$\mathrm H_2^+$ in a weak magnetic field

Abstract

The electronic energy of $\mathrm H_2^+$ in magnetic fields of up to $B=0.2B_0$ (or 4.7 $\times 10^4$ Tesla) is investigated. Numerical values of the magnetic susceptibility for both the diamagnetic and paramagnetic contributions are reported for arbitrary orientations of the molecule in the magnetic field. It is shown that both diamagnetic and paramagnetic susceptibilities grow with inclination, while paramagnetic susceptibility is systematically much smaller than the diamagnetic one. Accurate two-dimensional Born-Oppenheimer surfaces are obtained with special trial functions. Using these surfaces, vibrational and rotational states are computed and analysed for the isotopologues $\mathrm H_2^+$ and $\mathrm D_2^+$.