The microscopic structure of ice poses a long-standing challenge to theory^1,2,3. Because of their low mass, the protons in the hydrogen bonds that define the structures of crystalline ice are susceptible to quantum-mechanical effects such as tunnelling¹,^4,5,6,7,8. High pressure provides a means of controlling the length of the hydrogen bonds in order to investigate such effects. In particular, Holzapfel predicted 26 years ago that, under pressure, hydrogen bonds might be transformed from the highly asymmetric O–H···O configuration to a symmetric state in which the proton lies midway between the two oxygens⁹, leading to a non-molecular symmetric phase of ice, now denoted as ice ‘X’. The existence of this phase has been inferred from spectroscopy^{10,11,12,13,14}, but has still not been observed directly. Here we investigate the role of quantum effects in proton ordering and hydrogen-bond symmetrization within ice at high pressure by using a simulation technique that treats both electrons and nuclei quantum-mechanically^15,16,17. We find that the proton-ordered structure at low pressure, with asymmetric hydrogen bonds (ice VIII), transforms on increasing pressure to a proton-disordered asymmetric phase (ice VII) owing to translational proton tunnelling. On further compression, the zero-point fluctuations lead to strongly delocalized protons and hydrogen-bond symmetrization, even though the underlying character of the proton-transfer potential remains a double well. Only at still higher pressures does the double-well potential become transformed into a single well, whereupon the protons again become increasingly localized.

Based on ab initio constant pressure molecular dynamics simulation, we predict a new phase transition in ice from ice X to a new phase (ice XI) at $\sim 3\mathrm{Mbar}$ and room temperature. Ice XI preserves the symmetric hydrogen bond and is a wide gap insulator up to and beyond 7 Mbar. This new phase is stable up to 2000 K at 4 Mbar, where the system shows large protonic diffusion.

Hydrogen bonds in ${\mathrm{H}}_2\mathrm{O}$ ice change dramatically upon compression. Thereby a hydrogen-bonded molecular crystal, ice VII, is transformed to an atomic crystal, ice X. Car-Parrinello simulations reproduce the features of the x-ray diffraction spectra up to about 170 GPa but allow for analysis in real space. Starting from molecular ice VII with static orientational disorder, dynamical translational disordering occurs first via creation of ionic defects, which results in a systematic violation of the ice rules. As a second step, the transformation to an atomic solid and thus hydrogen-bond centering occurs around 110 GPa at 300 K and no novel phase is found up to at least 170 GPa.

We study a calcium aluminosilicate glass of composition (SiO2)0.67–(Al2O3)0.12–(CaO)0.21 by means of molecular-dynamics simulations, using a potential made of two-body and three-body interactions. In order to prepare small samples that can subsequently be studied by first principles, the finite size effects on the liquid dynamics and on the glass structural properties are investigated. We find that finite size effects affect the Si–O–Si and Si–O–Al angular distributions, the first peaks of the Si–O, Al–O, and Ca–O pair correlation functions, the Ca coordination, and the oxygen atoms’ environment in the smallest system (100 atoms). We give evidence that these finite size effects can be directly attributed to the use of three-body interactions.