The phase diagram of ice is studied by a quasi-harmonic approximation. The
free energy of all experimentally known ice phases has been calculated with the
flexible q-TIP4P/F model of water. The only exception is the high pressure ice
X, in which the presence of symmetric O-H-O bonds prevents its modeling with
this empirical interatomic potential. The simplicity of our approach allows us
to study ice phases at state points of the T-P plane that have been omitted in
previous simulations using free energy methods based on thermodynamic
integration. The effect in the phase diagram of averaging the proton disorder
that appears in several ice phases has been studied. It is found particularly
relevant for ice III, at least for cell sizes typically used in phase
coexistence simulations. New insight into the capability of the employed water
model to describe the coexistence of ice phases is presented. We find that the
H-ordered ices IX and XIV, as well as the H-disordered ice XII, are
particularly stable for this water model. This fact disagrees with experimental
data. The unexpected large stability of ice IX is a property related to the
TIP4P-character of the water model. Only after omission of these three stable
ice phases, the calculated phase diagram becomes in reasonable qualitative
agreement to the experimental one in the T-P region corresponding to ice Ih,
II, III, V, and VI. The calculation of the phase diagram in the quantum and
classical limits shows that the most important quantum effect is the
stabilization of ice II due to its lower zero-point energy when compared to
that one of ices Ih, III, and V.Comment: 13 pages, 8 figures, 5 table
