Anisotropy of the Shielding Tensor

The first B chemical shielding tensors have been measured. Trimesityl-borane gives an axially symmetric tensor with a span of 121 ppm and a positive skew, while triphenyl borate is characterized by a tensor that is less than 10 ppm wide. Interestingly, the span observed for trimesitylborane corresponds to the known chemical shift range of tricoordinated boron. Both RHF and B3LYP reproduce nicely these experimental findings. The and Se 

As novel solution and solid state experiments enabling the determination of shielding tensor quantities in peptides and proteins become widespread, it is strongly recommended that practitioners stick to precise definitions of terms that have accepted meanings within the solid state NMR community. As a reminder, we list again the modern terms The difference between the most shielded (ass) and the least shielded (an) tensor component is the span. 

the chemical shifts 6 = (v — Vref)/Vref = (cTref—cr)(l — Sref) then this leads to 5n 22 533 and 

The skew k characterizes the shielding tensor without being affected by the choice of reference substance. Converting shielding into chemical shift, 

The old conventions, are still in use, for example, in the compendium of chemical shift tensors by T. M. Duncan.Depending on which component 5ii or 5ss is farther from Sjso, for 5n -SisJ 8s3 -Sisol 

Chan and Tycko ° have introduced a novel solid state NMR experiment that combines ROCS A (recoupling of chemical shift anisotropy) and C- H dipolar dephasing. Designed for uniformly labeled samples, this technique is shown to correlate the carbonyl shielding and the dipolar tensors, thereby pro- 

Nishiyama et al have illustrated a way of measuring the principal components of carbon shielding tensors in uniaxially drawn polypropylene. 

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It can be seen that, in all cases, relaxation rates are directly proportional to (Aa). Because Aa reflects the anisotropy of the shielding tensor and because the chemical shift originates from the shielding effect, the terminology Chemical Shift Anisotropy is used for denoting this relaxation mechanism. Dispersion may be disconcerting because of the presence of Bq (proportional to cOq) in the numerator of and R2 (Eq. (49)). Imagine that molecular reorientation is sufficiently slow so that coo 1 for all considered values of coo from (49), it can be seen that R is constant whereas R2 increases when Bq increases, a somewhat unusual behavior. 

The first term is the Zeeman interaction with the applied field with a mean shielding o for nucleus i, which may differ somewhat from the value in isotropic solvents due to the anisotropy of the shielding tensor. The second term contains the well-known isotropic part of the indirect spin-spin coupling of nuclei i and /. For pairs of protons the Jq are a few hertz. The major contribution to the parameters Dq of the last term derives from the direct (dir) magnetic dipole interactions of pairs of nuclei, which will be denoted by Efjf1. The contribution from the indirect interactions is often negligible and will be discussed below. 

Physical aspects of nuclear shielding 2.1 Anisotropy of the shielding tensor... 

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 ... 

In principle, however, it is always possible to diagonalize the shielding tensor to its three principal components. Unless stated otherwise, it will be assumed that the shielding tensor is diagonal. The isotropic shielding is defined as one-third the trace of the shielding tensor. The anisotropy can be defined in several ways. Probably the most general definition is... 

Some early attempts were made to determine anisotropies from second-moment analysis in which use is made of the anisotropic contribution to the observed second moment.5 6 Limitations of this method are the need for large shifts and fields and the often-required assumption of axial symmetry of the shielding tensor. In 1968 a method was reported that uses coherent averaging techniques7 to effectively narrow the dipolar-broadened lines of powdered solids. The observed spectrum is curve-fitted using a computer-broadened theoretical chemical shift distribution to give the principal components of the shielding tensor. 

In solid-state NMR, the individual diagonal elements of the shielding tensor, on, 022, and CT33 can be determined, provided the molecule possesses appropriate symmetry (see below). The shielding anisotropy. Act, is a measure of the distortion from spherical symmetry (Eq. 5). Another parameter of interest is the asymmetry factor, ti, defined in eq. 6. Eta is a measure... 

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