The phase diagram of water, while extensively studied, remains incompletely understood, with uncertainties in some phase boundaries. This research computes the water phase diagram at three hybrid density-functional-theory (DFT) levels, incorporating thermal and nuclear fluctuations and proton disorder. Machine learning methods and advanced free-energy techniques enabled these computationally demanding calculations. The resulting phase diagram shows qualitative agreement with experimental data, particularly at pressures up to 8000 bar. The study suggests the completeness of the experimental phase diagram within the studied pressure range, as no hypothetical ice phases were found to be thermodynamically stable. This work demonstrates the feasibility of first-principles phase diagram prediction for polymorphic systems and provides a thermodynamic benchmark for quantum-mechanical calculations.

Aleks Reinhardt, Bingqing Cheng