Electronic bond structure of the ${\mathrm{H}}_2^{+}$ ion in a strong magnetic field: A study of the parallel configuration

A large number of magnetically dressed states of the hydrogen molecular ion for parallel internuclear and magnetic field axes are investigated. The numerical calculations of the molecular states and potential-energy curves in the fixed-nuclei approximation are based on a recently established and optimized atomic orbital basis set. We study electronic states within the range 0≤‖m‖≤10 of magnetic quantum numbers and for several field strengths. In particular, we also investigate many excited states within a subspace for fixed magnetic quantum number and parity. In order to understand the influence of the magnetic field on the chemical bond of excited molecular states, we perform a detailed comparison of the electronic probability distributions and potential-energy curves in the field-free space with those in the presence of a magnetic field. As a major result we observe the existence of two different classes of strongly bound, i.e., stable, magnetically dressed states whose corresponding counterparts in the field-free space exhibit purely repulsive potential-energy curves, i.e., are unstable. Corrections which are going beyond the fixed-nuclei approach, i.e., the coupling of the center of mass to the electronic motion, as well as the mass corrections are investigated in order to ensure the physical validity of our results.