Electric Field Gradient and Magnetic Spin-Spin Interactions in Isotopes of the Hydrogen Molecule

Abstract

Field gradients have been calculated at 12 values of the internuclear distance from 34-, 66-, and 87-term molecular wave functions expanded in prolate-spheroidal coordinates and $r_{12}$. Convergence of the gradients as the basis enlarges is indicated and the dissociation energy of ${\mathrm{H}}_2$ is in agreement with experiment. Using vibrationally averaged gradients, experimental values for the quadrupole-interaction constant, and estimating the error in the field gradients arising from truncation of the basis, the electric quadrupole moment of the deuteron is found to be 0.2875±0.002×${10}^{-26\mathrm{}}$ ${\mathrm{cm}}^2$, which is 2% larger than the most recent values. This disagreement as well as that among earlier authors is explained. First-order perturbation-theoretic results for the magnetic spin-spin interaction constant for ${\mathrm{H}}_2\mathrm{}(J=1\mathrm{})\mathrm{}$, $\mathrm{HD}\mathrm{}(J=1\mathrm{})\mathrm{}$, ${\mathrm{D}}_2\mathrm{}(J=1\mathrm{})\mathrm{}$, and ${\mathrm{D}}_2\mathrm{}(J=2\mathrm{})\mathrm{}$ are in agreement with experiment and, except for ${\mathrm{H}}_2$, well inside experimental error.