*I*= n/2 (n = 1, 3, 5 ....) quadrupolar nuclei are more complicated than many people realize. There are chemical shielding anisotropy effects and both first order and second order quadrupolar effects which must be taken into account. Magic angle spinning averages out the first order quadrupolar effects and the chemical shielding anisotropy however, these interactions may show up as spinning sidebands. The field dependant second order quadrupolar effects are only partially averaged by magic angle spinning. In an MAS spectrum, each transition of the spin

*I*= n/2 nucleus will have both a frequency shift and line shape characterized by the partially averaged second order quadrupolar interaction. The frequency shifts and lineshapes can provide valuable information about the quadrupolar coupling constant and the asymmetry parameter. The figure below shows the centerband region of the

^{27}Al (

*I*= 5/2) MAS NMR spectrum of aluminum-

*tris-*acetylacetonate (Al(acac)

_{3}) acquired at 11.75 Tesla. There is only one aluminium site in the asymmetric unit of this compound. The major component of the spectrum is the central transition (m=1/2 - m= -1/2). It is the most intense as it is unaffected by the first order quadrupolar interaction and therefore does not have its intensity spread over multiple spinning sidebands. The first satellite transitions (m=3/2 - m= 1/2 and m= -1/2 - m= -3/2) are affected equally by the second order quadrupolar interaction and appear as a narrow resonance to higher frequency than the central transition. The second satellite transitions (m=5/2 - m= 3/2 and m= -3/2 - m= -5/2) are also affected equally by the second order quadrupolar interaction and appear as a weak broad resonance to higher frequency than both the first satellite transition and the central transition. Both satellite transitions are weak as their intensity is spread over many spinning sidebands (not shown). The second satellite transition is weaker than the first as it has a much broader line shape.

## 7 comments:

I am surprised the first-order transition is sharper then the central transition. Any comments?

Anonymous,

The first satellite transition is indeed much sharper than both the central transition and the second satellite transition. Thats just the way the physics works out. It also explains the interest in satallite transition spectroscopy. One can imagine a situation where there are multiple sites where the spectra of the broad central transition overlap yet the spectra of the first satellite transition are chemical shift resolved.

Glenn

Following up on this comment, the first and second satellite transition lines are indeed broader overall than the central transition, but what Glenn is showing is just the centreband of each of these transitions under MAS conditions.

Dave

First, I really appreciate your blog as it is written for beginners in a comprehensive way.

My question is, may you post a calculated satic pattern of a 3/2 or 5/2 nucleus (with axial symmetry for reasons of simplicity)?

And is it true that the isotropic shift of the central transition and the one of the satellite transition(s) are identical for axial symmetry?

thank you very much

Dear Brent,

Thank you for your questions.

I will consider your first suggestion of posting a calculated static spectrum for an I=3/2 or I=5/2 nucleus in a future post.

The answer to your second question is "no". The isotropic quadrupolar shifts are different for the central and satallite transitions even when the asymmetry parameter is zero. This can be seen in the figure in the post as the asymmetry parameter in this case is (or is very close to) zero.

Glenn

Hello,

If I observe 2 peaks in my spectrum (in the centreband region), being very close to each other, how do I know if they are 2 central transitions due to 2 distinct sites in my sample?

Maybe one is a central transition and the other is just a satellite transition, belonging to the same site (as it is the case in your article)?!

Is there a way to excite only the central transitions to be able to identify the number of different sites unambiguously by removing all satellite transitions?.

Peter,

Much effort is directed in resolving the sites in the NMR spectra of quadrupolar nuclei. The most common mrthod is MQMAS. This is a 2D method where the isotropic chemical shifts are observed in the iddirect dimension.

It is rarely a problem to distinguish from the centerbands of central transitions and the centerbands of satellite transitions as the intensity of the centerband of the satellite transitions is usually very small. If this is a problem then I suppose that MQMAS would be able to sort it out.

Glenn

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