Exploring the configuration space of elemental carbon with empirical and machine learned interatomic potentials

We demonstrate how the many-body potential energy landscape of carbon can be explored with the nested sampling algorithm, allowing for the calculation of its pressure-temperature phase diagram. We compare four interatomic potential models: Tersoff, EDIP, GAP-20 and its recently updated version, GAP-20U. Our evaluation is focused on their macroscopic properties, melting transitions, and identifying thermodynamically stable solid structures up to at least 100 GPa. The phase diagrams of the GAP models show good agreement with experimental results. However, we find that the models’ description of graphite includes thermodynamically stable phases with incorrect layer spacing. By adding a suitable selection of structures to the database and re-training the potential, we have derived an improved model — GAP-20U+gr — that suppresses erroneous local minima in the graphitic energy landscape. At extreme high pressure nested sampling identifies two novel stable structures in the GAP-20 model, however, the stability of these is not confirmed by electronic structure calculations, highlighting routes to further extend the applicability of the GAP models.