How can the Anomalous Expansion of Water from 4$^\circ$C to 0$^\circ$C be explained with reference to subatomic particles?
I don't think there's a good general explanation of this; the best I can do is give a few hand waving arguments.
If you look at hydrogen sulphide, which the analogue of water moving one row down in the periodic table, you'll find it does shrink when it freezes, just like most other liquids. So the difference between the H$_2$S and H$_2$O molecules must be responsible for the anomalous behaviour of water.
The most obvious difference between the two molecules is the the H-O bond is highly polar and has a strong electric dipole associated with it. This means it interacts strongly with other H-O bonds; the interaction is known as hydrogen bonding. Hydrogen bonds are highly directional, as you'd expect for an electric dipole, so the water molecules can be fitted together in ice any old how. They adopt well defined positions relative to each other, and the directionality of the bonds forces the water molecules into a relatively low density arrangement.
It's interesting to note that the high pressure forms of ice are generally denser than water. Presumably at high pressure the reduction in energy by the denser arrangement outweighs the reduction in the strength of the hydrogen bonds.