Equation of State, Thermal Expansion Coefficient, and Isothermal Compressibility for Ices Ih, II, III, V, and VI, as Obtained from Computer Simulation^†

A relatively simple equation of state is proposed for several forms of ice, whose parameters have been fitted to the results of extensive computer simulations using the TIP4P/Ice and TIP4P/2005 models of water. Comparison with available experimental data for ice Ih shows that both models reproduce the experimental density and isothermal compressibility to good accuracy over the entire range of thermodynamic stability except at low temperatures. The predictions for the thermal expansion coefficient are slightly worse but still reasonable. Results obtained with the TIP4P/2005 model are slightly better than those obtained with the TIP4P/Ice model. At temperatures below 150 K, the predictions of both models deviate significantly from experiment. As expected, at low temperatures, quantum effects become increasingly important, and classical simulations are unable to accurately describe the properties of ices. In fact, neither the heat capacity nor the thermal expansion coefficient go to zero at zero temperature (as they should be according to the third law of thermodynamics). Predicted compressibilites are however reliable even up to 0 K. Finally, the relative energies of the ices at 0 K have also been estimated and compared with the experiments.