As explained earlier, NQEs tend to strengthen H-bonds and slow down the dynamical properties. This was seen in all PIMD calculations with BLYP-D3 180 , revPBE-D3 200 , SCAN , B97M-rV 114 , revPBE0-D3 , and RPA/ML 162 . The diffusion coefficients, in the absence of NQEs, should therefore be seen as overestimated, and relaxation times as underestimated. The diffusion with GGAs would therefore become even slower with NQEs. From the available data, hybrid and hybrid meta-GGA functionals generally give faster diffusion than GGAs, which indicates that the exact exchange is a key ingredient towards achieving accuracy for the dynamics, in the same way as for the structural properties. The revPBE0-D3 functional can be considered as the most effective hybrid in this regard. Other functionals like PBE0 or SCAN0 are likely to remain too slow even upon inclusion of NQEs.