Size and quality of quantum mechanical data-set for training Neural Network Force Fields for liquid water

Water is arguably the most important substance on Earth, however, there are still some of its properties that are not yet fully understood. Atomistic simulations have shown to be an important tool, providing one way to improve our comprehension of water. In particular, quantum mechanical simulations seem to be the most appropriate choice, since they have, by construction, an accurate predictive potential. Therefore, ab initio molecular dynamics (AIMD) has the accuracy of Density Functional Theory (DFT), and thus is limited to small systems and relatively short simulation time. In this scenario, Neural Network Force Fields (NNFF) have an important role, since it provides a way to circumvent these caveats. In this work we investigate NNFF designed at the level of DFT to describe liquid water, focusing on the size and quality of the training data-set considered. We show that structural properties are less dependent on the size of the training data-set compared to dynamical ones (such as the diffusion coefficient), and a good sampling (selecting data reference for training process) can lead to a small sample with good precision.