  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 = 100a.u. A variety of
interesting phenomena can be observed. For the ^1Sigma_g state we found a
monotonous decrease of the equilibrium distance and a simultaneously 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 first increasing and than decreasing internuclear
distance of the minimum. For this state the dissociation channel is H_2 to H^-
+ H^+ for magnetic-field strengths B greater than 20a.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 1.0a.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 0.2a.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.
