Hydrogen Molecule in a Magnetic Field: 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 with 1Σ_g, 3Σ_u, and 3∏_u symmetry are studied for a broad range of field strengths 0 ≤ B ≤ 100 a.u. As a major result we determine the transition field strengths for the crossings among these states: The global ground state for B ≲ 0.18 a.u. is the strongly bound 1Σ_g state. The crossing of the 1Σ_g with the 3Σ_u state occurs at B ≈ 0.18 a.u. while the crossing between the 3Σ_u and 3∏_u state occurs at B ≈ 12.3 a.u. Therefore, the global ground state of the hydrogen molecule for the parallel configuration is the unbound3Σ_u state for 0.18 ≲ B ≲ 12.3 a.u. The ground state for B ≳ 12.3 a.u. is the strongly bound 3∏_u state. This result is of great relevance to the chemistry in the atmospheres of magnetic white dwarfs and neutron stars.