On the Theory of Spin-Orbit and Hyperfine Interactions in Molecules. Application to the Hydrogen Molecule—Ion

Abstract

Previously, calculations on molecular systems have employed spin-orbit and hyperfine operators which possess strong singularities at the nuclei of the molecule. The matrix elements of the latter operators may, depending on the symmetries of the wave functions, involve divergent integrals. The spin-orbit and hyperfine interactions are re-examined. The correct operators are derived from a reduction of the Dirac equation. It is shown that the correct forms of the spin-orbit and hyperfine operators have finite and unique matrix elements. The theory is specifically applied to the hydrogen molecule—ion. It is found that the anisotropic part of the spectroscopic splitting factor is very small. The dipole—dipole coupling parameter D is calculated for the ground state of H2+. At the equilibrium internuclear distance, D=−0.1067. The latter result does not agree with the result of other authors who, by using the strongly singular operators, found a positive sign for D.