Why does water contract while increasing temperature from 0 to 4 degree C?

Water molecules are composed of one oxygen bound to two hydrogen atoms through a single covalent bond with each. These bonds are not evenly shared; oxygen has more positive charges in its nucleus and is able to exert a stronger pull on the electrons in the bond. Therefore, the electrons spend more of their time closer to the oxygen, which gives the oxygen a partial negative charge. The hydrogens, having less time around the electrons, do not have their single positive charge completely cancelled out, so they have a partial positive charge. We call this type of condition polarity. Water is one of the most polar molecules, and this explains a great deal about its properties.

The reason for the phenomenon observed when water is at 4 and 0 degrees is due both to the nature of this polarity, and to the behavior of molecules in their different phases. Liquids are typically higher in energy than their solid counterparts of the same substance under the same conditions. This means the liquid molecules are moving around more, and therefore will have a lower density. So, it shouldn't surprise us that as water cools, the trend is, on average, for the density to increase.

The polarity of water factors into the cooling as well. When water cools, the decreased motion of the molecules allows the molecules to "lock" themselves into the arrangement that best satisfies their polar charges; oxygens are near hydrogens, and vice versa. Due to the geometric shape of the water molecule, this results in a specific hexagonal crystal shape. These shapes are less dense, on average, than the liquid form of water because they don't have the energy to squeeze themselves into the less-favorable spaces.

When the water reaches 4 degrees, these shapes are beginning to take form, and the water is both increasing in density (as it cools) and decreasing in density (as the crystal shapes form and lock the molecules into a particular arrangement). By the time the water has reached 0 degrees Celsius, the locking effect is complete, and there's actually "wasted" space in the crystal that was once occupied by the slightly more energetic 4 degree water.