Nuclear spin interaction tensor

The nuclear spin interaction tensor is most readily expressed in its principal axis frame where only the M = 0, 2 terms are nonzero (and only the M = 0 term is nonzero for axial symmetry). It can then be expressed in the laboratory frame via... 

The basis of the studies is the orientation-dependence of nuclear spin interaction tensors which serves as a probe of the relative orientations of specific bond vectors. Under these conditions, the contribution of the aromatic carbon peaks, which overlapped the carbonyl carbon peak in the natural abundance CP spectrum, could be neglected in the analysis of NMR results. The NMR analysis used here is essentially similar to the N NMR analyses already applied to uniaxially aligned silk. 

In this section, solid-state NMR of fibrous proteins is reviewed. For solid-state NMR studies of oriented samples, orientation-dependent nuclear spin interaction tensors serve as probes with which the relative orientations of specific bond vectors can be determined as described in Chapter 8. 

Fundamental constants (Cx), spatial tensors in the principal axis frame ((fi3 m,)F), and spin tensors (Tjm) for chemical shielding (a), J coupling (J), dipole-dipole (IS), and quadrupolar coupling (Q) nuclear spin interactions (for more detailed definition of symbols refer to [50])... 

Multiplets in NMR. The second effect yields a spin-spin coupling constant / (usually quoted in hertz), which it generates a multiplet structure that is due to nuclear spin-nuclear spin interactions between equivalent or inequivalent protons (in H1 NMR). The spin interaction is actually a tensor quantity due to... 

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. 

One potential problem with chemical shift anisotropy lineshape analysis (or indeed analysis of lineshapes arising from any nuclear spin interaction) is that the analysis results in a description of the angular reorientation of the chemical-shielding tensor during the motion, not the molecule. To convert this information into details of how the molecule moves, we need to know how the chemical-shielding tensor (or other interaction tensor) is oriented in the molecular frame. A further possible complication with the analysis is that it may not be possible to achieve an experiment temperature at which the motion is completely quenched, and thus it may not be possible to directly measure the principal values of the interaction tensor, i.e. anisotropy, asymmetry and isotropic component. If the motion is complex, lack of certainty about the input tensor parameters leads to an ambiguous lineshape analysis, with several (or even many) possible fits to the experimental data. 

There are additional 2D methods that make use of information associated with nuclear spin interactions other than the H- C dipolar coupling [10]. As an example, Hu et al. [72] described a 2D experiment involving the correlation between C isotropic chemical shift and CSA in a subbituminous coal. The results, combined with spectral editing data, allowed further separation of different chanical groups due to the occurrence of distinct C CSA tensors for protonated, bridgehead, and alkyl-substituted aromatic carbons. 

Contents Introduction. - Nuclear Spin Interactions in Solids. -Multiple-Pulse NMR Experiments. - Double Resonance Experiments. - Two-Dimensional NMR Spectroscopy. - Multiple-Quantum NMR Spectroscopy. - Magnetic Shielding Tensor. - Spin-Lattice Relaxation. - Appendix. - References. - Subject Index. 

Spin-Rotation Interaction As explained above, the nuclear spin-rotation tensor consists of an electronic and a nuclear part, with the former computed as the second derivative of the electronic energy with respect to the rotational angular momentum and the appropriate nuclear spin as perturbations [38]. This is efficiently done using analytic second-derivative techniques [65], but, while calculations carried out using standard basis functions suffer from a slow basis set convergence, the use of perturbation-dependent basis functions significantly accelerates the basis set convergence [38]. 

Nuclear spin relaxation is caused by fluctuating interactions involving nuclear spins. We write the corresponding Hamiltonians (which act as perturbations to the static or time-averaged Hamiltonian, detemiming the energy level structure) in tenns of a scalar contraction of spherical tensors ... 

Equation (4.15) would be extremely onerous to evaluate by explicit treatment of the nucleons as a many-particle system. However, in Mossbauer spectroscopy, we are dealing with eigenstates of the nucleus that are characterized by the total angular momentum with quantum number 7. Fortunately, the electric quadrupole interaction can be readily expressed in terms of this momentum 7, which is called the nuclear spin other properties of the nucleus need not to be considered. This is possible because the transformational properties of the quadrupole moment, which is an irreducible 2nd rank tensor, make it possible to use Clebsch-Gordon coefficients and the Wigner-Eckart theorem to replace the awkward operators 3x,xy—(5,yr (in spatial coordinates) by angular momentum operators of the total... 

The leading term in T nuc is usually the magnetic hyperfine coupling IAS which connects the electron spin S and the nuclear spin 1. It is parameterized by the hyperfine coupling tensor A. The /-dependent nuclear Zeeman interaction and the electric quadrupole interaction are included as 2nd and 3rd terms. Their detailed description for Fe is provided in Sects. 4.3 and 4.4. The total spin Hamiltonian for electronic and nuclear spin variables is then ... 

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