Hydrogen molecule in magnetic fields: The ground states of the Σ manifold of the parallel configuration

The electronic structure of the hydrogen molecule is investigated for the parallel configuration. The ground states of the Σ manifold are studied for ungerade and gerade parity as well as singlet and triplet states covering a broad regime of field strengths from $B=0\mathrm{}$ up to $B=100\mathrm{}\mathrm{a}.\mathrm{u}.\mathrm{}$ A variety of interesting phenomena can be observed. For the ${}^1{\Sigma }_g$ state we found a monotonous decrease of the equilibrium distance and a simultaneous increase of the dissociation energy with growing magnetic-field strength. The ${}^3{\Sigma }_g$ state is shown to develop an additional minimum which has no counterpart in field-free space. The ${}^1{\Sigma }_u$ state shows a monotonous increase in the dissociation energy with a first increasing and then decreasing internuclear distance of the minimum. For this state the dissociation channel is ${\mathrm{H}}_2{\to \mathrm{H}}^{\mathrm{-}}{+\mathrm{H}}^{+}$ for magnetic field strengths $B\gtrsim 20\mathrm{a}.\mathrm{u}.\mathrm{}$ due to the existence of strongly bound ${\mathrm{H}}^{\mathrm{-}}$ states in strong magnetic fields. The repulsive ${}^3{\Sigma }_u$ state possesses a very shallow van der Waals minimum for magnetic-field strengths smaller than 1.0 a.u. within the numerical accuracy of our calculations. The ${}^1{\Sigma }_g$ and ${}^3{\Sigma }_u$ states cross as a function of $B$ and the ${}^3{\Sigma }_u$ state, which is an unbound state, becomes the ground state of the hydrogen molecule in magnetic fields $B\gtrsim 0.2\mathrm{a}.\mathrm{u}.\mathrm{}$ This is of particular interest for the existence of molecular hydrogen in the vicinity of white dwarfs. In superstrong fields the ground state is again a strongly bound state, the ${}^3{\Pi }_u$ state.