A high-dimensional neural network potential for Co₃O₄

The Co₃O₄spinel is an important material in oxidation catalysis. Its properties under catalytic conditions, i.e. at finite temperatures, can be studied by molecular dynamics simulations, which critically depend on an accurate description of the atomic interactions. Due to the high complexity of Co₃O₄, which is related to the presence of multiple oxidation states of the cobalt ions, to date<i>ab initio</i>methods have been essentially the only way to reliably capture the underlying potential energy surface, while more efficient atomistic potentials are very challenging to construct. Consequently, the accessible length and time scales of computer simulations of systems containing Co₃O₄are still severely limited. Rapid advances in the development of modern machine learning potentials (MLPs) trained on electronic structure data now make it possible to bridge this gap. In this work, we employ a high-dimensional neural network potential (HDNNP) to construct a MLP for bulk Co₃O₄spinel based on density functional theory calculations. After a careful validation of the potential, we compute various structural, vibrational, and dynamical properties of the Co₃O₄spinel with a particular focus on its temperature-dependent behavior, including the thermal expansion coefficient.