Spin Systems

Alright!…..mulitplicity part 2…..FINALLY!

So the coupling that I previously described applies to first order spin systems.  There are a number of criteria that define a truly first order system, but basically the designation ‘first order’ is given when multiplicity follows the ‘n + 1 rule’ and these multiplets have intensities defined by Pascal’s Triangle.  First order spectra are awesome because they can be solved through visual inspection (i.e., chemical shifts and coupling constants can be extracted).  This condition is satisfied if the difference between two chemical shifts (Δδ) is much larger than the coupling constant (J) between them.  Otherwise, this means you’re observing strong coupling and you’ve entered second order spin system land.  The physical basis of strong coupling is subtle, having to do with complex quantum-mechanical phenomena that I won’t go into here.  

Although second-order sounds bad – it isn’t necessarily.  Basically what we’re referring to here is that a spectrum will become increasingly complicated as this ratio of chemical shift difference and coupling constant (Δδ/J) gets smaller.  As Δδ/J decreases, the: (i) multiplets approach each other; (ii) do not follow the aforementioned rules; (iii) may give rise to inaccurate information; and (iv) may be impossible to solve through simple inspection.  In strongly coupled systems the lines of a multiplet can even disappear! 

Okay – so what value of Δδ/J are we talking about here?  When will we observe a second order spectrum?  Honestly, there’s no clear answer to this.  I’ve read many NMR textbooks/papers over the course of my chemistry career and I’m fairly certain that no two had the same value; AND even more annoyingly, I’ve seen the range from 4 to about 20.  So the rule is: ‘there is no rule’.  Basically you want Δδ >>> J.  Okay, that may be a few too many ‘greater thans’ but, like I said, there is no magic ratio, but the chemical shift difference should be more than approximately 10x the coupling constant.  That is a good rough estimate.

So what can you expect to see as Δδ/J gets smaller?  Well, depending on your spectrum, one thing that you will observe is differences in the predicted line intensities.  Two doublets, for example, instead of being 1:1, will slope towards each other creating a tenting or leaning effect.  That is, the outside doublet lines decrease in intensity relative to the inside peaks, creating a sloping effect.  Depending on the degree that this occurs, it may actually be helpful as it gives you added information of what is bonded together.  As the ratio decreases, the signal looks more and more like a quartet instead of two doublets. See this figure taken from Silverstein, for example.

From: Silverstein, R. M.; Webster, F. X.; Kiemle, D. J.; “Spectrometer Identification of Organic Compounds” 7th Ed. John Wiley & Sons Inc.: USA

This can get complicated quickly.  Using the Pople Notation can help simplify this – you assign letters to the nuclei of a chemical shift with magnetic equivalence.  The most downfield resonance is assigned the latest letter in the alphabet and the increasingly upfield resonances, the preceding letters, ending in ‘A’ for the most upfield resonance.  Whether the assigned letters are separated or consecutive is dependent on the spin system.  First order systems are assigned separated letters (e.g., AX, or AMX), whereas second order systems get allocated consecutive letters (e.g., AB or ABC).  Although every magnetically equivalent nucleus gets the same letter, you denote the number of nuclei with a subscript of the number (i.e., CH = ‘A’, CH2 = ‘A2’, CH3 = ‘A3’).  For magnetically inequivalent, but chemically equivalent, nuclei they get denoted with a ‘prime’ (e.g., o-dichlorobenzene will have a spin system of AA’BB’).  For the two doublet situation described above, with pronounced tenting, it is referred to as an ‘AB quartet’ (as opposed to ‘two doublets’ as would be the case in first order spectra).

So why am I bringing this up?  Well, as we’ve previously discussed, 60 MHz spectrometers have inherently lower resolution in terms of chemical shift dispersion.  Because you’re working with a smaller spectral window (in Hz), the difference between chemical shift is lower by definition.  That is, second order effects are far more probable.

Look at the below spectra of 4’-hydroxypropiophenone, for example.  I’ve made an MNova stack plot of 400 MHz data versus 60 MHz data.  Is there a difference in the structural information that can be obtained at each field?  No…absolutely not!  Every resonance is well-resolved, chemical shift, integration and coupling constants can all be easily extracted.  That means that the lower field does not ‘hide’ or provide false information about the structure even though, you may notice, that there ARE second order effects in the 60 MHz data.  The multiplets lean.


Does that make sense?  It’s so well resolved.  Sure it does – if you look at the ethyl resonances (δ 3.42 ppm, quartet 3JH-H = 7 Hz; 1.18, triplet, 3JH-H = 7 Hz).  You’ll see that:

For 60 MHz:
Δδ= 2.24 ppm or 135 Hz and 3JH-H = 7 Hz,
so Δδ = 20J

For 400 MHz:
Δδ = 2.24 ppm or 890 Hz and 3JH-H = 7 Hz,
so Δδ = 128J

So are we in second order territory?  Again, as per the definition above, it’s questionable – but no.  But we do see tenting, so there are subtle second order effects that occur through the strongly coupled moieties.  However, the effects are minimal and only the line intensities are affected.  So despite the stigma that people often attribute to low-field NMR, low-field does not mean have to mean low information.  There are many applications that can be performed with low-field NMR without sacrificing any of the important information!