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

The electronic structure of the hydrogen molecule is investigated for the parallel configuration. The ground states of the Sigma 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 up to B=100 a.u. 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 H-2-->H-+H+ for magnetic field strengths B greater than or similar to 20 a.u. due to the existence of strongly bound H- 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 greater than or similar to 0.2 a.u. 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.