Vibrational and Centrifugal Effects on the Magnetic Susceptibility and Rotational Magnetic Moment of the Hydrogen Molecule

The effects of nuclear motion on the magnetic susceptibility and rotational magnetic moments of ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ are considered. The magnetic susceptibility and the rotational magnetic moment have been evaluated as a function of the internuclear distance by a variational procedure using the accurate wave functions of Kolos and Roothaan. A careful vibrational averaging has been performed to obtain these magnetic properties for ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ in a number of vibrational-rotational states. A critical test of these calculations is provided by a comparison of the calculated ${〈{{\mu }_R}^e〉}_{v,J}\text{'}\mathrm{s}$ (electronic contribution to the rotational magnetic moment) with experiment. While our one-parameter variational calculations only account for 70% of the experimental ${〈{{\mu }_R}^e〉}_{v,J}\text{'}\mathrm{s}$, ratios of the calculated ${〈{{\mu }_R}^e〉}_{v,J}\text{'}\mathrm{s}$ between the three isotopic molecules in their respective vibrational-rotational states are in remarkable agreement with the experimental ratios (within 0.3%). A similar vibrational averaging of ${{\mu }_R}^e\mathrm{}\left(R\right)\mathrm{}$ obtained by Espe using a four-parameter variational calculation based upon the zero-order wave function of Newell indicates that while the theoretical ${〈{{\mu }_R}^e〉}_{v,J}\text{'}\mathrm{s}$ are now within 10% of the experimental values, the ratios of the ${〈{{\mu }_R}^e〉}_{v,J}\text{'}\mathrm{s}$ are not in as good agreement with experiment. The implication of these results on the molecular-beam method of obtaining molecular dipole moments from isotopic variations of the rotational magnetic moment is discussed.