Shielding tensor

Anet F A L and O Leary D J 1992 The shielding tensor. Part II. Understanding its strange effects on relaxation Concepts Magn. Reson. 4 35-52... 

Champmartin D and Rubini P 1996 Determination of the 0-17 quadrupolar coupling constant and of the C-13 chemical shielding tensor anisotropy of the CO groups of pentane-2,4-dione and beta-diketonate complexes in solution. NMR relaxation study/norg. Chem. 35 179-83... 

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. 

R. Cheeseman, G. W. Trucks, T. A. Keith and M. J. Frisch, A Comparison of Models for Calculating Nuclear Magnetic Resonance Shielding Tensors, /. Chem. Phys., 104, 5497(1996). 

Since HF calculations have a tendency to underestimate the N—N and the C—N bond lengths in triazoles [98JPC(A)620, 98JPC(A) 10348], the structural parameters should be computed at least at the DFT or MP2 levels. This is particularly true if electron-donating substituents are attached to the ring. Nitrogen NMR shielding tensors were computed for a set of methylated triazoles and tetrazoles but will be discussed in the context of tetrazoles (cf. Section IV,B). 

The shielding tensor, and its diamagnetic and paramagnetic components, are not necessarily symmetric in the Cartesian indices [25-29], and the shielding tensor can in general be decomposed into a symmetric and an antisymmetric component, i.e. 

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 the display of the field in Section V, we apply the above separation into parts generated by the various components of the shielding tensor. The secular part of the shielding vector, eqs.(23,24), and the intensity quantities / (R us) and 7 (R ujg), obtained from eq.(21) as discussed above, lend themselves immediately to the response graph technique described in ref. [14], as illustrated in Figures (1-3,5), while the antisymmetry vector is illustrated in Figure 4. 

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... 

A common origin paramagnetic contribution can subsequently be obtained as the difference between the LORG total shielding tensor and the diamagnetic contribution from eq.(29), i.e. 

---