Free energy calculations for a flexible water model

In this work, we consider the problem of calculating the classical free energies of liquids and solids for molecular models with intramolecular flexibility. We show that thermodynamic integration from the fully-interacting solid of interest to a Debye crystal reference state, with anisotropic harmonic interactions derived from the Hessian of the original crystal, provides a straightforward route to calculating the Gibbs free energy of the solid. To calculate the molecular liquid free energy, it is essential to correctly account for contributions from both intermolecular and intramolecular motion; we employ thermodynamic integration to a Lennard-Jones reference fluid, coupled with direct evaluation of the molecular ro-vibrational partition function. These approaches are used to study the low-pressure classical phase diagram of the flexible q-TIP4P/F water model. We find that, while the experimental ice-I/liquid and ice-III/liquid coexistence lines are described reasonably well by this model, the ice-II phase is predicted to be metastable. In light of this finding, we go on to examine how the coupling between intramolecular flexibility and intermolecular interactions influences the computed phase diagram by comparing our results with those of the underlying rigid-body water model.