For GGAs, both BLYP-DCACP and revPBE-D3 functionals have a diffusion coefficient and relaxation times very close to the experiment, which is also true for the diffusion modelled by the B97M-rV meta-GGA. In contrast to the statement that the selfinteraction error slows down the dynamics of liquid water, we have found that the M06-L, revM06-L and M11-L semilocal functionals exhibit a complete opposite trend, generally leading to faster dynamics. This is obviously due to their distortion of the hydrogen bonding network (Fig. ) and incorrect structuring (Fig. ). The diffusion coefficients predicted by MN12-L and MN15-L functionals appear to be in good agreement with experimental values (Fig. ), but this is fortuitously caused by an error compensation between the lack of hydrogen bonds (Fig. ) and their overly strong (incorrect) structure (Fig. ). Their rotational dynamics is indeed significantly faster than observed experimentally (Fig. ).