Chemical shielding tensor, nuclear

Facelli, J. C., Molecular Structure and Carbon-13 Chemical Shielding Tensors Obtained from Nuclear Magnetic Resonance, 19, 1. 

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. 

The quantity a is known as the chemical shielding tensor associated with that particular nuclear site. The tensorial character of a implies that B/oc is in general in a direction different from that of Bo, which reflects the anisotropy of the molecular environment of the considered nucleus. As this is a purely magnetic interaction, analogous to the Zeeman one, the Hamiltonian Hcs is given by ... 

Figure 6 Fragments of the peptide 34-42 showing the cis and trans conformations. Also indicated is the orientation of the carbonyl carbon chemical shielding tensor, with perpendicular to the plane. Note the different orientations of the C-C inter-nuclear vector with respect to the CS tensor components. Reprinted with permission of the American Chemical Society from Costa PR, Kocisko DA, Sun BQ, Lansbury PT Jr and Griffin RG (1997) Journal of the American Chemical Society, 119 10487-10493)...

The methods listed thus far can be used for the reliable prediction of NMR chemical shifts for small organic compounds in the gas phase, which are often reasonably close to the liquid-phase results. Heavy elements, such as transition metals and lanthanides, present a much more dilficult problem. Mass defect and spin-coupling terms have been found to be significant for the description of the NMR shielding tensors for these elements. Since NMR is a nuclear effect, core potentials should not be used. 

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])... 

The spin interactions, dipole-dipole (D), nuclear electric quadrupole (Q) and chemical shielding (C.S), may be formally written in terms of irreducible tensors of rank l34 in Hz ... 

N shielding tensors, 34 331, 333 [NTc(p-0)2TcN]"+ dimers, 41 90-91 Nuclear activation chemical bond... 

Solid-state high-resolution NMR spectroscopy, combined with quantum chemistry, is able to provide detailed information on the electronic and stereochemical structures of molecules[l]. Quantum-chemical calculations produce three principal values of the nuclear shielding tensor. These principal values have more detailed information about structure of molecules as compared with isotropic chemical shifts. Comparison of the observed chemical shift and chemical shift tensor with the calculated shieldings, produced by quantum-chemical calculations, permits deep insight into the structures of the molecules under investigation. 

Another important extension of the theory concerns NMR chemical shift. Yamazaki et al. proposed a theory for computing the chemical shift of solvated molecules [17]. The nuclear magnetic shielding tensor o-x of a nucleus X can be represented as a mixed second derivative of the free energy A with respect to the magnetic field B and the nuclear magnetic moment mx ... 

The presence of magnetic moments /lia, b, of nuclei A,B,... in a molecule are responsible for the two observables of the NMR experiment that are most frequently utilized in chemical applications. They are physically observed in form of quantized energy differences AE that can be measured very precisely. These two observables are the nuclear shielding tensor cr for nucleus A and the so-called indirect reduced coupling tensor KAB for a pair of nuclei A,B. Both crA and Kab are second-rank tensors that are defined via the phenomenological Hamiltonians... 

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