Do chemists use X-NMR where the spin of X is greater than a half?

[etotheipi]

If the nuclear spin quantum number of a particular type of nucleus is $I$, then the $z$-component of spin can take values $m_I = -I, \dots, I$, and since the energy of a dipole is $E = - \vec{\mu} \cdot \vec{B} = - \gamma m_I \hbar B_0$ (with $\vec{B} = B_0 \hat{z}$), you end up with $2I+1$ nuclear energy levels.

If $I =1$, for instance, the nucleus will have 3 energy levels, and there will be two possible transitions each of magnitude $\Delta E_1 = \gamma \hbar B_0$ and $\Delta E_2 = 2\gamma \hbar B_0$. That suggests that you'd obtain two peaks for that nucleus in the spectrum. For even larger values of $I$, it seems that the spectrum would get quite complicated, with multiple peaks for each nucleus even without taking into account coupling.

I know that it's quite common to look at coupling to nuclei with spins greater than $1/2$, e.g. coupling to deuterium in $^1\mathrm{H}$-NMR or $^{13}\mathrm{C}$-NMR, but do chemists also perform e.g. $^2 \mathrm{H}$-NMR, or more generally $\mathrm{X}$-NMR where the spin of $X$ is greater than $1/2$? If so, is most of the analysis done computationally?

 

[DrClaude]

Chlorine NMR exists, with both isotopes 35 and 37 having $I=3/2$.

Yes, it makes the spectra more complicated, but these complications can also come from other factors, e.g.,

^35/37Cl NMR spectroscopy studies of organic systems are very rare, with only a few neat liquids having been studied.1 The lack of chlorine NMR spectroscopy data may be explained by the fact that ³⁵Cl and ³⁷Cl are quadrupolar (spin I=3/2) and low-frequency isotopes. The quadrupole moments of the chlorine nuclei couple with the electric field gradient (EFG) tensor at the nuclei; this phenomenon is known as the quadrupolar interaction (QI). The quadrupolar coupling constant, C_Q, and the quadrupolar asymmetry parameter, η_Q, describe the magnitude and asymmetry of the QI. In solution, one of the consequences of the QI is fast relaxation, which means that the ^35/37Cl NMR signals for covalently bound chlorines are very broad and are of low intensity.1 For these reasons, chemically distinct chlorine sites are very difficult to distinguish with solution NMR spectroscopy. However, in the solid state, nuclear spin relaxation is typically slower, thus enabling higher quality ³⁵Cl NMR spectra to be collected, at least in principle. Unfortunately, the magnitude of the QI for covalently bound chlorines is very large because of the substantial, anisotropic EFG at the Cl atom, owing mainly to its electronic configuration when it forms a chlorine–carbon bond. Conventional wisdom is that such chlorine sites cannot be studied in powders by solid-state NMR spectroscopy as the central transition (CT; m_I=1/2 ↔ −1/2) can span tens of megahertz in typical commercially available magnetic fields. For this reason, only ionic chlorides2 and inorganic chlorides3 have been studied, as the EFG at these chlorides is often an order of magnitude smaller than at covalently bound chlorine atoms in organic molecules.

 

[TeethWhitener]

All the time. Deuterium NMR and ¹⁴N-NMR are pretty useful. I personally have also used ⁷Li and ¹¹B NMR (as well as some others I’m sure I’m forgetting). As mentioned, the quadrupole moment that exists for nuclei with spin > 1/2 causes fast relaxation and therefore line broadening, but that difficulty can be mitigated with clever pulse sequences.

 

[etotheipi]

Interesting, thanks! I'll see what I can find out about the quadrupolar interaction, a quick search brought up this page, and another here, both of which seem pretty good.

 

[TeethWhitener]

I’ll also point out that it’s not necessarily just chemical information that we’re after when we do NMR. For example, the lithium NMR I did was DOSY (diffusion ordered spectroscopy), aimed at finding the diffusion of lithium ions in a solvent. You can imagine that this method gets a lot of use in areas like battery research, where we’re often more concerned about things like diffusion constants, and less concerned about the exact chemical behavior of a lithium-containing electrolyte. In this case, the quadrupole-induced relaxation won’t matter so much. (NB—obviously some folks are interested in these chemical issues, so they’ll have a different answer to this question.)

 

[etotheipi]

For example, the lithium NMR I did was DOSY (diffusion ordered spectroscopy), aimed at finding the diffusion of lithium ions in a solvent

That sounds pretty cool! I don't really understand how DOSY works, how does one go about finding diffusion coefficients using NMR?

The references I could find were all a little too technical. As far as I could tell, you have a position dependent magnetic field, you assign nuclei an initial phase (?), let them diffuse for a time $\Delta$ and then check whether the spins are still the same [by checking the phase?]. And some stuff about different pulse sequences.

I wondered if you have a good way of explaining it?

 

[TeethWhitener]

That sounds pretty cool! I don't really understand how DOSY works, how does one go about finding diffusion coefficients using NMR?

The references I could find were all a little too technical. As far as I could tell, you have a position dependent magnetic field, you assign nuclei an initial phase (?), let them diffuse for a time $\Delta$ and then check whether the spins are still the same [by checking the phase?]. And some stuff about different pulse sequences.

I wondered if you have a good way of explaining it?

It's kind of tough to know how to explain it well without knowing what background in NMR you have.

The experiment itself is pretty simple. It's just a spin echo experiment with a few gradient pulses thrown in. (Here's the wiki page for spin echo with a good animation.) The spins begin with a net magnetization oriented along a large static z-oriented B field. Once the 90° pulse is applied, the spins begin precessing in the xy plane about the z-axis. The rate at which they precess is a distribution which is determined by the local electric and magnetic fields that each nucleus sees.

In DOSY, the trick is to deliberately apply a spatially varying magnetic field (the magnetic field "gradient") to the sample, which affects the precession of the spins based on their spatial location in the sample (basically, the precession rate is dependent on magnetic field, which itself is dependent on spatial location). If the nuclei didn't diffuse at all, then reversing this field and applying a 180° pulse would give you your standard spin echo. However, if the nuclei diffuse--that is, if they move away from their initial positions--then the refocusing pulses (the negative gradient and 180 pulses) will not completely refocus the spin magnetization and the measured spin echo will be less intense than if the nuclei had stayed in one place. By recording how the spin echo intensity changes when you vary the steepness of the magnetic field gradient, you can get a gaussian(-ish) curve that has a width related to the diffusion constant of the nuclei in question.

 

[etotheipi]

That really is an excellent explanation, thanks for taking the time to write that up! I think I now understand the basic conceptual principle, that whether a nucleus has diffused or not can be detected by applying those two pulses a time $\Delta$ apart (with the magnetic field being position dependent), and checking how much the spin has changed at the end - i.e. if the spin is unchanged, the nucleus hasn't moved, etc.

I'm sure it's a lot more complicated, but I'll take some more time to see if I can understand it better. Thanks!

 

[TeethWhitener]

It’s important to keep in mind that this is an ensemble of spins. I haven’t gone through the math in a while, but I seem to recall that at room temperature, the overall net magnetization of the sample, even in a large (>1T) magnetic field, is only roughly one excess spin per several thousand pointed along the B field. So what you’re really measuring is the net magnetization, rather than any individual spin. So you can measure a bulk property like diffusion constant, but you can’t track individual particles.