Three-body tight-binding for the periodic table

Over the past two decades, density functional theory calculations (DFT) have become the workhorse method for electronic structure calculations; however, there are always limitations in terms of the number of calculations or sizes of unit-cells. Tight-binding calculations fit to DFT are a way to bridge this gap, but appropriate models are not always available, especially for materials design applications where many materials may be studied.  In this work, we introduce a versatile tight-binding model that builds the Hamiltonian from both the typical two-body interactions between atoms plus three-body interactions. The three-body terms allow the local neighborhood of a pair of atoms to modify their interaction. These terms allow the model to fit a wide range of structures and stoichiometries without loss of accuracy. We fit this model to a database of over 800,000 DFT calculations of elemental and binary systems, allowing users of the model to immediately begin calculations. To ensure the fitting produces accurate predictions out-of-sample, we use the model to relax new structures from random starting structures, and then compare the energies to new DFT calculations. These new calculations are added to the fitting until the performance improves.