# What's the exact mechanism of spin coupling in NMR?

The most common one that's found nearly in every textbook and site is that splitting occurs due to the alignment of neighboring proton either with or against the external magnetic field so as it's B effective is increased or decreased, However in Pavia's "Introduction To Spectroscopy" a different mechanism of coupling is described, in chapter 7.1 -Although the first mechanism is mentioned in chapter 5.1- where Dirac vector model is used with pauli exclusion principle to explain coupling, It doesn't state or mention the first mechanism, and actually I'm pretty confused how come both of two mechanisms can be used to explain the same phenomenon, They seem to be contraindicated with the first mechanism stating to be a matter of alignment with external field and second one stating to be a matter of internal electron and protons alignment, I understand both but I'm just not sure I can use them in the right place.

In a system with only one spin, the energy levels available to that spin depend on the strength of the external magnetic field (there is a direct proportionality).

In more complex systems, spin–spin coupling happens when the energy levels of spin 1 are affected by the spin state of spin 2, i.e. whether spin 2 is pointing up or down. This can happen in (at least) two ways:

• through-bond coupling, also known as scalar coupling and referred to with the symbol $$J$$. This is primarily (though not exclusively) mediated by the Fermi contact interaction, which is all the electrons-in-bonds and Pauli exclusion principle stuff that you may have seen.

This only works if the two spins are 'connected' via a series of bonds that isn't too long.

• through-space coupling, also known as dipolar coupling and referred to with the symbol $$D$$. This is because spin 2 generates its own magnetic field, which can either oppose or reinforce the external magnetic field.

This doesn't require the two spins to be linked by covalent bonds. However, in solution-state NMR where molecules rotate freely, the dipolar coupling is averaged to zero* and is therefore not observed in the spectrum.

These two interactions are not mutually exclusive, and the observed coupling can be a sum of both of these. However, in solution-state spectra you only really see scalar coupling because the dipolar coupling is averaged out, and people tend to loosely use the more general term 'coupling' to refer to scalar coupling.

Chances are, what you've been reading is a mixture of both. Practically speaking, for an introductory NMR course on organic molecules, you will only ever really encounter scalar coupling. Dipolar coupling is important in more advanced NMR, as well as solid-state NMR, but most people don't really deal with that at the undergraduate level.

* Higher-order effects of dipolar coupling, such as relaxation and the NOE, do still persist in solution.

• I'm very thankful for this explanation, However I don't understand why if it's almost the scalar coupling we're encountering most textbooks and common websites uses the explanation of dipolar coupling, The literature doesn't seem consistent to me at this point, Our doctor talked only about the dipolar mechanism referring to - and using - diagrams of scalar coupling, Is it just a huge misconception? Mar 19 at 22:59
• I can't really comment without looking at the specific source you're using, unfortunately. Mar 19 at 23:02
• Pavia's "introduction to spectroscopy" Chapter 5.1, also if there's a way i can upload Our doctor's PowerPoint. However I think this well enough for my question, Just one last question, If coupling depends on carbons which are non chemically equivalent then why there's a coupling constant for benzene ortho and para protons even though they're the same? Mar 20 at 13:38
• Yup - I don't have that book on hand, though, sorry. Anyway, you're probably asking about magnetically equivalent spins, which is not exactly the same thing as chemically equivalent. Magnetically equivalent spins still have a coupling constant between them, it's just that we don't see it in the spectrum, because of quantum mechanics (see e.g. chemistry.stackexchange.com/q/53478/16683). It's a bit weird, but that's how it is. Mar 20 at 13:49
• Can't describe how much your answer helped me, it took me a whole day searching and trying to understand how both the mechanisms relate, Also that coupling constant puzzled me and I couldn't move further, Thx so much! Mar 20 at 14:21