Learning to Use the Force: Fitting Repulsive Potentials in Density-Functional Tight-Binding with Gaussian Process Regression

The Density-Functional Tight Binding (DFTB) method is a popular semiempirical approximation to Density Functional Theory (DFT). In many cases, DFTB can provide comparable accuracy to DFT at a fraction of the cost, enabling simulations on length- and time-scales that are unfeasible with first principles DFT. At the same time (and in contrast to empirical interatomic potentials and force-fields), DFTB still offers direct access to electronic properties such as the band-structure. These advantages come at the cost of introducing empirical parameters to the method, leading to a reduced transferability compared to true first-principle approaches. Consequently, it would be very useful if the parameter-sets could be routinely adjusted for a given project. While fairly robust and transferable parameterization workflows exist for the electronic structure part of DFTB, the so-called repulsive potential Vrep poses a major challenge. In this paper we propose a machine-learning (ML) approach to fitting Vrep, using Gaussian Process Regression (GPR). The use of GPR circumvents the need for non-linear or global parameter optimization, while at the same time offering arbitrary flexibility in terms of the functional form. We also show that the proposed method can be applied to multiple elements at once, by fitting repulsive potentials for organic molecules containing carbon, hydrogen and oxygen. Overall, the new approach removes focus from the choice of functional form and parameterization procedure, in favour of a data-driven philosophy.