The self-diffusion coefficient, D, was also calculated to investigate the dynamical property of liquid water at ambient condition. The results are listed in Table . With classical MD, D is predicted as 0.185 ± 0.004 Å 2 /ps which is lower than the experimental value of 0.230 Å 2 /ps. With PIMD, a higher diffusion coefficient (0.233 ± 0.027) is observed and agrees better with experiment. The significant change of diffusion coefficients in PIMD simulation is due to nuclear quantum effects. As indicated in Ref. 60, there exist two competing nuclear quantum effects in liquid water, intramolecular and intermolecular quantum effects. The former weakens the covalent bond and induces a larger molecular dipole moment. The later weakens the hydrogen bond and results in a less structured H-bond network. From our work with q-AQUA-pol potential, the latter (intermolecular) effect dominates over the former one (intramolecular ZPE). Liquid water has a destabilized hydrogen-bonding network and larger diffusion coefficients. This observation also agrees with our previous NVT simulation with the original q-AQUA potential.