Calculation of nuclear magnetic shielding using a parametric gauge for the vector potential Original Research Article

A transformation of the transverse Coulomb vector potential was implemented to calculate magnetic shielding tensor via the random-phase approximation (RPA) within the framework of a `parametric gaugeʹ. The main features of our formulation are focused in the fact that even keeping unaltered the expressions coming from the use of the Coulomb `gaugeʹ for the magnetic susceptibility tensor, it provides alternative ones for the nuclear magnetic shielding tensor. These new expressions depend on an arbitrary parameter and on the gradient electric field exerted by the electrons on the position of the nuclei, in an explicit manner. Sum rules for charge and current conservation and `gaugeʹ invariance are also derived. Near Hartee-Fock nuclear magnetic shielding tensors were evaluated for some small molecules: H2O, NH3 and CH4, and the fulfilment of a series of sum rules, which must be satisfied to guarantee gauge invariance of total, nuclear magnetic shielding tensors, were exploited to check the degree of confidence and, or, the advantages of the proposed gauge.