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

[ 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.