Hyperfine structure in the hydrogen molecular ion

The hyperfine splitting of energy levels in the H₂⁺ molecular ion is calculated within the framework of the spin-dependent part of the Breit-Pauli Hamiltonian. This is the first ab initio calculation based on the precise variational solution of the three-body Schr\"odinger equation. It is shown that inclusion of the nuclear spin-spin tensor interaction, neglected in previous theoretical considerations, brings agreement with the most precise hyperfine transition measurements obtained by Jefferts to about 10.3em0exkHz for the lower-frequency intervals in the 5--1000.3em0exMHz range. Finally, we investigate the hyperfine structure of some transitions, candidates for high-precision two-photon spectroscopy.