  Strong magnetic fields have a large impact on the dynamics of molecules. In
addition to the changes of the electronic structure, the nuclei are exposed to
the Lorentz force with the magnetic field being screened by the electrons. In
this work, we explore these effects using ab-initio molecular dynamics
simulations based on an effective Hamiltonian calculated at the Hartree-Fock
level of theory. To correctly include these non-conservative forces in the
dynamics, we have designed a series of novel propagators that show both good
efficiency and stability in test cases. As a first application, we analyze
simulations of He and H$_2$ at two field strengths characteristic of magnetic
white dwarfs (0.1 $B_0 = 2.35 \times 10^4$ T and $B_0 = 2.35 \times 10^5$ T).
While the He simulations clearly demonstrate the importance of electron
screening of the Lorentz force in the dynamics, the extracted rovibrational
spectra of H$_2$ reveal a number of fascinating features not observed in the
field-free case: couplings of rotations/vibrations with the cyclotron rotation,
overtones with unusual selection rules, and hindered rotations that transmute
into librations with increasing field strength. We conclude that our presented
framework is a powerful tool to investigate molecules in these extreme
environments.
