There is a nice Nature paper from 1998 Tunnelling and zero-point motion in high pressure ice by Benoit, Marx, and Parrinello. The figure below is of particular interest to me. It shows the OH bond length as a function of the O-O distance (bottom scale) in the crystal. The latter can be tuned continuously with pressure (top scale).
The non-solid points are from a classical calculation at two different temperatures. The solid points are when one takes into account the full quantum dynamics of the protons, thus taking into account the effects of tunneling and zero point motion.
The proton becomes equidistant between the two oxygen atoms (solid line) for pressures larger than about 70 kbar, consistent with experiment.
The figure above is similar to a figure in my recent paper about hydrogen bonding, and is consistent with comments I made there about the importance of zero-point motion.
I thank Christiaan Bekker [who is doing an undergraduate research project with me] for bringing the paper to my attention.
In liquid water, from the theoretical viewpoint, the zero point energy and the tunneling was reported to be significant to the structure and dynamics for liquid water, however it is difficult for think visually about their roles according experiments.
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