High-precision calculation of the hyperfine structure of the HD+ ion

High-precision laser spectroscopy of ultracold hydrogen molecular ions has the potential of improving the precision of the electron-to-proton mass ratio. An accurate knowledge of the spin structure of the transition is required in order to permit precise comparison with experimental transition frequencies. We calculate with a relative accuracy of the order of O(alpha(2)) the hyperfine splitting of the rovibrational states of HD+ with orbital momentum L <= 4 and vibrational quantum numbers up to v=17, using the Breit-Pauli spin interaction Hamiltonian. These are the first complete ab initio calculations at this order of accuracy. A discrepancy between experiment and previous theory is resolved.