Critical assessment of machine-learned repulsive potentials for the Density Functional based Tight-Binding method: a case study for pure silicon

We investigate the feasability of improving the semi-empirical density functional based tight-binding method (DFTB) through a general and transferable many-body repulsive potential for pure silicon using a common machine-learning framework. Atomic environments using atom centered symmetry functions fed into flexible high-dimensional neural-networks allow to overcome the limited pair potentials used until now, with the ability to train simultaneously on a large variety of systems. We achieve an improvement on bulk systems, with good performance on energetic, vibrational and structural properties. Contrarily, there are difficulties for clusters due to surface effects. To deepen the discussion, we also put these results into perspective with two fully machine-learned numerical potentials for silicon from the literature. This allows us to identify both the transferability of such approaches together with the impact of narrowing the role of machine-learning models to reproduce only a part of the total energy.