What exchange timescales are needed to cause decoupling in NMR?

I'll try to explain the source of my confusion as clear as possible:

(*) The methyl protons in toluene are decoupled because the C-C bond between the methyl group and benzene allows very fast rotation. Hence, on average, these protons will see the same environment.

It is said that the time scale for the rotation must be faster than the time scale of the instrument. For a 250 MHz apparatus this would be (1/250MHz)=4 nanoseconds.

(*) In impure solvent the methylene protons of ethanol don't couple to -OH, since fast exchange of the OH protons results in decoupling and the protons will see an average environment.

Here it is said that this occurs if the timescale of exchange must be faster than the coupling constant J for the coupling. This is typically around 5-10 Hz. So in this case, if the exchange is in the 100 millisecond timescale decoupling already occurs.

This utterly confuses me, in the first case averaging requires nanosecond timescales (related to the frequency of the instrument) and in the second case almost second timescales (related to the small difference in frequency between coupled peaks)? Why?

ALSO and maybe related to this, why do we see in the spectrum of ethanol peak broadening for the OH proton, but not for the methylene group?

• The first statement ist imo wrong. With a good enough spectrometer, you should be able to see the $^4J$ coupling between ortho and methyl. Unless the rotation would average the coupling to zero. In ethanol, the methyl group rotates quite as fast, and you get a fine $^3J$ coupling.
– Karl
Mar 4, 2020 at 23:26
• If a teacher says this averages on the NMR time scale, he either means bear with me for the moment, i´ll come back to it later or you all know what I mean, let´s not split that hair again, and/or he hasn´t got the foggiest idea why exactly. :-))
– Karl
Apr 28, 2020 at 20:33

You need to differentiate what gets averaged, a CS difference or a scalar coupling.

Methyl protons have a different chemical shift depending on the current conformation, but they rotate so fast this gets averaged out perfectly, and they have a very sharp signal. They show no coupling between themselves because it´s an $$AB_2$$ system with CS difference zero, so $$A_3$$ actually.

$$J$$ coupling to a methyl group (e.g. the ethyl group in ethanol) gives sharp lines and clear splitting, because the coupling varies very rapidly (with the methyl rotation) around a stable and finite value, and it only depends on the occupation of the spin states in both groups.

The coupling methylene to OH is inverted every time the proton gets exchanged for one with different spin state, so it averages to zero. The exchange happens so often that the methylene group still gives a sharp quartett from the methyl.

The OH group coalesces with the water peak. Because the exchange happens randomly and differently for each molecule, the coherence in your spin ensemble deteriorates, hence the line broadening. Note: It´s not a splitting that get´s averaged out, but a change in chemical shift.

If the proton exchange was even faster, the line would sharpen again at some point I guess. Just like the methyl protons themselves. If the exchange was even slower (milliseconds), the line would broaden so much it became invisible. If you have a really dry sample, the exchange becomes so slow it does not happen on the NMR time scale, the line becomes sharp, and you even see the $$^3J$$ coupling to the methylene group.

• Dear Karl, I see what you mean between the difference between CS and coupling in these two examples. Nonetheless I think my main confusion is, what is meant with the NMR timescale? Quite often this term is used, it is fast 'compared to the NMR timescale'. But in the case of rotation it is claimed in a text I've read the timescale is nanoseconds, for exchange milliseconds. That's 10^6 difference! Mar 6, 2020 at 10:05
• In the mean while I've found this blog: u-of-o-nmr-facility.blogspot.com/2008/08/nmr-time-scale.html. Here the time scale is also linked to the difference in frequency between the two peaks (ie in Hz), and not to the frequency of the spectrometer (ie in MHz). I conclude thus that my first statement was wrong..? Mar 6, 2020 at 10:13
• The timescale of one NMR experiment is between the dwell time (time distance between two points in your FID) and the length of the FID. Generally, it can be between two times the Lamor frequency (for double quantum NMR) and five times the longest longitudinal relaxation time, i.e. hours in extreme cases. The term is not exactly well defined, per se. ;)
– Karl
Mar 6, 2020 at 17:06
• The maximal resolution (frequency difference between two points in the Fourier transform) is the inverse of the length of the FID recorded, no matter how many points you sample in that time. The spectrum just gets broader.
– Karl
Mar 6, 2020 at 17:13