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Simulating Mutual Exchange

Rotation around an amide bond or a change of position of two ligands around a metal center are two phenomena that can fall into the NMR time scale. Sometimes the final product is equivalent to the starting product. This case is called Mutual Exchange. A well known example is given by DMF (dimethylformamide), where the two methyl groups take the place of each other.
Mutual exchange is governed by the same rules of a generic exchange. What's different is that now the populations of the two sites are necessarily equal, and the rates of forward and backward exchange are equal too.

How to Define a System subject to Mutual Exchange:

Step 1

Choose Simulate > New.

Step 2

Define the whole molecule as a a single spin system.

In the absence of exchange, it's possible to factorize the problem into spin systems, corresponding to the fragments of the molecule.
This is no more possible when iNMR has to simulate the exchange: in this case each page (still called “system”) describes an exchanging site. All the “systems” must have an identical number of spins; apart lucky exceptions, this restriction means that a single document can simulate a single exchange only.
Let's consider the familiar DMF. Both methyl groups must be defined into the same page, despite the fact that they don't belong to the same spin system, chemically speaking. You should define a system of 2 protons with no coupling. Defining 6 nuclei would require much more computing time and the calculations would also be less precise (no computers is perfect when dealing with real numbers).

Step 3

Though not a necessity, at this stage you can close the dialog to verify that the simulation, before introducing the exchange, is correct. Then reopen the dialog with Simulate > Define Systems.

Step 4

Click the button duplicate. This creates and shows a new system identical to the first one.

Step 5

If the exchange moves the nucleus A in the position of B (and vice versa) select A and B from the menus at the bottom.

Do swap A with B
Step 6

Click the button Do. All the values (shifts and couplings) into the the two rows A and B will be exchanged.

Step 7

If other nuclei exchange, swap them too. Do this in the second system only (the copy).

Step 8

Close the dialog and choose Simulate > Dynamic: a new parameter (k12) appears at the bottom of the list, at the left of the plot. It's the rate of exchange (in sec-1).

Step 9

Select k12 and use the little arrows above the list to increase it. If this is too slow, you can edit the value directly, or increase the value of step.

As long as the little arrows are clicked, the value of step is continuously added or subtracted from the rate of exchange and the plot updated in real time.

The procedure is almost identical in the general case of non-mutual exchange. Instead of performing steps 5-7 you will be typing the numerical values of shifts and couplings for the second system. iNMR implicitly assumes that nucleus A of the first system takes, after the exchange, the place of A in the second system, B takes the place of B, etc...

In the general case you can define up to 9 sites (“systems”). iNMR will create all the possible exchange rates, but this does not imply that all the paths are possible: if a constant is zero, no exchange is simulated along that path.

Related Topics

The Dialog to Define Spin Systems

Dynamic NMR