Using Clustering to Compute Properties of Fluids like boiling, freezing and the critical point

Water has lots of interesting features:

• it is liquid at room temperature,
• it boils at 100 degrees Celsius 
• it forms different ice crystals below zero degrees Celsius
• and ice has less density than the liquid form.

All of these features have their origins in the simple structure of the H2O molecule. So we should be able to predict all of the properties from our knowledge of the molecule. It turns out that this is a very difficult task.

One possible solution is to do a molecular dynamics simulation, but this is computationally very demanding.
An alternative method is to calculate cluster diagrams, which can yield already quite good results with low computational effort. A problem with this method is that the derivation is very demanding and tedious. With Mathematica, all of the steps in the derivation can be visualised and large classes of cluster diagrams can be calculated automatically.
Finally, the theory is applied to argon and compared with observations to demonstrate the performance.