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Dynamic NMR

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. Common 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 configurations of the same molecule) and then go on simulating the exchange between them.
To fully understand this chapter you must already know how to simulate a static spin system with iNMR.

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 the 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 by 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 ones) simply using the “duplicate” and the “swap” buttons. The step-by-step chapter 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 rate parameters have been created but their value is 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. 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 degenerates (mathematically speaking) 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. If you are trying to fit an experimental spectrum, 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. 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 menu option “Lock Equal Letters”. In this way you are sure that the chemical shift difference, between the exchanging sites, remains constant.

Relations Between the Parameters

iNMR automatically generates as many k parametes as possible. For example, if you define 4 systems, iNMR will generate 6 parameters of type kp->q, if you define n systems, iNMR will generate n(n-1)/2 such parameters. In real cases, however, the exchange under observation can be described with only a few rate constants (or a single one). The other parameters are either zero or equal to the first rate. If you know, for example, that k3->4 = k1->2, look into the sidebar for the line corresponding to k34. Substitute its numerical value with k12. Initially nothing happens, but the next time you change the value of k12, the same value will be assigned to the connected parameter k34.

If, instead, you know that the rates are proportional but not equal, for example: k3->4 = 1.25 k1->2, add a symbol, like: k12x. Any symbol is valid. Now open the dialog Simulate > Your Constants and define x = 1.25. You can define 100 different symbols.

Step increments

When the rate of exchange becomes high (> 100 sec-1), and the step parameter is < 100, the latter is interpreted as a percentage increment, not as an absolute increment. This is very advantageous, because you can use the little arrows for the whole range of possible values, without changing the parameter “step”. Just remember that step must be < 100.

If you need some practice, you are invited to read the web tutorial (see link below).

Related Topics

Mutual Exchange

Spin Systems

Creating a Simulated Spectrum

Parameters and Controls


Web Tutorials

Measuring Rates by NMR

Simulate Chemical Exchange with iNMR



Binsch, G., J. Am. Chem. Soc., 91, 1304-1309 (1969)