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Spectroscopy of the hydrogen molecular ion

The theory and spectroscopy of the hydrogen molecular ion in its isotopic forms H2+, HD+ and D2+ is reviewed. Theoretical treatments are directed towards the calculation of potential energy curves, vibration-rotation energies and nuclear hyperfine constants. In the Born-Oppenheimer approximation the Schrodinger equation for H2+ can be solved exactly, but further approximations must be developed to describe the coupling of electronic and nuclear motion. The lack of a centre of symmetry in HD+ creates difficulties in the theory. Radiofrequency hyperfine transitions have been measured for H2+ using quadrupole trapping and photoalignment. Ion beam methods have been used to measure vibration-rotation transitions in HD+, and attention has been paid to levels very close to the dissociation limit. Analysis of proton and deuteron nuclear hyperfine structure reveals extreme asymmetry of the electron distribution in these levels. The hyperfine interactions have been measured by radiofrequency/infrared and microwave/infrared double resonance experiments. An electronic spectrum of D2+ arising through excitation from the ground electronic state to the excited long-range state has been measured using both infrared and microwave radiation. Observation of a microwave electronic transition in H2+ has provided experimental identification of the related H;H long-range complex.