Classical PT rates

The most important difference between the application of ISM to H-atom transfers in the gas phase and PT in solution is the calculation of the reaction energy. In the first case, the classical potential energy of the H-atom transfer, AV°, is obtained as the difference between the classical potential energies of the HA bond in the reactants and the HB bond in the products. Then the vibrationally adiabatic potential energy is obtained by adding the difference in zero point-energies between reactants and products. For PT in solution the reaction free energy is directly obtained from the difference in acidity constants. 

The reaction free energy is simple to obtain experimentally for most PTs of interest. However, its decomposition in enthalpy and entropy contributions requires the measurement of acidity constants as a function of temperature. The entropies of reaction are not usually known, but, for the calculation of PT rates, the participation of the entropy in the reaction coordinate can be limited to the determination of the partition functions. In the simplest approximation, it can be assumed that the ratio of the transition state versus reactant vibrational partition functions is close to unity. Ignoring tunnelling corrections and vibrational frequency changes along the reaction coordinate, the classical rate for PT is, following eq. (6.80) 

Acid-Base Catalysis and Proton-Transfer Reactions 

These equations have a simple solution for nearly symmetrical reactions, when AV° 0 and wO.5. In this case, following ISM, the transition state bond lengths are given by 

This simple method to calculate classical rates is conveniently illustrated by the deprotonation of the conjugated acid of azulene in aqueous solution, mechanism (13.XXIV). In the absence of data on the radical ion of azulene, we take the ionisation potential and electron affinity of the molecule, 7p = 7.42 eV and Ea = 0.79 eV, to calculate m = 1.238. The e,HA Pba and HA,eq values of the two acidic C-H bonds of azulene can be taken from those of benzene. Using these parameters and eq. (13.89), we obtain AV, j = 56.1 kJ mol . With e,HA Pha and /nA.eq 

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