Water is one of the most abundant substance on the planet, however its thermodynamic and dynamic properties are away from being fully understood. Unlike other liquids, its specific volume at ambient pressure increases when cooled below T = 4oC. Besides, the isothermal compressibility, κT and the specific heat at constant pressure, CP , have a minimum at T = Tmin. For temperatures below Tmin, κT and CP increase with temperature decrease and above Tmin, κT and CP increase with temperature increase.

In the last years the interest the supercooled region of the pressure temperature phase diagram has increased. In this region water is forced to be in liquid state due to fast freezing of the system. Different from normal liquids, the self diffusion, D, of the supercooled water increases with the compression up to maximum value Dmax(T) at p = pDmax. Beyond this maximum value, for higher pressures, the ”normal” behaviors is restored, and diffusion decreases with pressure. This results are supported by numerical simulation using the SPC/E water model where the supercooled region is easily accessed.

In this talk we present a lattice model in which the directionality present in the hydrogen bonds of water is introduced. This model is capable to reproduce qualitatively the density and diffusion anomalies observed in liquid water. In addition it provides a new scenario for the liquid-liquid phase transition proposed for liquid water.