Machine learning universal empirical pseudopotentials for density functional theory calculations

Traditional empirical pseudopotentials allow for efficient calculations of electronic band structures. Such potentials, however, are not so versatile enough to reproduce wave functions and related quantities, and their transferability to different environments is limited. Here, we introduce a method to generate universal empirical pseudopotentials for density functional theory calculations with machine learning. The transferability of empirical pseudopotentials could be achieved by using both atom-density representations and machine-learning procedures. We demonstrate that these empirical pseudopotentials produce not only band structures, but also wave functions, total energies, forces, and other physical quantities without the self-consistent conditions. We apply the method to a few examples such as Si, Ge, and SiO₂, finding excellent agreements with density functional theory results.