Electron-Coupled Interaction between Nuclear Spins in HD Molecule

Abstract

Electron-coupled interaction between two nuclear spins ${\mathrm{I}}_A$ and ${\mathrm{I}}_B$ is of the form $h{\delta }_{\mathrm{AB}}{\mathrm{I}}_A·{\mathrm{I}}_B$. In this paper, formulas for calculating ${\delta }_{\mathrm{AB}}$ are derived by using the variational method. By using these formulas, we have calculated ${\delta }_{\mathrm{AB}}$ of the HD molecule at internuclear distances of 1.3, 1.4, and 1.5 atomic units. The total wave function was chosen as a linear combination of seven independent functions of ${{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}$ symmetry, representing the unperturbed state, and several additional functions, to represent the perturbation. The average value of ${\delta }_{\mathrm{AB}}$ over the zero-point vibration, ${〈{\delta }_{\mathrm{AB}}〉}_{00}$, is found to be 37.138 cps. Further, the refinement of a part of the calculations is undertaken by use of the 11-term James and Coolidge wave function. The final result is ${〈{\delta }_{\mathrm{AB}}〉}_{00}=35.217\mathrm{}$ cps. The agreement with the observed value of 42.7±0.7 cps is satisfactory, considering that we have used only a few terms for the additional perturbative wave function and that the result is a sum of terms which cancel each other appreciably. Contributions from each perturbing Hamiltonian and also from a set of wave functions with different symmetry character were obtained separately. The various results are presented and discussed.