  [ This article may be downloaded for personal use only. Any other use
requires prior permission of the author and AIP Publishing. This article
appeared in The Journal of Chemical Physics, 157, 024504 (2022) and may be
found at: https://doi.org/10.1063/5.0093958 ]
  Despite its simple molecular formula, obtaining an accurate in silico
description of water is far from straightforward. Many of its very peculiar
properties are quite elusive, and in particular obtaining good estimations of
the diffusion coefficients of the solvated proton and hydroxide at a reasonable
computational cost has been an unsolved challenge until now. Here I present
extensive results of several unusually long ab initio MD simulations employing
different combinations of the Born--Oppenheimer and 2$^\mathrm{nd}$-generation
Car--Parrinello MD propagation methods with different ensembles (NVE and NVT)
and thermostats, which show that these methods together with the RPBE-D3
functional provide a very accurate estimation of the diffusion coefficients of
the solvated H$_3$O$^+$ and OH$^-$ ions, together with an extremely accurate
description of several properties of neutral water (such as the structure of
the liquid and its diffusion and shear viscosity coefficients). In addition, I
show that the estimations of $D_\mathrm{H_3O^+}$ and $D_\mathrm{OH^-}$ depend
dramatically on the simulation length, being necessary to reach timescales in
the order of hundreds of picoseconds to obtain reliable results.
