Nuclear site symmetry and nuclear magnetic shielding in a uniform electric field

Abstract

In a uniform electric field F, the component σαβ of a nuclear magnetic shielding tensor can be expanded as a power series; thus The numbers of non-vanishing components of the tensors σ(0), σ(1) and σ(2) depend on the nuclear site symmetry. Earlier work of Buckingham and Malm for σ(0) is extended to deal with σ(1) and σ(2). It is found that the presence of even just a few elements of symmetry is sufficient to cause a large number of components of σ(1) and σ(2) to vanish and that many of the non-vanishing components are simply related to others. The results are discussed in relation to their significance for the electric-field dependence of the mean shielding (=1/3σαα). This is of importance in understanding nuclear shielding changes in molecules brought about by protonation, the substitution of polar groups and the effects of intermolecular electric fields.