Energies as a function of time. All the results from SQW are expressed by the solid lines, while the results from FCW are shown by the dashed lines. of SQW fluctuates not only in subpicoseconds but also in tens of picoseconds, while of FCW is well conserved (the upper figure). The newly introduced degrees of freedom behave just like an energy reservoir. The intramolecular energy is smaller in SQW than in FCW due to the additional energy distribution to the semiquantum degrees of freedom (the upper-middle figure), while the intermolecular potential energy is higher due to the poorer liquid structure (the lower-middle figure). The kinetic energy exhibits no significant difference between SQW and FCW except that the fluctuation is slightly larger in SQW (the lower figure).
New energies introduced by SQTDH. is complementary to in SQW. mainly consists of . and fluctuate similarly and generate the multiscale modulation of .
RDFs for oxygen-oxygen atom pairs (the upper figure), for oxygen-hydrogen atom pairs (the upper-middle figure), and for hydrogen-hydrogen atom pairs (the lower-middle figure). The solid and dashed lines express the semiquantum and classical results, respectively. The liquid becomes less structured and the hydrogen bonds are weakened in SQW. The lower figure shows the difference between the semiquantum and classical 2D distribution functions of the radial distance for oxygen-oxygen atom pairs and the dipolar angle, Eq. (26). The structure rearrangement in SQW is quite systematic.
Time-dependent self-diffusion. The solid and dashed lines denote the semiquantum and classical results, respectively. The converged values corresponds to the diffusion coefficients. The mobility of each water molecule increases in SQW.
for SQW and FCW shown by the solid and dashed lines, respectively. The split two bending peaks are merged into the one peak in SQW (the upper-middle figure). The semiquantum OH stretching modes are redshifted reflecting the softened poor structure due to the semiquantum hydrogen atoms and the potential anharmonicity picked up by the ZPE (the lower-middle figure). The significant peak originated from the quantum effect appears around (the lower figure).
Power spectra of the OH stretching mode (the upper figure) and of the rotational motion of a water molecule (the upper-middle and the lower-middle figures). The solid and dashed lines express the semiquantum and classical results, respectively. The lower-middle figure demonstrates that the rotational motion of a water molecule is coupled with the symmetric OH stretching mode. The power spectrum of the time-dependent WP width in the lowest figure demonstrates that the vibrational motion of the WP width has the frequency of . The energy exchange between the WP width dynamics and the coupling of the symmetric OH stretching mode and the rotational motion induces the significant peak around .
Schematic illustration of the free energies in SQW and FCW. Our simulation results indicated that the free energy landscape should be smoothed in SQW compared to the classical one. The representative trajectories along a reaction coordinate are also shown for reference. A state in SQW moves more smoothly along the reaction coordinate due to the smoothed free energy landscape.
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