partial \Delta ^{\ddagger }S}{\partial T})_{p}\] If the @R05138@ is expressible in the form \[\ln k = \frac{a}{T}+b+c\ \ln T + \text{d}T\] then: \[\Delta ^{\ddagger}C_{p} = (c - 1)\ R+2\ \text{d}(R\ T)\] SI unit: \(\text{J mol}^{-1}\ \text{K}^{-1}\).
Sources:
PAC, 1994, 66, 1077. (Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)) on page 1120 [Terms] [Paper]
PAC, 1996, 68, 149. (A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)) on page 168 [Terms] [Paper]