Liquid water can be cooled below 0 degrees Celsius without immediately freezing because the formation of ice crystals requires nucleation. This made me think about the reverse situation: can ice nucleation occur above 0 degrees Celsius? It seems that there should be a statistical chance of water molecules aligning to create an ice crystal (even if that crystal is thermodynamically unstable and quickly returns to the liquid state). Is there a numerical way of describing the odds of nucleation sites forming at any given temperature?
Yes, there are several numerical (computer simulation) ways to quantify the odds of formation of nucleation sites. One of them is a modern molecular sampling technique called Metadynamics (For eg: See https://doi.org/10.1107/S2052252514027626). Here, the free energy of the nucleation process can be estimated along a strategically chosen crystallization pathway or "collective variable". The likelihood of crossing barriers along this free energy curve can be used to estimate the frequency of nucleation events. I believe the nucleation barrier would be much greater than thermal energy (kT) at 1 bar and T >273 K leading to very large barrier crossing time.. (that is never..)