Dipolar shift anisotropy

Fig. 2 Spatial dependence of the dipolar shift anisotropy (a) and of the pseudocontact shift in the magnetic susceptibility principal axis system (b). The position of the nucleus is defined by its spherical coordinates (r, 6, tp) in the PAS of the x tensor. Violet surfaces represent isosurfaces of Aa, and blue and red surfaces represent respectively positive and negative isosurfaces of...

Dipolar shift anisotropy. The first quantitative interpretation of the intensity pattern of spinning sidebands observed in MAS NMR spectra of paramagnetic solids was provided by Nayeem and Yesinowski in an investigation of MAS spectra acquired from residual protons in a largely deuterated sample of polycrystalline CuCl2 2H20. 

The second-order quadnipolar broadening of tire - transition can be further reduced by spiiming at an angle other than 54.7° (VAS), the width being a minimum between 60-70°. The reduction is only 2 however, and dipolar and shift anisotropy broadening will be reintroduced, thus VAS has only found limited application. 

The measurement of correlation times in molten salts and ionic liquids has recently been reviewed [11] (for more recent references refer to Carper et al. [12]). We have measured the spin-lattice relaxation rates l/Tj and nuclear Overhauser factors p in temperature ranges in and outside the extreme narrowing region for the neat ionic liquid [BMIM][PFg], in order to observe the temperature dependence of the spectral density. Subsequently, the models for the description of the reorientation-al dynamics introduced in the theoretical section (Section 4.5.3) were fitted to the experimental relaxation data. The nuclei of the aliphatic chains can be assumed to relax only through the dipolar mechanism. This is in contrast to the aromatic nuclei, which can also relax to some extent through the chemical-shift anisotropy mechanism. The latter mechanism has to be taken into account to fit the models to the experimental relaxation data (cf [1] or [3] for more details). Preliminary results are shown in Figures 4.5-1 and 4.5-2, together with the curves for the fitted functions. 

Instead of measuring only the time-dependent dipolar interaction via NOE, it is also possible to determine dipolar couplings directly if the solute molecule is partially aligned in so-called alignment media. The most important resulting anisotropic parameters are RDCs, but residual quadrupolar couplings (RQCs), residual chemical shift anisotropy (RCSA) and pseudo-contact shifts (PCSs) can also be used for structure determination if applicable. 

As we shall see, all relaxation rates are expressed as linear combinations of spectral densities. We shall retain the two relaxation mechanisms which are involved in the present study the dipolar interaction and the so-called chemical shift anisotropy (csa) which can be important for carbon-13 relaxation. We shall disregard all other mechanisms because it is very likely that they will not affect carbon-13 relaxation. Let us denote by 1 the inverse of Tt. Rt governs the recovery of the longitudinal component of polarization, Iz, and, of course, the usual nuclear magnetization which is simply the nuclear polarization times the gyromagnetic constant A. The relevant evolution equation is one of the famous Bloch equations,1 valid, in principle, for a single spin but which, in many cases, can be used as a first approximation. 

Conventional utilization of solution-phase NMR data acquisition techniques on solid samples yields broad, featureless spectra (Fig. 1A). The broad nature of the signal is due primarily to dipolar interactions, which do not average out to zero in the solid state, and chemical shift anisotropy (CSA), which again occurs because our compound of interest is in the solid state. Before one describes the two principal reasons for the broad, featureless spectra, it is important to understand the main interactions that a nucleus with a magnetic moment experiences when situated within a magnetic field in the solid state. In addition, manifestations of these interactions in the solid state NMR spectrum need to be discussed. 

A new NMR method for the determination of the anomeric configuration in mono- and disaccharides has been described.18 The protocol is based on the different cross-correlated relaxation between proton chemical shift anisotropy (CSA) and dipolar relaxation for the a and (3 anomers of sugars. Only the ot-anomers show the presence of CSA (HI or Hl )-proton dipole (H1-H2 or Hl -H2 ) in the longitudinal relaxation of the anomeric protons. The method is of special interest for cases in which vicinal coupling constants between HI and H2 in both anomers a and (3 are similar and small, such as D-mannose, and the non-ambiguous description of the anomeric configuration needs additional measurements. 

As an example of the measurement of cross-correlated relaxation between CSA and dipolar couplings, we choose the J-resolved constant time experiment [30] (Fig. 7.26 a) that measures the cross-correlated relaxation of 1H,13C-dipolar coupling and 31P-chemical shift anisotropy to determine the phosphodiester backbone angles a and in RNA. Since 31P is not bound to NMR-active nuclei, NOE information for the backbone of RNA is sparse, and vicinal scalar coupling constants cannot be exploited. The cross-correlated relaxation rates can be obtained from the relative scaling (shown schematically in Fig. 7.19d) of the two submultiplet intensities derived from an H-coupled constant time spectrum of 13C,31P double- and zero-quantum coherence [DQC (double-quantum coherence) and ZQC (zero-quantum coherence), respectively]. These traces are shown in Fig. 7.26c. The desired cross-correlated relaxation rate can be extracted from the intensities of the cross peaks according to ... 

Clore et al. [63] have noticed that for an isotropic distribution of dipolar bond-vectors the probabilities resemble the shape of a chemical shift anisotropy powder pattern... 

It is worth mentioning that parameter p is insensitive, to first order approximation, to modulation of the residue-specific 15N chemical shift anisotropy tensor and/or dipolar interaction, as the (d2 + c2) term in the R) / R ratio is canceled out. The noncollinearity of the CSA and dipolar tensors will require corrections to Eqs. (10) and (12) for high degrees of rotational anisotropy (D /D > 1.5), as described in detail in Ref. [22]. 

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