Calculation of Molecular Magnetic-properties Within the Landau Gauge

A theoretical procedure for calculating magnetic susceptibility and nuclear magnetic shieldings in molecules in the presence of a spatially uniform time-independent magnetic field, within the Landau gauge for the vector potential, is described. Sum rules for charge and current conservation and gauge invariance have been derived. A computational scheme based on the random-phase approximation has been used to calculate magnetic susceptibility and shielding tensors in the water molecule, adopting fairly flexible Gaussian basis sets of large size. The results show that very accurate molecular wave functions are needed to obtain paramagnetic contributions to the magnetic susceptibility of the same quality as those obtainable within the Coulomb gauge for the vector potential. The theoretical nuclear magnetic shielding tensors in the Landau gauge are characterized by the same quality as those in the Coulomb gauge.