We have investigated various anomalous properties of water such as the divergent character of the thermodynamic functions and liquid-liquid transition in supercooled water, the phase behaviors of water and new ices in nanoscale confinement, the thermodynamic stability of clathrate hydrates over a wide range of pressure, and anomalous thermodynamic and structural properties of ices. These are studied by some theoretical calculations and Monte Carlo/molecular dynamics computer simulations. It is demonstrated that the potential energy surface and the connectivity of supercooled water are keys to understand why liquid-liquid transition can take place in deeply supercooled water. A tetrahedral coordination of water is preserved even in extreme confinements, forming tubule ice and bilayer crystalline (or amorphous) ice, although the heavy stress makes the bond angles and lengths different from the ideal values. Thermodynamic stability of clathrate hydrates, including double occupancy, is more accurately predicted by considering the host-guest coupling and other factors. The negative thermal expansivity and the change in slope of the Debye-Waller factor of ice are explained with a simple model of water.
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