A semi-empirical model of the energy barrier

Energy barriers and isotope effects in proton transfer reactions 4.1 A SEMI-EMPIRICAL MODEL OF THE ENERGY BARRIER 

Proton transfer reactions are fast and essentially diffusion controlled if a hydrogen bond can be formed between proton donor and acceptor. They are slow if a hydrogen bond cannot be formed [129] (see Vol. 2, pp. 346—351). The rates of slow proton transfer reactions may be correlated with the differences of pK values of donor and acceptor. On the other hand, the pK difference cannot be the only important quantity. Therefore, a need exists for a better qualitative or semi-quantitative understanding of the factors which govern the height of the energy barrier to proton transfer. 

Furthermore, some knowledge of the approximate position of the proton on the reaction coordinate in the transition state as well as of the curvature of the barrier is needed for a calculation of the primary isotope effect in proton transfer reactions [93—96, 130]. 

A semi-empirical model of the energy barrier to proton transfer is based on a Johnston type equation. According to Johnston [131], the energy barrier in gas phase hydrogen atom abstraction reactions is described by the equation 

A rough estimate of the free energy of heterolytic cleavage of the H20— H+ bond of H30+ in aqueous solution is obtained from a simple Born-type calculation and gives [132] AG = 70 kcal. mole-1). If corrected for a statistical factor of 3, it follows that V = 70.65 kcal. mole-1 for a three-center system with X = H20, or V2 - 70.65 kcal. mole-1 if Y = H20, respectively. If the pK of the base X or Y is known, the corresponding value of V can be calculated from 

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