Hydrogen molecule in a magnetic field:: The lowest states of the Π manifold and the global ground state of the parallel configuration

The electronic structure of the hydrogen molecule in a magnetic field is investigated for parallel internuclear and magnetic field axes. The lowest states of the Pi manifold are studied for spin singlet and triplet (M-s = -1) as well as gerade and ungerade parity for a broad range of field strengths 0 less than or equal to B less than or equal to 100 a.u. For both states with gerade parity we observe a monotonic decrease in the dissociation energy with increasing field strength up to B = 0.1 a.u. and metastable states with respect to the dissociation into two H atoms occur for a certain range of field strengths. For both states with ungerade parity we observe a strong increase in the dissociation energy with increasing field strength above some critical field strength B-c. As a major result we determine the transition field strengths for the dressings among the lowest (1) Sigma(g), (3) Sigma(u), and (3) Pi(u) states. The global ground state for B less than or similar to 0.18 a.u. is the strongly bound (1) Sigma(g) state. The crossings of the (1) Sigma(g), (3) Sigma(u), (3) Pi(u) state occur at B approximate to 0.18 and B approximate to 0.39 a.u., respectively. The transition between the (3) Sigma(u) and the (3) Pi(u) state occurs at B approximate to 12.3 a.u. Therefore, the global ground state of the hydrogen molecule for the parallel configuration is the unbound (3) Sigma(u) state for 0.18 less than or similar to B less than or similar to 12.3 a.u. The ground state for B greater than or similar to 12.3 a.u. is the strongly bound (3) Pi(u) state. This result is of great relevance to the chemistry in the atmospheres of magnetic white dwarfs and neutron stars.