We describe the effective Lorentz forces on the ions of a generic insulatingsystem in an magnetic field, in the context of Born-Oppenheimer ab-initiomolecular dynamics. The force on each ion includes an important contribution ofelectronic 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 forfuture first principles classical dynamics simulations based {\it e.g.,} ondensity functional methods. As a preliminary analytical demonstration wepresent the dynamics of an H$_2$ molecule in a field of intermediate strength,approximately describing the electrons through Slater's variationalwavefunction.
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