Quasi-harmonic approximation of thermodynamic properties of ice Ih, II, and III

Several thermodynamic properties of ice Ih, II, and III are studied by a quasi-harmonic approximation and compared to results of quantum path integral and classical simulations. This approximation allows to obtain thermodynamic information at a fraction of the computational cost of standard simulation methods, and at the same time permits studying quantum effects related to zero-point vibrations of the atoms. Specifically, we have studied the crystal volume, bulk modulus, kinetic energy, enthalpy, and heat capacity of the three ice phases as a function of temperature and pressure. The flexible q-TIP4P/F model of water was employed for this study, although the results concerning the capability of the quasi-harmonic approximation are expected to be valid independently of the employed water model. The quasi-harmonic approximation reproduces with reasonable accuracy the results of quantum and classical simulations showing an improved agreement at low temperatures (T< 100 K). This agreement does not deteriorate as a function of pressure as long as it is not too close to the limit of mechanical stability of the ice phases.