Anisotropic nuclear spin interactions

NMR images by conventional saturation recovery, inversion recovery, and spin-echo techniques (cf. Chapter 7). 

The interaction energies of the spins determine the resonance frequencies and, thus, the separation of the energy levels of the nuclear spin states. The energy levels are the eigenvalues of the Hamilton operator H of the spin system. This operator is the sum of operators Hx for each individual interaction X, 

The frequencies under each operator indicate the size of the interaction. The largest interaction next to the Zeeman interaction Hz is the quadrupole interaction Hq, followed by the coupling Hrf of the spins to the exciting rf field, the dipole-dipole coupling Hd, the chemical shift H , and the indirect coupling Hj. 

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Anisotropic nuclear spin interactions, such as chemical shift anisotropy (CSA) and heteronuclear dipolar coupling, are highly valuable in understanding the nature of chemical bonding, structure, dynamics, and function of chemical and biological molecules. For example, chemical shifts of H, N, and nuclei are routinely used in the structural and motional studies of proteins using solution and solid-state NMR methods.Spectra of aligned solid-state... 

MAS) to remove the effects of the anisotropic nuclear spin interactions from one dimension of a multi-dimensional experiment.2 In the review period, one nice development in this area is the use of magic-angle turning... 

Instead of averaging away the anisotropic nuclear spin interactions by MAS or multiple pulse sequences, it is possible to take advantage of the anisotropy of these interactions, provided that macro-scopically oriented samples are available. This kind of static solid state NMR approach is entirely different from the experiments discussed above. It can lead to highly resolved H and spectra with narrow lines, whose position carries information about... 

Although the same nuclear spin interactions are present in solid-state as in solution-state NMR, the manifestations of these effects are different because, in the solid, the anisotropic contribution to the spin interactions contributes large time-independent terms to the Hamiltonian that are absent in the liquid phase. Therefore, the experimental methods employed in solids differ from the ones in the liquid state. The spin Hamiltonian for organic or biological solids can be described in the usual rotating frame as the sum of the following interactions ... 

Since nuclear spin interactions are anisotropic, the observed NMR frequency depends on the position of the principal axis systems of 170 EFG and CS tensors with respect to the external magnetic field. In the following, 170 NMR frequencies under quadrupolar and/or CS interactions that will be used for spectral simulations are described in detail. It is convenient to separate the cases into static solid-state NMR techniques and MAS experiments. First, the static conditions are explained. 

The isotropic g and a values are now replaced by two 3x3 matrices representing the g and A tensors and which arise from the anisotropic electron Zeeman and hyperfine interaction. Other energy terms may also be included in the spin Hamiltonian, including the anisotropic fine term D, for electron-electron interactions, and the anisotropic nuclear quadrupolar interaction Q, depending on the nucleus. Usually the quadrupolar interachons are very small, compared to A and D, are generally less than the inherent linewidth of the EPR signal and are therefore invisible by EPR. They are readily detected in hyperfine techniques such as ENDOR and HYSCORE. All these terms (g. A, D) are anisotropic in the solid state, and must therefore be defined in terms of a tensor, which will be explained in this section. 

The demand for efficient numerical methods in biological solid-state NMR may be explained not only by the interest in studying larger and more complex molecular systems, but also by the fact that most of the nuclear spin interactions are anisotropic (i.e., dependent on the orientation of the molecule relative to the external magnetic field) which complicates the NMR spectra as well as the transfers of polarization and coherence... 

The aim of this section is to provide an overview about the development and application of solid state NMR spectroscopic techniques for the study of molecular structures and dynamics on the molecular and intermolecular length scale (lA-lOA). In particular, anisotropic magnetic nuclear spin interactions like chemical shielding anisotropy (CSA), magnetic dipolar interaction and quadrupolar interaction are used as probes for interatomic distances and orientations of molecular groups, i.e. structures, and changes of these interactions are monitored and used as a measure of dynamic processes inside the system. 

Based on methods which rely on the manipulation of the anisotropic terms of the nuclear spin interactions and on the combination of different basic NMR techniques, such as MAS and decoupling, an enormous number of solid-state NMR pulse sequences were proposed in the last 20 years. SoUd-state NMR provides powerful techniques for elucidating details of segmental dynamics and local conformation in solid materials. NMR methods allow the study of dynamics occurring in a wide frequency range (fi om the order of 1 Hz to... 

Lipid orientational information By exploiting the anisotropic properties of the nuclear spin-interactions of H, and - N (Table 1), placed at specific positions in peptides and ligand, rather precise bond vectors have been determined in oriented membranes. 

It is now necessary to examine the mechanisms by which the hyperfine interactions arise. Two types of electron-spin-nuclear-spin interactions must be considered, of isotropic and anisotropic nature. 

The electron-spm echo envelope modulation (ESEEM) phenomenon [37, 38] is of primary interest in pulsed EPR of solids, where anisotropic hyperfme and nuclear quadnipole interactions persist. The effect can be observed as modulations of the echo intensity in two-pulse and three-pulse experiments in which x or J is varied. In liquids the modulations are averaged to zero by rapid molecular tumbling. The physical origin of ESEEM can be understood in tenns of the four-level spin energy diagram for the S = I = model system... 

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