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[ This article may be downloaded for personal use only. Any other userequires prior permission of the author and AIP Publishing. This articleappeared in The Journal of Chemical Physics, 157, 024504 (2022) and may befound at: https://doi.org/10.1063/5.0093958 ]  Despite its simple molecular formula, obtaining an accurate in silicodescription of water is far from straightforward. Many of its very peculiarproperties are quite elusive, and in particular obtaining good estimations ofthe diffusion coefficients of the solvated proton and hydroxide at a reasonablecomputational cost has been an unsolved challenge until now. Here I presentextensive results of several unusually long ab initio MD simulations employingdifferent combinations of the Born--Oppenheimer and 2$^\mathrm{nd}$-generationCar--Parrinello MD propagation methods with different ensembles (NVE and NVT)and thermostats, which show that these methods together with the RPBE-D3functional provide a very accurate estimation of the diffusion coefficients ofthe solvated H$_3$O$^+$ and OH$^-$ ions, together with an extremely accuratedescription of several properties of neutral water (such as the structure ofthe liquid and its diffusion and shear viscosity coefficients). In addition, Ishow that the estimations of $D_\mathrm{H_3O^+}$ and $D_\mathrm{OH^-}$ dependdramatically on the simulation length, being necessary to reach timescales inthe order of hundreds of picoseconds to obtain reliable results.

Accurate diffusion coefficients of the excess proton and hydroxide in water via extensive ab initio simulations with different schemes