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

Abstract

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 ${〈{{\ensuremath{\mu}}_{R}}^{e}〉}_{v,J}'\mathrm{s}$ (electronic contribution to the rotational magnetic moment) with experiment. While our one-parameter variational calculations only account for 70% of the experimental ${〈{{\ensuremath{\mu}}_{R}}^{e}〉}_{v,J}'\mathrm{s}$, ratios of the calculated ${〈{{\ensuremath{\mu}}_{R}}^{e}〉}_{v,J}'\mathrm{s}$ 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 ${{\ensuremath{\mu}}_{R}}^{e}(R)$ obtained by Espe using a four-parameter variational calculation based upon the zero-order wave function of Newell indicates that while the theoretical ${〈{{\ensuremath{\mu}}_{R}}^{e}〉}_{v,J}'\mathrm{s}$ are now within 10% of the experimental values, the ratios of the ${〈{{\ensuremath{\mu}}_{R}}^{e}〉}_{v,J}'\mathrm{s}$ 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.