The method of local fields: A bridge between molecular modelling and dielectric theory

At the nanoscale, the charge distribution in a cluster of several atoms or molecules can be calculated ab initio, i.e. without free parameters. Molecular modelling is limited to a relatively small number of atoms compared to macroscopic materials with myriads of atoms. On the other hand, dielectric and ferroelectric properties of macroscopic matter are described by classical theory using mean-field approximations, e. g. the formula of Clausius–Mossotti for dielectrics and the Landau–Ginzburg–Devonshire theory or rather the molecular field theory by Weiss for ferroelectrics. In the context of multiscale simulations we present a microscopic model for dielectrics and ferroelectrics consisting of discrete atoms and / or dipoles. Parameters calculated from molecular modelling can be used here as input to our simulations in order to calculate bigger systems now. All electrostatic interactions are considered and the electrodes are taken into account using the method of images. Based on thermally activated processes, permanent dipoles fluctuate in double well potentials according to the Boltzmann statistics. Neutral atoms are modelled by induced dipoles having dipole moments proportional to the locally prevailing field. The numerical calculations are based on deterministic local field computations and on weighted probabilistic dynamic Monte Carlo steps.