Chemical shift anisotropy relaxation

Relaxation is a complex phenomenon, depending on many factors [2], such as dipole-dipole relaxation, chemical shift anisotropy, spin-rotation relaxation, quad-rupolar relaxation etc. Examples for macroscopic factors are sample and magnetic field homogenity and the viscosity of the NMR solvent. When running NMR experiments on ionic liquids, we have to deal with three main challenges ... 

We now return to discussing some other relaxation mechanisms which involve random motions of molecules, namely the scalar relaxation of the first and second kinds, quadrupolar relaxation, chemical shift anisotropy relaxation, and spin rotation relaxation. 

Pervushin K, Riek R, Wider G and Wuthrich K 1997 Attenuated T relaxation by mutual cancellation of dipole-dipole coupling and chemical shift anisotropy indicates an avenue to NMR structures of very... 

Tjandra N, Szabo A and Bax A 1996 Protein backbone dynamics and N-15 chemical shift anisotropy from quantitative measurement of relaxation interference effected. Am. Chem. Soc. 118 6986-91... 

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. 

The process of spin-lattice relaxation involves the transfer of magnetization between the magnetic nuclei (spins) and their environment (the lattice). The rate at which this transfer of energy occurs is the spin-lattice relaxation-rate (/ , in s ). The inverse of this quantity is the spin-lattice relaxation-time (Ti, in s), which is the experimentally determinable parameter. In principle, this energy interchange can be mediated by several different mechanisms, including dipole-dipole interactions, chemical-shift anisotropy, and spin-rotation interactions. For protons, as will be seen later, the dominant relaxation-mechanism for energy transfer is usually the intramolecular dipole-dipole interaction. 

When other relaxation mechanisms are involved, such as chemical-shift anisotropy or spin-rotation interactions, they cannot be separated by application of the foregoing relaxation theory. Then, the full density-matrix formalism should be employed. 

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. 

NMR spin relaxation is not a spontaneous process, it requires stimulation by a suitable fluctuating field to induce an appropriate spin transition to reestablish equilibrium magnetization. There are four main mechanisms for obtaining relaxation dipole-dipole (most significant relaxation mechanism for I = 1/2 nuclei), chemical shift anisotropy, spin rotation, and quadrupolar (most significant relaxation mechanism for I > 1/2 nuclei) (Claridge, 1999). 

Let us consider a Hn- l 5N spin pair - the transverse relaxation T2 for the 15N spin (and HN as well) is mainly dictated by the dipole-dipole (DD) interaction between the spin pair, and the chemical shift anisotropy (CSA) of... 

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. 

The hydrogen bond length in Watson-Crick base pairs can be characterized using the recently developed method of measuring the cross-correlated relaxation [61] between H chemical shift anisotropy and dipole-dipole coupling of H and its hydrogen bond donor... 

The characterisation of the angular dependence of the interaction of two dipole tensors A1 A2 and B B2 is therefore straightforward, namely it depends on the projection angle of the two bonds between A1 and A2 and between B1 and B2. The orientation and magnitude of the chemical shift anisotropy (CSA) tensor, which also can cause cross-correlated relaxation, is not know a priori and therefore needs to be determined experimentally or... 

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 ... 

Apart from the relaxation mechanism described here, other mechanisms such as relaxation involving cross-correlation between dipole-dipole coupling and chemical shift anisotropy (CSA) can also provide structural information [48, 49]. The expression for this relaxation rate in case of axial symmetric CSA tensors is... 

CCR Cross-correlated relaxation CSA Chemical shift anisotropy... 

J-splitting, when it exists, imposes the definition of new spin quantities. These quantities also evolve according to relaxation phenomena and may interfere (by relaxation) with the usual magnetization components. This latter interference stems precisely from cross-correlation rates, i.e., relaxation parameters which involve two different mechanisms, for instance the dipolar interaction and the so-called Chemical Shift Anisotropy (27,28) (csa)... 

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. 

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