Quantum effects in H-bond symmetrization and in thermodynamic properties of high pressure ice

We investigate the structural and thermodynamic properties of high-pressure ice by incorporating quantum anharmonicity at a nonperturbative level. Quantum fluctuations reduce the critical pressure of the phase transition between phase VIII (with asymmetric H bonds) and phase X (with symmetric H bonds) by 65 GPa from its classical value of 116 GPa at 0 K. Moreover, quantum effects make it temperature independent over a wide temperature range (0-300 K), in agreement with experimental estimates obtained through vibrational spectroscopy and in striking contrast to the strong temperature dependence found in the classical approximation. The equation of state shows fingerprints of the transition in accordance with experimental evidence. Additionally, we demonstrate that, within our approach, proton disorder in phase VII has a negligible impact on the occurrence of phase X. Finally, we reproduce with high accuracy the 10-GPa isotope shift caused by the hydrogen-to-deuterium substitution.