Calculations of energies of the hydrogen molecular ion

We report high precision calculations of nonrelativistic energies of the hydrogen molecular ion H₂⁺ in some low-lying states, using a variational method in multiple Hylleraas basis sets. For the ground state, for example, the energy is established to an accuracy of 8 parts in 10³⁰, which represents 8 orders of magnitude improvement over the best previous value of Cassar and Drake [J. Phys. B 37, 2485 (2004)]. Our calculations lay a firm foundation for studying higher-order relativistic and QED effects.