Quantum-mechanical exploration of the phase diagram of water

The set of known stable phases of water may not be complete, and some of the phase boundaries between them are fuzzy. Starting from liquid water and a comprehensive set of 50 ice structures, we compute the phase diagram at three hybrid density-functional-theory levels of approximation, accounting for thermal and nuclear fluctuations as well as proton disorder. Such calculations are only made tractable because we combine machine-learning methods and advanced free-energy techniques. The computed phase diagram is in qualitative agreement with experiment, particularly at pressures less than or similar to 8000 bar, and the discrepancy in chemical potential is comparable with the subtle uncertainties introduced by proton disorder and the spread between the three hybrid functionals. None of the hypothetical ice phases considered is thermodynamically stable in our calculations, suggesting the completeness of the experimental water phase diagram in the region considered. Our work demonstrates the feasibility of predicting the phase diagram of a polymorphic system from first principles and provides a thermodynamic way of testing the limits of quantum-mechanical calculations. Complex interatomic interactions and diverse structures make computing the phase diagram of water very challenging. Here, a combination of machine learning and advanced free-energy methods at three levels of hybrid DFT enables the prediction of the phase diagram in close agreement with experiment.

Automated summary

By combining machine learning methods and advanced free-energy techniques, this study successfully predicts and calculates the phase diagram of water at three levels of hybrid density-functional theory, showing good agreement with experimental results, especially at pressures below 8000 bar. The research demonstrates the completeness of the experimental water phase diagram in the region considered, provides a feasibility of predicting a polymorphic system's phase diagram from first principles, and tests the limits of quantum-mechanical calculations through a thermodynamic approach.