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 ${\chi }_{\alpha \beta }$. A variational calculation using a zero-field orbital of Coulson then yields ${\chi }_{\perp }=-4.107\mathrm{}\times {10}^{-6\mathrm{}}$ ${\mathrm{cm}}^3$/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 ${\chi }_{\mathrm{av}}$ and ${\chi }_{\perp }-{\chi }_{\parallel }$ that compare well with experiment.