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

Abstract

In a uniform electric field F, the component σ_αβ 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 (=1/3σ_αα). 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.