Theoretical Studies of Water by Climbing Jacob’s Ladder with Deep Learning*

Climbing up the so-called Jacob’s ladder within density functional theory is essential in order to accurately predict the properties of water. We use the Deep Potential (DP) model, a deep learning based potential energy model, to generate molecular dynamics trajectories with the accuracy of the fourth rung of Jacob's ladder of density functional, i.e., the SCAN meta-GGA functional mixed with a fraction of exact exchange (SCAN0). We further develop a deep learning methodology to characterize electronic properties of liquid water based on maximally localized Wannier functions. Due to the mitigation of self-interaction error and the ability to deal with large systems within the DP model, we observe systematically improved electronic, structural, and dynamical properties of liquid water. The excellent performance here leads to a new scheme in predicting water as well as aqueous solutions accurately.