The dipole polarizability of the hydrogen molecular ion

The separation of nuclear and electronic motion is the underlying principle of the theory of molecular structure. The theory is challenged by recent measurements of Jacobson et al. [1] of the electric dipole polarizabilities of H2 and D2 which have a precision beyond that obtained in the Born-Oppenheimer approximation. The measurements stimulated the introduction of methods [2–5] that take into account the diabatic coupling omitted in the earlier calculations and they led to polarizabilities that agree with the measured values within the combined experimental and theoretical uncertainties. We present here new theoretical predictions of much greater accuracy which in turn pose a significant challenge to experiment. The accuracy of our method can be assessed by the use of sum rules and we predict nonrelativistically the polarizabilities of H2 and D2 to a precision well beyond that achieved by the experiments. The method is general and it should be possible to apply it to manyelectron diatomic molecules. Separating out the center of mass motion we may write for the Hamiltonian of H2 or D2 in an electric field F = Fn̂ lying along the Z-axis of the space-fixed frame