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

TL;DR

This paper investigates the electronic energy, magnetic susceptibilities, and vibrational and rotational states of $ ext{H}_2^+$ in weak magnetic fields up to 0.2 times a reference field, providing detailed numerical data and analysis.

Contribution

It provides new numerical calculations of magnetic susceptibilities and energy surfaces for $ ext{H}_2^+$ in weak magnetic fields, including vibrational and rotational states for isotopologues.

Findings

Both diamagnetic and paramagnetic susceptibilities increase with inclination.

Paramagnetic susceptibility is significantly smaller than diamagnetic susceptibility.

Accurate two-dimensional Born-Oppenheimer surfaces enable detailed vibrational and rotational analysis.

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 $\mathrm D_2^+$.