Shielding anisotropy

The nuclear screening and hence chemical shift of a nucleus in a molecule will usually be anisotropic, so that when the molecule tumbles the nucleus will experience a fluctuating magnetic field. The resulting expressions for T, and T2(SA) are analogous to those for dipolar relaxation, except that the spin system is only two-level. It may, however, be complicated by the possibility of asymmetry in the screening tensor. 

Here Aa = a -a. Once again, the expression for l/7 2 is half that for l/T, plus a frequency-independent term arising from spin precession phase jumps induced by the fluctuating field. However, in the motional narrowing limit (cuiT 1) one now finds that ri(SA)/7 2(SA) = 7/6. This relationship has yet to find clear experimental verification. 

Aff is of the order of 200 at for a carbonyl double bond, but may easily rise to 5000 ppm and more, for example around linear Hg or square-planar Pt. Thus these resonances will often be noticeably broadened in a high-field spectrometer (fio-9T), with l/Ti commonly 50s The presence of SA relaxation is unambiguously proved by its dependence upon the square of B.  

When the nuclear screening is completely anisotropic, or even symmetric but with principal axes different from those for molecular tumbling (e.g., a meta or ortho phenyl carbon), then the appropriate equations are more complex. They may be found in a paper by Lynden-Bell.  

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However, because of chemical shielding anisotropy (CSA) and quadnipolar and dipolar effects, the Lamior... 

Dipolar coupling and 3C shielding anisotropy cause unequal intensity of spinning side bands. The scalar coupling enabled magic angle rotation to distinguish two sets of sub-spectra.58... 

When l l, the above gives the so-called cross-correlation functions and the associated cross-correlation rates (longitudinal and transverse). Crosscorrelation functions arise from the interference between two relaxation mechanisms (e.g., between the dipole-dipole and the chemical shielding anisotropy interactions, or between the anisotropies of chemical shieldings of two nuclei, etc.).40 When l = 1=2, one has the autocorrelation functions G2m(r) or simply... 

When r s, one has interconversion between operators Br and Bs, and Rrs is a cross-relaxation rate. Note that the cross-relaxation may or may not contain interference effects depending on the indices l and /, which keep track of interactions Cyj and C,. Cross-correlation rates and cross-relaxation rates have not been fully utilized in LC. However, there is a recent report41 on this subject using both the 13C chemical shielding anisotropy and C-H dipolar coupling relaxation mechanisms to study a nematic, and this may be a fruitful arena in gaining dynamic information for LC. We summarize below some well known (auto-)relaxation rates for various spin interactions commonly encountered in LC studies. 

For the axially asymmetric powder pattern, the shielding anisotropy was calculated using the following expression... 

In order to discuss the origin of these terms we need to allow the spins to have anisotropic shielding tensors. Molecular tumbling in solution makes the chemical shielding in the direction of the external magnetic field a stochastic function of time and acts therefore as a relaxation mechanism, called the chemical shielding anisotropy (CSA) mechanism. The Hamiltonian for each of the two spins, analogous to Eq. (5), contains therefore two... 

The complications that arise in solid state NMR spectra as compared to NMR spectra in solution are the consequence of the fixed orientation of the sample relative to the external magnetic field Bq. Mainly three interactions are responsible for the enormous linebroadening that can be observed for solid powder samples. These are (1) the shielding or chemical shift, including the chemical shift or shielding anisotropy CSA or Acr Hqsa) (2) homo- and/or heteronuclear dipole-dipole coupling (ffoo) and (3) in addition, for nuclei with spin >1/2, the quadrupolar interactions (Hq). 

The expressions for the various parts of the Hamiltonian (equation 1) are well documented and for our purpose and the following discussion it suffices to summarize the results for axially symmetric situations in angular frequency units with the equations 2-6, where and Ashielding tensor and the shielding anisotropy, respectively, D is the dipole coupling, eq or V is the electric field gradient at the nucleus, eQ is the nuclear quadrupole moment and the other symbols have their usual meaning ... 

The chemical shift of a particular atom varies with the orientation of the molecule to the field. In a solid this gives a range of values, an effect known as the chemical shielding anisotropy, which broadens the band. 

Skibsted, J., Vosegaard, T., Bildsoe, H., and Jakobsen, H. J. (1996). Cs chemical shielding anisotropies and quadrupole coupling constants from magic angle spinning NMR of cesium salts. J. Phys. Chem. 100, 14872-81. 

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