Magnetic shielding constant tensor

Nuclear shielding reflects changes to the nuclear Zeeman splitting by an external magnetic field and is phenomenologically defined by eq. 1, where the effective magnetic field at the position of the nucleus in question is modified relative to the external field B by the shielding constant (tensor) a. 

The last two terms of the free energy in Eq. (8.2) are studied in NMR spectroscopy, and the one linear in the applied field involves the shielding constant tensor a, which arises from various terms in Eq. (7.15). The origin in shielding calculations is usually put at the nucleus in question (for a discussion of the origin dependence, see the section on magnetic properties). 

O A is a shielding constant tensor of the nucleus A. Due to this shielding, nucleus A feels a local field Hioc = (l < a)H — H — a aH instead of the external field H applied (due to the tensor character of o a, the vectors Hioc and H may differ by their length and direction). The formula assumes that the shielding is proportional to the external magnetic field intensity that causes the shielding. Thus, the first term in the Hamiltonian ii may also be written asa YaHJ Ja-... 

J. Mason, Conventions for the reporting of nuclear magnetic shielding (or shift) tensors suggested by participants in the NATO ARW on NMR shielding constants at the University of Maryland, College Park, July 1992. Solid State Nud. Magn. Reson., 1993, 2,285-288. 

The NMR characteristics of phosphirenes once again include a strong upfield shift of the 31P resonance and very high J (C—P) coupling constants. The parameters for a representative phos-phirene are listed in Table 4. The 31P magnetic shielding tensor components of phosphirene (3) have also been measured <87CPL(136)224>. 

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