Simulating Mutual Exchange
Rotation around an amide bond and ligand exchange at a metal center are common processes that can occur on the NMR timescale.
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 as a generic exchange. The difference 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:
- Choose Simulate > New.
-
Define the whole molecule as a single spin system.
In the absence of exchange, it is possible to break the problem into independent spin systems, corresponding to the fragments of the molecule.
This is no longer 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 the same number of spins.
Let's consider the familiar DMF. Both methyl groups must be defined in the same page, despite the fact that they do not belong to the same spin system, chemically speaking. You should define a system of two protons with no coupling. Defining six nuclei would increase the computation time significantly while providing no additional information. With two nuclei the computation is both faster and more accurate. - 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.
- Click the button duplicate. This creates and shows a new system identical to the first one.
-
If the exchange moves nucleus A into the position of B (and vice versa)
select A and B from the menus at the bottom.
- Click Do. All the values (shifts and couplings) in the two rows A and B will be exchanged.
- If other nuclei exchange, swap them too. Do this in the second system only (the copy).
- Close the dialog and choose Simulate > Dynamic: a new parameter (k12) appears in the parameter list beside the plot. It is the rate of exchange (in sec-1).
-
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 is updated in real time.
The procedure is almost identical in the general case of non-mutual exchange. Instead of performing steps 5–7, define the shifts and couplings of the second system directly. 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 generates all possible exchange-rate constants between the defined sites, but this does not imply that all the paths are possible: if a constant is zero, no exchange is simulated along that path.