From Clusters to Bulk: Searching for the Stability Crossover between I_h and I_c via AVBMC Simulations

Among the more than 20 known crystalline phases of ice, hexagonal (I_h) and cubic (I_c) ice are the dominant polymorphs at ambient pressure. Their relative thermodynamic stability and competition have been the subject of extensive investigation. This work presents a systematic study of the free energy landscape spanning from small clusters to the bulk for both polymorphs using a lattice-based aggregation-volume-bias Monte Carlo (LB-AVBMC) approach. Simulations were performed with the TIP4P/2005 water model at 300 K. Although this temperature exceeds the model's melting point, the lattice constraint stabilizes crystalline clusters even at small sizes. It was found that the relative stability of I_h and I_c exhibits nontrivial size dependence, with their free energies interweaving in the small-cluster regime. Nucleation free energies computed for large clusters were analyzed within the Tolman-corrected classical nucleation theory framework to extrapolate bulk chemical potentials. While I_h is more stable than I_c, both crystalline phases remain thermodynamically metastable relative to the liquid phase at 300 K. By combining bulk chemical potentials with enthalpy data obtained from additional NpT simulations, the melting temperature is estimated to be around 250 K, in good agreement with previous studies. The enthalpy difference between I_h and I_c is approximately 20 J/mol at 300 K and decreases with decreasing temperature.