A computationally efficient molecular dynamics implementation of a polarizable force field parametrized from ab initio data is presented. Our formulation, based on a second-order expansion of the energy density, models the density response using Gaussian basis functions derived from density functional linear response theory. Polarization effects are described by the time evolution of the basis function coefficients propagated via an extended Lagrangian formalism. We have devised a general protocol for the parametrization of the force field. We will show that a single parametrization of the model can describe the polarization effects of LiI in the condensed phase.