Vibrational and Centrifugal Effects on Nuclear Interactions and Rotational Moments in Molecules

The effects of zero point vibration and centrifugal stretching of molecules upon the spin-spin magnetic interaction, the spin-rotational magnetic interaction, the molecular rotational magnetic moment, the magnetic shielding of the nucleus, and the molecular diamagnetic susceptibility of the molecule are discussed. Expressions for these quantities with vibrational and centrifugal effects included are given in detail for diatomic molecules and numerical calculations for the cases of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$. It is shown that from measurements of the rotational magnetic moments of both ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ or of ${\mathrm{H}}_2$ in two different rotational states, one can calculate the variation with internuclear separation of the high frequency terms of the molecular diamagnetic susceptibility. Measurements on the spin-rotational magnetic interactions in both ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ provide information on the variation of this interaction with internuclear spacing and thereby supply important corrections that are needed in calculating the nuclear magnetic shielding from the spin rotational magnetic interaction and in measuring the ratio of the proton magnetic moment to that of the deuteron. These calculations also supply a correction to the spin-spin magnetic interaction that must be used in determining the deuteron quadrupole moment from experiments with ${\mathrm{D}}_2$.