  Motivated by the very low diffusivity recently found in ab initio simulations
of liquid water, we have studied its dependence with temperature, system size,
and duration of the simulations. We use ab initio molecular dynamics (AIMD),
following the Born-Oppenheimer forces obtained from density-functional theory
(DFT). The linear-scaling capability of our method allows the consideration of
larger system sizes (up to 128 molecules in this study), even if the main
emphasis of this work is in the time scale. We obtain diffusivities that are
substantially lower than the experimental values, in agreement with recent
findings using similar methods. A fairly good agreement with D(T) experiments
is obtained if the simulation temperature is scaled down by ~20%. It is still
an open question whether the deviation is due to the limited accuracy of
present density functionals or to quantum fluctuations, but neither technical
approximations (basis set, localization for linear scaling) nor the system size
(down to 32 molecules) deteriorate the DFT description in an appreciable way.
We find that the need for long equilibration times is consequence of the slow
process of rearranging the H-bond network (at least 20 ps at AIMD's room
temperature). The diffusivity is observed to be very directly linked to network
imperfection. This link does not appear an artefact of the simulations, but a
genuine property of liquid water.
