The static dielectric constant ${ϵ}_0$ and its temperature dependence for liquid water is investigated using neural network quantum molecular dynamics (NNQMD). We compute the exact dielectric constant in canonical ensemble from NNQMD trajectories using fluctuations in macroscopic polarization computed from maximally localized Wannier functions (MLWF). Two deep neural networks are constructed. The first, NNQMD, is trained on QMD configurations for liquid water under a variety of temperature and density conditions to learn potential energy surface and forces and then perform molecular dynamics simulations. The second network, NNMLWF, is trained to predict locations of MLWF of individual molecules using the atomic configurations from NNQMD. Training data for both the neural networks is produced using a highly accurate quantum-mechanical method, DFT-SCAN that yields an excellent description of liquid water. We produce $280\times {10}^6$ configurations of water at 7 temperatures using NNQMD and predict MLWF centers using NNMLWF to compute the polarization fluctuations. The length of trajectories needed for a converged value of the dielectric constant at $0\mathrm{°C}$ is found to be 20 ns ($40\times {10}^6$ configurations with 0.5 fs time step). The computed dielectric constants for 0, 15, 30, 45, 60, 75, and $90°\mathrm{C}$ are in good agreement with experiments. Our scalable scheme to compute dielectric constants with quantum accuracy is also applicable to other polar molecular liquids.

• Received 24 December 2020
• Accepted 30 March 2021
• Corrected 9 July 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.216403