Gauge-invariant calculation of the magnetic properties of the hydrogen molecule

Abstract

Components of the magnetic shielding and dipole magnetizability tensors of the hydrogen molecule are calculated in a gauge-invariant manner. The orbital approximation is employed using the LCAO form of Coulson and a five term SCF orbital of Kolos and Roothaan which is near the Hartree-Fock limit. Accurate values of the shielding are obtained when the standard 1/r ³ integral factor is reduced to a 1/r dependence by an appropriate transformation. In the orbital approximation our gauge-invariant method will give values that approach those obtained by the Hartree-Fock perturbation method, if the induced current is nearly perpendicular to the magnetic field when this field is perpendicular to the molecule's axis. An earlier calculation showed j · B = 0 to be an excellent approximation for the magnetizability. Additional support for this approximation is found in the agreement of our results with those of Sadlej and Raynes [1978, Molec. Phys., 35, 101]. The induced current density in our method automatically satisfies ∇ · j = 0 and it is plotted in different regions of the molecule. The current is found to be molecular-like rather than atomic-like and this is attributed to the delocalization of the electrons in hydrogen.