  We describe the effective Lorentz forces on the ions of a generic insulating
system in an magnetic field, in the context of Born-Oppenheimer ab-initio
molecular dynamics. The force on each ion includes an important contribution of
electronic origin, which depends explicitly on the velocity of all other ions.
It is formulated in terms of a Berry curvature, in a form directly suitable for
future first principles classical dynamics simulations based {\it e.g.,} on
density functional methods. As a preliminary analytical demonstration we
present the dynamics of an H$_2$ molecule in a field of intermediate strength,
approximately describing the electrons through Slater's variational
wavefunction.
