Shielding tensors nucleus

In an NMR context, i.e. when the field point coincides with the position of a magnetic nucleus, the implications of the separation of the response fields in eqs. (18-20) into parts generated by the various components of the shielding tensor, are appreciated by first noting that the resonance frequency for the nucleus can be written as [28]... 

In previous presentations [16-19,28], the LORG equations are formulated in a nucleus centered coordinate system. Explicit reference to a field point R, can be introduced following eq.(13), and the resulting LORG equations for the i, j th element of the shielding tensor become... 

The diamagnetic contribution to the shielding tensors can be defined as the derivative of this Hamiltonian with respect to the magnetic moment Uk=YkIk of nucleus K and the external magnetic field... 

The expressions for the various parts of the Hamiltonian (equation 1) are well documented and for our purpose and the following discussion it suffices to summarize the results for axially symmetric situations in angular frequency units with the equations 2-6, where and Ashielding tensor and the shielding anisotropy, respectively, D is the dipole coupling, eq or V is the electric field gradient at the nucleus, eQ is the nuclear quadrupole moment and the other symbols have their usual meaning ... 

Optimized Geometries. As the elements of the NMR shielding tensor for a nucleus represent local properties, the most important geometrical parameter influencing the value of the 19F shielding constant can be expected to be the length of the bond which attaches the fluorine to the benzene ring. The optimized values of the carbon-fluorine... 

Let us now have a look at the possibility to modelize NMR shielding tensors using the same theoretical frame. In an appropriate PAS, the nine-component shielding tensor oap which describes the very small magnetic fields arising from electronic motions around the nucleus can be diagonalized leading to (49) ... 

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... 

The expression for the nuclear shielding tensor a a does not depend on any particular value of ha- Though the spin magnetic moment of the nucleus must not be zero in order for magnetic resonance to occur at all in an experiment, in the theoretical formalism the nuclear shielding can be calculated anyway. In consequence, an explicit expression for <7 depends only on the position of the... 

Isotropic chemical shifts, obtained from solution studies, are useful indicators of the electronic environment around the nucleus, but they provide only a fraction of the available information. The shielding tensor components, which can be extracted from spinning sidebands in solid-state spectra, also contain useful information on bonding and structure, because they are sensitive to bond type. Techniques other than nitrogen NMR, such as spin-rotation 165) or relaxation 166) measurements, can be used to determine the nitrogen shielding tensor. 

---