  Within the framework of Kohn-Sham density functional theory (DFT), the
ability to provide good predictions of water properties by employing a strongly
constrained and appropriately normed (SCAN) functional has been extensively
demonstrated in recent years. Here, we further advance the modeling of water by
building a more accurate model on the fourth rung of Jacob's ladder with the
hybrid functional, SCAN0. In particular, we carry out both classical and
Feynman path-integral molecular dynamics calculations of water with the SCAN0
functional and the isobaric-isothermal ensemble. In order to generate the
equilibrated structure of water, a deep neural network potential is trained
from the atomic potential energy surface based on ab initio data obtained from
SCAN0 DFT calculations. For the electronic properties of water, a separate deep
neural network potential is trained using the Deep Wannier method based on the
maximally localized Wannier functions of the equilibrated trajectory at the
SCAN0 level. The structural, dynamic, and electric properties of water were
analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion
coefficients, and dielectric constants of water, in the electronic ground
state, are computed using a large simulation box and long simulation time. For
the properties involving electronic excitations, we apply the GW approximation
within many-body perturbation theory to calculate the quasiparticle density of
states and bandgap of water. Compared to the SCAN functional, mixing exact
exchange mitigates the self-interaction error in the meta-generalized-gradient
approximation and further softens liquid water towards the experimental
direction. For most of the water properties, the SCAN0 functional shows a
systematic improvement over the SCAN functional.
