Efficient Automatized Density-Functional Tight-Binding Parametrizations: 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.