Vapor–liquid equilibrium of water with the machine-learned ML-BOP model

Over the past few decades, many classical force-fields have been developed to model water. However, capturing the properties of water across its solid, liquid, and vapor phases remains a challenge. The coarse-grained machine-learned bond order potential (ML-BOP) model accurately reproduces the structural and thermodynamic properties of liquid water in both stable and supercooled states, as well as the thermodynamics of ice-water equilibrium and polyamorphism, comparable to all-atom models TIP4P/2005 and TIP4P/Ice, but with nearly 100 times lower computational cost. In this study, we evaluate the ability of ML-BOP to describe vapor-liquid coexistence properties of water, despite its development excluding any such training data. We find that ML-BOP underestimates the surface tension at ambient conditions and its slope of temperature dependence, a trend common among coarse-grained models lacking explicit hydrogen atoms. Nevertheless, ML-BOP accurately reproduces vapor-liquid coexistence densities and predicts the critical point (Tc = 653.27 ± 3.0 K and ρc = 0.328 ± 0.004 g cm-3) in excellent agreement with experiment and comparable to TIP4P/2005. ML-BOP outperforms the widely used mW model in reproducing vapor-liquid coexistence properties of water. ML-BOP also captures the high-temperature inflection in the surface tension curve and the specific surface entropy anomaly, predicting the temperature of maximum surface entropy closer to experiment than TIP4P/2005. Furthermore, we investigate the Guldberg and Eötvös empirical relationships in ML-BOP, demonstrating quantitative predictions of boiling-critical temperature scaling and enthalpy of vaporization. Overall, ML-BOP offers a promising balance of accuracy and efficiency, making it the most capable coarse-grained water model currently available for simulating water across various regimes.