Estimation of solid-liquid coexistence curve for coarse-grained water models through reliable free energy method

The anomalies properties of water have been interpreted theoretically using several all-atom and coarse-grained water models. Here we use a robust and traditional free energy approach to develop the solid-liquid coexistence curve for water using coarse-grained monatomic mW and machine-learned bond order potential (ML-BOP) water models. We employ the pseudo-supercritical thermodynamic path in combining multiple histogram reweighting (MHR) and Gibbs-Duhem integration. The ML-BOP model has a broad density-temperature hysteresis loop and shows lower maximum and minimum densities as compared to the mW model. The computed excess Helmholtz free energy and the Gibbs free energy at the approximate melting temperature are higher for the ML-BOP model in comparison with the mW model. The pressure dependence fusion curve for both water models aligns with the literature. This analysis indicates that the free energy method accurately captures the solid-liquid transformation and the thermodynamic melting point of water.