Modeling liquid water by climbing up Jacob's ladder in density functional theory facilitated by deep neural network*

Climbing Jacob's ladder up to the fourth rung is essential in order to build a more accurate model of water within the framework of density functional theory (DFT). Also, ideally due to the light-mass of the protons, quantum effects need to be considered simultaneously via Feynman's path integral technique. In this work, we model the structural and dynamic properties of liquid water by ab inito molecular dynamics (MD) based on the hybrid functional (SCAN0) of the recently developed SCAN meta-GGA functional. Furthermore, in order to carry out larger and longer MD simulations to be able to predict the properties of liquid water with the same accuracy as DFT, we employ Deep Neural Network models based on both DeePMD and Deep Wannier. Specifically, we are able to predict not only thermodynamic properties but also dynamic properties (e.g., the diffusivity), and the electronic response (e.g., dielectric constant and infra spectroscopy). The results indicate that the structural, electronic, and dynamic properties of liquid water are systematically improved due to the mitigated self-interaction error and inclusion of nuclear quantum effect in the modeling.