Chemical shielding tensors, nuclear magnetic

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

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 ... 

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... 

P. Mansfield, M. J. Orchard, D. C. Stalker and K. H. B. Richards, Symmetrized multipulse nuclear-magnetic-resonance experiments in solids measurement of the chemical-shift shielding tensor in some compounds. Phys. Rev., 1973, B7, 90-105. 

The most common interactions are dipolar coupling between two spins, chemical shielding and quadrupolar interaction for spins I> 1. The chemical-shielding interaction arises from the motion of electrons around a nucleus induced by the external applied static magnetic field. This motion generates local magnetic fields that modify the total field experienced by the nucleus, and are characteristic of the local chemical environment of the nuclei. All nuclei with a spin /> 1 possess a quadrupolar moment Q that interacts with the EFG Vrs — d2 V/dXfdx at the nuclear site. The EFG tensor Vrs is a symmetric tensor with zero trace Tr( E) = A E = 0 (from Laplace equation). 

For the quantum chemical calculation of NMR chemical shifts, it is essential to realize that the shielding tensor a in Eq. (6.3) appears in a term bilinear in the external magnetic field B and the nuclear magnetic moment nij of interest. This means that the shielding tensor is a second-order property... 

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