J-Coupling & Tin Can Phones

NMR is a ubiquitous analytical technique.  Why??  Because NMR provides a wealth of information that other analytical techniques (e.g., MS, UV-Vis, IR etc.) simply cannot.  It provides evidence for BOTH the structural components (via chemical shift and integration) AND their connectivity within a molecule (peak splitting).  Seasoned chemists are generally familiar with what causes J-couplings, and for those that aren’t, this is the first entry in a three-part series that will attempt to explain: (i) what causes peak splitting; (ii) first and second order spin systems; and then finally (iii) heteronuclear coupling.

Sooooo…..what exactly causes peaks to split??

Well, it’s due to spin coupling (aka multiplicity aka J-coupling ).

Of course these terms don’t offer much in the way of explanation, and, as anyone who’s taught organic chemistry knows, coupling is one of the hardest concepts for students to wrap their brains around – at first.

When solving a spectrum – the basic concept that one should remember is that the chemical shift of a particular resonance is determined by the chemical and/or steric environment a ‘type of hydrogen’ is located in.  Although the chemical shift is a constant value (in ppm or Hz), instead of being observed as a single peak, it can be split into several lines split around the absolute chemical shift due to small perturbations in the field.  This splitting happens because nuclei can ‘talk’ with their neighbours.

The nuclei ‘talk’? What??  This communication phenomenon is sort of akin to those tin can phones we all constructed in our respective childhoods.  Connect a can on each side of the string, pull it tight and the string will vibrate to transmit audible information.  On the molecular level, the chemical bonds between nuclei act as the ‘string’.  Instead of transmitting sound waves, the bonds allow adjacent nuclei to communicate through ordering the spins.  In case you’re scratching your head and wondering what I mean when I say ‘spin ordering’ reach into your memory’s chemistry databanks and dust off the ‘Lewis Model’.  This protocol views each element by the number of unpaired electrons it has in its valence shell (e.g., carbon has 4 unpaired electrons, hydrogen has one).  To build an organic molecule you pair these electrons – two electrons between atoms means there is a single covalent bond between them.  Of course, electrons, like nuclei, have spin.  When these electrons are confined to a bonding orbital, they adopt spins that are anti-parallel (one up and one down) to minimize the repulsion (i.e., the Pauli Principle).  In technical discussions these electrons are often referred to as ‘intervening bonding electrons’ and allow nearby nuclear spins to communicate.1

Within an external magnetic field, some nuclei spins align themselves relative to the electron spins (antiparallel being the slightly more thermodynamically favourable position).  So, like we said before, the characteristic chemical shift of a ‘type of hydrogen’ is produced by the environment of the nuclei, but depending on the spin orientation of the neighbouring protons, there are slight perturbations to the chemical shift that result in characteristic line splitting (i.e., spin multiplicity).

So how do you determine if you’re observing J-coupling or you have a collection of singlets?  Unfortunately, the real answer is: experience and/or the chemical intuition gained with experience.  But don’t despair!  Nuclei are split by
multiplicity = 2nI + 1
where I is the spin (½ for 1H)
n = number of neighbours
e.g., 3 neighbours: 2(3)(1/2) + 1 = 4.  For proton spectra multiplicity will always be the one number larger than the number of equivalent neighbours.

Moreover, for nuclei that have a nuclear spin of I = ½ (e.g., 1H, 13C, 19F, 31P), the line intensities will follow intensities defined by Pascal’s Triangle.  These repeated patterns make it easy to become familiar with multiplicity and rapidly pick out coupling versus separate resonances.

If n = 1 (i.e., there is one neighbour), the nuclear spin in question will see the neighbour’s spin as either:
1)   up
2)   down
As there are only two options, there is a 50:50 chance that either one is being observed so the chemical shift will be split into a doublet with a 1:1 ratio.  The chemical shift of this resonance is taken as the center point of the doublets.

If n = 2 (i.e., there are two neighbours), the neighbour’s nuclear spins can be aligned:
1)   down/down
2)    down/up, up/down
3)   up/up
Down/up and up/down are effectively the same orientation, so there is a higher probability the mixed alignment will be observed, and the chemical shift will be split into three lines with a 1:2:1 ratio (referred to as a triplet).  The reported chemical shift for a triplet is the most intense line.

If n = 3 (i.e., there are three neighbours), the neighbour’s nuclear spins can adopt four unique alignments via 8 orientations:
1) down/down/down
2) down/down/up, down/up/down, up/down/down
3) down/up/up, up/down/up, up/up/down
4) up/up/up
This means that this resonance will experience four unique environments and split into a four lines with a 1:3:3:1 ratio (a quartet).  The center point of this is reported as the chemical shift.

You could continue to work out these permutations, but again, nuclei with a spin of ½ afford multiplicity line intensities that will follow Pascal’s Triangle (see cartoon below).



Side bar on nomenclature: Unfortunately, coupling constants (J) are denoted a bunch of different ways.  Sometimes, J is in italics – sometimes, not.  Sometimes the nuclei involved in a particular reaction are separated by a dash, sometimes a comma.  They all denote the same thing but personally, I prefer:
Y is the number of bonds between the nuclei of interest
X1 and X2 denote nuclei that are involved in interaction
e.g., 3JH-H refers to a three-bond proton-proton coupling).


For 1H NMR, we can see 2-bond coupling (referred to as geminal) and 3-bond coupling (referred to as vicinal).  Although higher order bond couplings are also possible, they are weaker, smaller and usually only observable in specialized systems (e.g., molecules with ring strain, delocalization or conjugated unsaturates, protons in the ‘W configuration’).

When using coupling to derive connectivity and molecular structure, we rely primarily on the vicinal couplings (i.e., three bonds means multiplicity tell you about the proton neighbours! (H1-C1 is one bond, C1-C2 is two bonds, and C2-H2 is the third bond!)).  Honestly, although geminal couplings can be useful in structural assignment (e.g., (E) vs. (Z)) , they are less common and only observed when these protons are diastereotopic.  Until you get the hang of them – mostly they just complicate things and we’ll exclude geminal couplings from the remainder of this discussion.

Coupling constants vary in magnitude and sign (although they are usually just reported as an absolute value – rarely is the sign specified).  For vicinal couplings, thetorsional aka dihedral angle is of primary importance for determining the magnitude of the coupling constant.  I previously talked about that in the Karplus’ 2013 Nobel Prize entry!  The correlation of dihedral angle and magnitude of 3JH-H (in Hz) can be determined via this model.  Although, this model is still commonly used, there are some holes (e.g., it doesn’t account for electronegative substituents).

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