Quadruplet, triplet … so simple?

In the picture below I’m showing the ‘synthetic’ NMR spectrum of Ethanol. It has been synthesized using Mnova Spin Simulation capabilities and the experimental values (chemical shifts and couplings) taken from the NMR spectrum of ethanol recorded at 600 MHz in water, so the OH signal will not show up.

Nothing new under the sun. This is a very simple spectrum where the two observed multiplets seem to follow very nicely the well-known first order multiplet rules that most chemists use on daily basis. In this case, a very simple A3X2 spin system.

But does this mean that this spectrum is actually composed by only 7 peaks? The answer is, of course not, there are many more peaks! But because of the very limited resolution, most of them are not observed and merge in such a way that only 7 peaks are ultimately observed.

In other words, the number of NMR transitions is usually much larger than the number of peaks we actually observe in the spectrum. Just to give an example: A molecule containing 30 coupled protons will result in a spectrum having 16106127360 (=1.61E+10) transitions. As its corresponding NMR spectrum will show only about 100-200 peaks, that makes it well over eighty million quantum transitions per resolved peak!

For example, let’s magnify the quadruplet and use Mnova unique capabilities to display the individual transitions by simply hovering with the mouse cursor over the atoms in the molecule (CH2 in this case). We can see that there are some ‘hidden peaks’, these are the NMR transitions calculated by diagonalizing the NMR Hamiltonian.

These transitions are so close that they cannot be resolved under the usual NMR resolution conditions. In fact, to separate all these signals, it would be necessary to have a spectral resolution of < 0.01 Hz

Whilst this is far from being feasible experimentally nowadays, it is easy to do numerically. In the figure below I’m displaying the same synthetic spectrum of Ethanol but this time synthesized using a line width of just 0.01 Hz and 1 MB of digital data points. Now the individual transitions can be seen as resolved peaks so in this example a transition will be virtually equivalent to an NMR peak.   

Simply put, an NMR spectrum is just a superposition of all spectral transitions (which can be in the order of millions), transitions compose peaks, peaks group into multiplets, and multiplets compose the spectrum.

The ability of Mnova to show the individual NMR transitions in a synthetic spectrum can be a good teaching tool

For a more theoretical and rigorous discussion on NMR transitions, see A.D. Bain, D.A. Fletcher and P. Hazendonk. "What is a transition?" Concepts in Magnetic Resonance 10 85- 98 (1998) (link)