Dependence of the shielding tensor with a proposed local gauge

Abstract

A theoretical procedure for evaluating nuclear magnetic shielding and magnetic susceptibility tensors in molecules within a `local gauge' transformation is presented. The main features of our formulation are centred on the fact that, even though the expressions resulting from the use of the Coulomb `gauge' for the magnetic susceptibility tensor remain unchanged, it provides alternative expressions for the nuclear magnetic shielding tensor. This new result may be considered as an advantage because it allows a dependence of the nuclear magnetic shielding tensor on the electric field and gradient field exerted by the electrons on the position of the nuclei to be shown in an explicit manner. Sum rules for charge and current conservation and `gauge' invariance are also derived. Finally we mention that all these results are only valid for external uniform and time independent magnetic fields.