  We improve a lattice model of water introduced by Sastry, Debenedetti,
Sciortino, and Stanley to give insight on experimental thermodynamic anomalies
in supercooled phase, taking into account the correlations between
intra-molecular orientational degrees of freedom. The original Sastry et al.
model including energetic, entropic and volumic effect of the
orientation-dependent hydrogen bonds (HBs), captures qualitatively the
experimental water behavior, but it ignores the geometrical correlation between
HBs. Our mean-field calculation shows that adding these correlations gives a
more water-like phase diagram than previously shown, with the appearance of a
solid phase and first-order liquid-solid and gas-solid phase transitions.
Further investigation is necessary to be able to use this model to characterize
the thermodynamic properties of the supercooled region.
