Approximate Calculations of Nuclear Shielding

Approximate methods within the framework of LCAO MO theory for calcu-lating the different contributions to a in Eq. (3.7) have been developed by Pople [161,164], Karplus and Pople [162,163], Karplus and Das [165] and others [166,167]. These methods were originally derived mainly with shielding effects in first and second row elements in mind. The influence of d-orbitals which may play an important role in the higher halogens, was not considered. The Karplus and Das treatment 

To provide a background to the discussion of halogen shifts in covalent compounds we will give a brief review of the Pople LCAO method 

Saika-Slichter breakdown of a (cf. Eq. (3.7)) is used. The average value of the diamagnetic shielding tensor may according to Pople be written 

The early calculations by Dickinson [168] of the diamagnetic shielding in atoms using Hartree or Hartree-Fock SCF atomic orbitals made it clear that the major contribution to is due to inner shell electrons and that the relative contribution of the outer electrons decreases markedly with atomic number Z. As a consequence of this are the values for atoms rather insensitive to the effective atomic 

Recent ab initio type calculations of nuclear shielding of carbon, nitrogen and oxygen in small molecules by Ditchfield et al, [171], essentially show that the diamagnetic contribution to the total shielding for second row nuclei does not vary appreciably from one molecule to another. 

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