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

The perpendicular component of the magnetic susceptibility of the hydrogen molecule is calculated in a gauge-invariant manner. This is accomplished by implementing the approximation in which the induced current density is taken perpendicular to the uniform magnetic field when this field is along a principal axis of χ_αβ. A variational calculation using a zero-field orbital of Coulson then yields χ_⊥=-4.107×10^-6 cm³/mole. This value falls within the theoretical bounds determined by Rebane with a maximum error of less than one percent. The Coulson orbital gives results for χₐᵥ and χ_⊥-χ_∥ that compare well with experiment.