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

A quantity related to the temperature coefficient of Δ‡H (enthalpy of activation) and Δ‡S (entropy of activation) 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 rate constant 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: J mol-1 K-1.
PAC, 1994, 66, 1077. 'Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)' on page 1120 (https://doi.org/10.1351/pac199466051077)
PAC, 1996, 68, 149. 'A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)' on page 168 (https://doi.org/10.1351/pac199668010149)