A method for parametrizing, from first principles density functional theory calculations, a model of the interactions between the ions in an ionic liquid and a metallic (electrode) surface is described. The interaction model includes the induction of dipoles on the ions of the liquid by their mutual interaction and the interaction with the electrode surface as well as the polarization of the metal by the ionic charges and dipoles ('image' interactions). The method is used to obtain a suitable interaction model for a system consisting of a LiCl liquid electrolyte and a solid aluminium electrode. The model is then used in simulations of this system for various values of the electrical potential applied to the electrode. The evolution of the liquid structure at the electrochemical interface with applied potential is followed and the capacitance of the electrochemical interface is measured. The electrolyte is found to exhibit a potential-driven phase transition which involves the commensurate ordering of the electrolyte ions with the electrode surface; this leads to a maximum in the differential capacitance as a function of applied potential. Away from the phase transition the capacitance was found to be independent of the applied potential.