Efficient automatized density-functional tight-binding parameterizations: Application to group IV elements

Density-functional tight-binding methods stand out as a very good compromise between accuracy and computational efficiency. These methods rely on parameter sets that have to be determined and tabulated for every pair of chemical elements. We describe an efficient, and to a large extent automatic, procedure to build such parameter sets. This procedure includes the generation of unbiased training sets, and subsequent optimization of the parameters using a pattern search method. As target for the optimization we ask that the formation energy and the forces on the atoms calculated within tight-binding reproduce the ones obtained using density-functional theory. We then use this approach to calculate parameter sets for group-IV elements and their binaries. These turn out to yield substantially better results than previously available parameters, especially in what concerns energies and forces.