Fitting to ab initio data by ``force matching''

  We have seen in §4.5.1 how analytical forms can become pretty complicated when we strive for realism in modeling. Parametrizing the function appearing in a complex Hamiltonian can then become a tiresome task, and people often resort to very simple parametrizations. For instance, Tersoff potentials have only 12 parameters: an average of 2 parameters to describe each of the 6 functions constituting the model.

A first-principles molecular dynamics program can easily produce huge quantities of useful and reliable data, such as forces acting on atoms in a variety of different geometries and coordinations. These data can complement the experimental quantities normally used to fit potentials, helping to construct more realistic potentials. Recently, a scheme called ``force matching method'' [38] has been developed. It consists of a numerical optimization procedure which tries to match as closely as possible ab initio-derived forces with a classical potential, using a rich parametrization (10-15 parameters for each function in the potential). By explicitly including different geometries and different temperatures in the data set, one can attack the transferability problem at its very heart. One can says that the potential is constructed by learning from first-principles.

Several groups are now working on this front, so that potentials for classes of materials so far unexploited by classical molecular dynamics are likely to appear in the next years.