# Relative magnitudes of 2- and 3-bond coupling constants

Why is geminal coupling weaker than 3-bond coupling in complex coupling? It would make more sense that atoms that are closer to each other influence each other more. Take methyl acrylate for example. The $\mathrm{H_a}$ is causing the bigger split, and the $\mathrm{H_b}$ the smaller ones. Why?

• chem.wisc.edu/areas/reich/nmr/05-hmr-04-2j.htm – DavePhD Apr 26 '16 at 20:03
• J coupling is mediated by the interaction of spin-polarised molecular orbitals. 120° bond angle geminal orbitals just don't interact well, as opposed to the situation at an sp3-hybridised CH2 group. – Karl Apr 26 '16 at 20:21
• What do you mean by weaker (and stronger)? You can’t weakly couple with pregnancy (i.e. can’t be a little bit pregnant). Unless you are talking about the magnitude of coupling? – Jan Apr 26 '16 at 20:43
• @DavePhD - Hooray! Someone else is onto Hans Reich's page as a great resource. – long Apr 26 '16 at 21:38
• @Jan - Take care when using the terms weaker and stronger when referring to coupling in NMR. A weakly coupled system is one where the distance between resonances is much greater than the coupling constant. Strongly coupled nuclei are closer together, and give rise to roofing/tenting in spectra. An AB spin system is a strongly coupled system. – long Apr 26 '16 at 21:45

## 1 Answer

Be careful when generalizing from a single example. There are many situations where the geminal coupling is much larger than vicinal coupling. Pick pretty much any molecule that has an aliphatic CH2 where the two H's are diastereotopic and you'll find that the geminal coupling for those two H's can be 12-16 Hz vs. the typical ~7 Hz vicinal couplings. However, if you're familiar with 6-membered rings in chair conformations, you've also seen vicinal coupling that range from ~2-15 Hz which leads us to the real answer to your question: the Karplus relationship.

Martin Karplus (who got a nobel prize for completely different work) is most well known in the NMR community for his theoretical work relating the values of J coupling to bond angles, bond lengths, electronegativity of substituents, etc. In other words, there's no reason that 2 bond coupling is necessarily larger (or smaller) than a 3 bond coupling – the exact values will depend on the functional group and local geometry of the molecule. Most organic chemistry texts describe a highly simplified Karplus relationship (ignoring all effects except for bond angles) for 2-bond and 3-bond J values. I've attached two common examples.

You can see that for a typical aliphatic CH2, a bond angle of ~109° would predict a 2J ~ 14 Hz. Whereas, a terminal alkene with a bond angle of ~120° would predict a 2J ~ 3 Hz. Comparing this with the 3-bond Karplus relationship, the vicinal coupling for alkenes should be 8 Hz or 10 Hz depending on the cis/trans relationship. For an aliphatic system with free rotation about a C-C bond, you have to average the Karplus relationship over all angles and you end up predicting ~ 7 Hz. For a cyclohexane derivative in a chair conformation, you can see that an axial-axial coupling (180°) is predicted to be ~10 Hz, while an axial-equatorial coupling (~60°) is predicted to be < 2 Hz!

Qualitatively, this matches what we observe quite well. Quantitatively, we quickly run into a lot of problems. Many axial-axial couplings are 12-15 Hz and the J coupling observed in alkenes typically deviates quite a bit from the predictions given by these graphs. Again, these graphs are grossly oversimplified - the real theory would fold in information about nearby substituants and steric effects, etc. However, you'd then need run a bunch electron structure calculations and average these over many different conformations, etc. So most people just live with the qualitative nature of these graphs to rationalize the patterns that they see.

• Sorry about the large images, I'm not sure how to shrink them using the markup commands... – S. Burt Apr 29 '16 at 0:55