Shift anisotropy relaxation mechanism

Sturz and DoUe measured the temperature dependent dipolar spin-lattice relaxation rates and cross-correlation rates between the dipolar and the chemical-shift anisotropy relaxation mechanisms for different nuclei in toluene. They found that the reorientation about the axis in the molecular plane is approximately 2 to 3 times slower than the one perpendicular to the C-2 axis. Suchanski et al measured spin-lattice relaxation times Ti and NOE factors of chemically non-equivalent carbons in meta-fluoroanihne. The analysis showed that the correlation function describing molecular dynamics could be well described in terms of an asymmetric distribution of correlation times predicted by the Cole-Davidson model. In a comprehensive simulation study of neat formic acid Minary et al found good agreement with NMR relaxation time experiments in the liquid phase. Iwahashi et al measured self-diffusion coefficients and spin-lattice relaxation times to study the dynamical conformation of n-saturated and unsaturated fatty acids. 

Kay LE, Nicholson LK, Delaglio F, Bax A, Torchia DA (1992) Pulse sequences for removal of the effects of cross correlation between dipolar and chemical-shift anisotropy relaxation mechanisms on the measurement of heteronuclear Tl and T2 values in proteins. J Magn Reson 97 359-375... 

Double-resonance Experiments. - TROSY-type experiments have been traditionally based on the cross-correlation between dipolar and chemical shift anisotropy relaxation mechanisms. Tugarinov et al. extended the application of the relaxation compensation principles to cancellation of the intra-methyl H- H and dipole-dipole interactions. The analysis of the relaxation of the... 

Cotton et al. (42) have also investigated a series of chromium carbene complexes (CO)5CrCRR (Table XXXVII). They observed upfield shifts of the carbene carbon resonance as the basicity of the amine ligand (R ) increased. In addition, for (CO)sCrC(OEt)Me, values of Tt of = 1 to 2 sec were determined for all three types of carbons directly bonded to chromium. These values are especially small for carbons not directly bonded to nuclei with spin = 1/2 (i.e., small for carbons not allowed to relax via dipolar coupling). Possibly a shift anisotropy relaxation mechanism is operative. 

Slow motions have also been studied by measuring the differential line broadening (DLB) of proton 7-coupled nuclei [81]. Here the difference in bandwidth of the different resonances in a multiplet can be attributed to the interplay between the dipole-dipole and chemical shift anisotropy relaxation mechanisms, and information on the slow motion can be obtained by analyzing the difference. 

Shielding anisotropies can be obtained from measured relaxation times when the chemical shift anisotropy relaxation mechanism or the spin-rotation mechanism is dominant. The correlation time has to be estimated or otherwise derived. There are large uncertainties associated with this method. 

The examples discussed illustrate that assignment of the resonances is usually relatively straightforward. This combined with the 100% natural abundance of the nucleus may explain the popularity of the P-NMR technique for the study of phosphoproteins. The sensitivity is about 5% of H-NMR sensitivity. For most other nuclei, this disadvant e can be overcome by the use of higher magnetic fields. However, as discussed for the study of phosphoproteins, contributions of the chemical-shift anisotropy relaxation mechanism often prohibit advantageous appUcation of such instruments, much as was observed for the F nucleus (Sykes and Weiner, 1980). Table IV presents an overview of the majority of P-NMR studies presented in this chapter. Some biochemically interesting generalizations can be made on the basis of these results and are discussed further. 

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. 

Although it had been known for some time that the chemical-shift anisotropy (CSA) mechanism could contribute significantly to the relax-... 

Phosphorus-31 NMR offers the observation of a single, readily assignable resonance with good sensitivity. In certain cases two resonances are observed (see Section III). Analysis of P relaxation must take into account the contribution from the chemical-shift anisotropy (CSA) mechanism as well as dipolar coupling to protons (see Section II, A). This additional complication can be dealt with by using chemical-shift anisotropy data provided by solid-state NMR (Terao et a/., 1977 Shindo, 1980 Opella eta/., 1981 Nall... 

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). 

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... 

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. 

Yang, D. W., Konrat, R., and Kay, L. E. (1997). A multidimensional NMR experiment for measurement of the protein dihedral angle psi based on cross-correlated relaxation between (H alpha-13C alpha) XH dipolar and 13C (carbonyl) chemical shift anisotropy mechanisms. J. Am. Chem. Soc. 119,11938-11940. 

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