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Thursday, August 11, 2011

Virtual Coupling

When the chemical shift difference between two J coupled nuclei is of the same order as the coupling constant, second order spectra are obtained. See this and this. One, often unrecognized, second order effect is virtual coupling which is often misinterpreted as first order weak coupling. In a three-spin system, virtual coupling occurs when the observed nucleus appears to be coupled to both of the other two nuclei even though it is only coupled to one of them. This arises in AA'X and ABX spin systems when X (the observed nucleus) is coupled to only one of the other two strongly coupled spins. This is illustrated in the figure below. The figure consists of simulations of X in an AA'X spin system as a function of JAA' with JAX set at 10 Hz and no coupling between A' and X. Clearly, the spectrum of X is affected by the coupling between A and A'. When JAA' = 0, a first order doublet is observed with a coupling constant of 10 Hz. As JAA' increases, complicated second order multiplets are observed. When JAA' = 50 Hz (or more) a "virtual triplet" with a coupling constant of 5 Hz is observed. This appears to be identical to a 1:2:1 triplet in a first order spectrum with a coupling constant of 1/2 JAX. It is however a second order spectrum and should not be misinterpreted as first order weak coupling. An example of this is illustrated in the figure below. The figure shows the 13C NMR signals for the ipso and ortho aromatic carbons of 1,2-bis(diphenylphosphino)ethane (DPPE). These carbon atoms are coupled to the nearest phosphorus but not to the remote phosphorus. The two phosphorus atoms are strongly coupled to one another. The ortho carbons appear as a "virtual triplet" and the ipso carbons, a second order multiplet.

7 comments:

Virtual Receptionist said...

Quite interesting - I'm glad you posted the graphics to go with. This takes me back to my college days... :)
-David

Anonymous said...

Thanks, that post helped me a lot. Just one question concerning the DPPE-molecule: if the two phosphorus atoms are strongly coupled to another, why is there just one singulet in the 31P-NMR? Is the chemical shift difference just too small?

Glenn Facey said...

Anonymous,

Thank you for your comment. Yes, the 31P resonances are isochronous and therefore appear as a singlet in the 31P spectrum. The two P atoms are however coupled to one another.

Glenn

Anonymous said...

Is it published somewhere?

Glenn Facey said...

Anonymous,

The spectra in this post are not published. You can find a general discussion of virtual coupling here:

N.E. Jacobsen, NME Spectroscopy Explained. Chapter 2, pp 69-71.

Glenn

Anonymous said...

Dr. Glenn

I am a big fan of your blog/web. The example is excellent. If I understand well then 31P spectrum has only singlet since the phosphorous atoms are chemically equivalent in the major isotopomer, which is measured, thus they have identical shift and thus their coupling is non-observable, e.g. as between hydrogens in methane.

The virtual coupling in 13C spectrum is also clear. However, when 13C spectrum is measured then each carbon signal comes from different 13C-isotopomer, in which the phosphorous are not chemically equivalent; they have probably very similar but not identical chemical shift in principal. Based on that, I thing, that the spin system should not be categorized as AA´X, which is reserved for chemically equivalent but magnetically nonequivalent nuclei, but ABX. I am right or wrong?

Glenn Facey said...

Dear Anonymous,

Thanks for your comments. I suppose you are right, but I do not think calling the difference between an ABX and an AA'X is a big deal when the only difference is 13C / 12C.

Glenn