Binding energy and triplet-singlet splitting for the hydrogen molecule in ultrahigh magnetic fields

The energy difference of triplet and singlet states due to exchange coupling, the energy levels, the ground binding state, and the wave functions is calculated for a hydrogen molecule in an ultrahigh magnetic field when the distance between the Landau levels eħH/mc exceeds the Coulomb unit (Rydberg) ${\mathit{me}}^4$/2${\mathrm{ħ}}^2$. The results are asymptotically exact at the interatomic distance R, which is large compared with the atomic size and for high magnetic fields. It is shown here that the triplet electron term has a minimum at large interatomic distances corresponding to the formation of the ground state of a stable ${\mathrm{H}}_2$ molecule. For the hydrogen molecule in an ultrahigh magnetic field, the energy of the singlet state also has a deep minimum at R