Symmetry Effects on NMR Lineshapes of Hydration Reactions

In thermal equilibrium the number of particles in energy interval [W, W + dW] is given by the Boltzmann distribution 

If T W) is the transition probability at energy W, the number of particles per second, vhich pass the energy barrier is 

Quantum mechanically the transition rate Jqyi of the Bell model is calculated by inserting Eq. (21.53) into Eq. (21.55). 

Comparing this to the classically allowed rate from Arrhenius law 

For the numerical evaluation, Eq. (21.58) can be approximated by replacing the integration with a discrete sum over a set of energy levels. The result of such an evaluation is displayed in Fig. 21.5(d), which compares the classical Arrhenius rate with the quantum mechanical rates calculated from Eq. (21.56). 

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