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  Simulating Chemical Exchange

Many spectra acquired in routine NMR spectroscopy, at an accurate inspection, show signs of chemical exchange. Probably half of the spectra acquired in solution have this characteristic. The commonest examples are exchangeable hydrogens, tertiary amides, aliphatic cycles and hetero-cycles, etc... The effect of exchange on simple 1D spectra, acquired at equilibrium, is to broaden lines. It may be useful to simulate these spectra at the computer, either for curiosity or to measure the activation energy of the process. You start from defining two or more chemical sites (often different conformations or configuration of the same molecule) and then can simulate the exchange between them.

A little of planning is needed. Count the number of chemical species. They must contain the same number of nuclei. Label each nucleus with a letter, starting from A. The iNMR convention is that a nucleus labeled with “A” can only exchange with other A nuclei, B with B, C with C, etc...
If you want to employ magnetic equivalence, for example defining the first system as A2B, then be sure that all remaining systems can be defined in the same way and that A keeps changing with other As and B with other Bs.
In case a nucleus doesn't change chemical shift when changing state, you can declare that shift numerically for the first system and through literal references in other systems (sites). In this way only one parameter is created (it's easier, later, to correct a single parameter than many copies of it). If the sites are equivalent (e.g. the two chair conformations of cyclo-hexane), only the first site will be described by numerical parameters, and the rest by literal references. In practice you will define the second site (and following) simply using the “duplicate” and the “swap” button. An illuminating step-by-step example on mutual exchange is a suggested reading.

After you have defined the systems as explained, we are still in the field of static NMR. To switch from static to dynamic (and back) there's the command “Simulate/Dynamic”, after which... the spectrum remains just the same! because the exchange constants have been created but remain set to zero. From this moment on, you can manipulate the spectrum just like a static one, with the difference that now you can also change the kinetic constants. You will only see the constants for forward transformation, like k1->2, which will be written as k12. Being at equilibrium, the backward transformation k2->1 is completely determined by the populations as in the formula:
Pop1 k1->2 = Pop2 k2->1 .

If the command “Dynamic” remains dimmed, it means that not all the declared systems are equivalent. Note, also, that the X approximation cannot be used in conjunction with dynamic NMR.

The calculation time increases ten or more times for each nucleus you add. A methyl group contributes to slowing down the process more than 3 independent hydrogens. To simulate DMF and other molecules containing methyl singlets, declare them as single isolated protons! When each system contains 6 or more nuclei, the calculation can be extremely time-consuming.
In very rare cases (for particular combinations of parameters) the system can become degenerate and the results are wrong. You can tell this fact from a reduction of the total area of the spectrum.It is enough to increase or decrease the exchange constant(s) by 0.01 to remove the degeneracy.

When you increase the exchange rate you are simulating the heating of the sample. It is natural to expect a drift of the chemical shifts upon such an heating. You have to change the chemical shifts manually, because iNMR will not do it for you. Remember it when you are trying to simulate an experimental spectrum. Above the coalescence you will see a single peak and two chemical shifts labels under it. How to drag the labels together? It is highly recommended to activate the option "Lock Equal Letters". In this way you are sure that the chemical shift difference, between the exchanging sites, remains constant.

See also

introduction to simulation

the dialog to define spin systems

the drawer

total line shape fitting

fitting the frequencies