  Among all fluids, water has always been of special concern for scientists
from a broad variety of research fields due to its rich behavior. In
particular, some questions remain unanswered nowadays concerning the
temperature dependence of bulk and interfacial transport properties of
supercooled and liquid water, e.g. regarding the fundamentals of the violation
of the Stokes-Einstein relation in the supercooled regime or the subtle
relation between structure and dynamical properties. Here we investigated the
temperature dependence of the bulk transport properties from ab initio
molecular dynamics based on density functional theory, down to the supercooled
regime. We determined from a selection of functionals, that SCAN better
describes the experimental viscosity and self-diffusion coefficient, although
we found disagreements at the lowest temperatures. For a limited set of
temperatures, we also explored the role of nuclear quantum effects on water
dynamics using ab initio molecular dynamics that has been accelerated via a
recently introduced machine learning approach. We then investigated the
molecular mechanisms underlying the different functionals performance and
assessed the validity of the Stokes-Einstein relation. We also explored the
connection between structural properties and the transport coefficients,
verifying the validity of the excess entropy scaling relations for all the
functionals. These results pave the way to predict the transport coefficients
from the radial distribution function, helping to develop better functionals.
On this line, they indicate the importance of describing the long-range
features of the radial distribution function.
