# The hydrogen molecule $\rm{H}_{2}$ in inclined configuration in a weak magnetic field

## TL;DR

This study uses high-precision variational methods to analyze the hydrogen molecule in inclined configurations under weak magnetic fields, revealing the stability, susceptibilities, and rovibrational spectra, and identifying the critical magnetic field where the ground state changes.

## Contribution

It provides the first calculations of susceptibilities at a 45° inclination and the rovibrational spectra of H₂ in magnetic fields, enhancing understanding of molecular behavior in such conditions.

## Key findings

- The ground state favors parallel configuration for B ≤ 0.178 a.u.
- The 1_g state remains bound and becomes metastable beyond B_cr.
- Rovibrational spectra are calculated for the first time.

## Abstract

Highly accurate variational calculations, based on a few-parameter, physically adequate trial function, are carried out for the hydrogen molecule \hh in inclined configuration, where the molecular axis forms an angle $\theta$ with respect to the direction of a uniform constant magnetic field ${\bf B}$, for $B=0,\, 0.1,\, 0.175$ and $0.2\,$a.u. Three inclinations $\theta=0^\circ,\,45^\circ,\,90^\circ$ are studied in detail with emphasis to the ground state $1_g$. Diamagnetic and paramagnetic susceptibilities are calculated (for $\theta=45^\circ$ for the first time), they are in agreement with the experimental data and with other calculations. For $B=0,\, 0.1$ and $0.2\,$a.u. potential energy curves $E$ vs $R$ are built for each inclination, they are interpolated by simple, two-point Pad\'e approximant $Pade[2/6](R)$ with accuracy of not less than 4 significant digits. Spectra of rovibrational states are calculated for the first time. It was found that the optimal configuration of the ground state for $B \leq B_{cr}=0.178\,$a.u. corresponds always to the parallel configuration, $\theta=0$, thus, it is a $^1\Sigma_g$ state. The state $1_g$ remains bound for any magnetic field, becoming metastable for $B > B_{cr}$, while for $B_{cr} < B < 12$\,a.u. the ground state corresponds to two isolated hydrogen atoms with parallel spins.