Spin coupling constants and hyperfine transition frequencies for the hydrogen molecular ion

We have calculated for the ten lowest vibrational levels of H₂⁺ the first-order hyperfine and spin-rotation constants with the inclusion in perturbation theory of the first-order coupling of the electron and nuclear motion and have determined the hyperfine transition frequencies. The calculated frequencies agree to better than 175 kHz with all the experimentally determined hyperfine frequencies for the N=1 rotational level and to better than 3 kHz for the N=2 rotational level. Relativistic and radiative effects may account for the remaining discrepancy.