Intermediate exchange region

In the intermediate exchange region, where Q2 A2, the signal is spread over the whole frequency range d> A, for details see Refs. 16-1S 27,43). 

In the so-called intermediate exchange region, eqn (5.18) is not easily tractable and recourse is usually made to computer simulations. Qualitatively, however, it is clear that as the rate increases, the separate resonances of the slow exchange limit broaden, shift together, coalesce and then begin to sharpen into the single line of the fast exchange limit. 

Fig. 3. Simulation of the lineshape of the aldehyde proton in furfural in the intermediate exchange region, and its constituents (lower lines). The lineshape consists of two components, each normal NMR lineshapes but distorted in position, phase, intensity by the dynamics.

When the lines in the spectrum are broad and starting to coalesce, we are in the intermediate exchange region. The best way to measure rates here is to simulate the lineshape and compare it, visually or numerically, with the observed spectrum. Several ways of calculating the lineshape are available, but we like the formulation that treats the spectrum always as a sum of transitions, rather than as a single lineshape. 

Clearly, the expressions in the fast and intermediate exchange region are complex [1, 38, 39], even when valid approximations can be made to simplify the equations. Moreover, a substantial experimental effort is sometimes required before it can be ascertained whether such simplifications are justified. The most reliable and probably the best method for the determination of exchange rate constants in nontrivial cases is the matching of experimental and calculated spectra by computer modeling. 

From the researcher s point of view, the intermediate exchange region often provides the best conditions for line-broadening experiments [42], but data treatment requires computer simulations based on different theoretical models. 

The most accurate method in the intermediate exchange region and the one applicable over the largest range of lifetimes is the generation of the line shape and direct comparison with experiment. 

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