Of course there is an equation to compute the nucleation energy barrier. The general formula involves the calculation of the saddle point for the free energy required to form a cluster. However, the most widely used is that coming from Classical Nucleation Theory which is simple and effective. A very nice explanation of such a theory can be found in the book: "Nucleation: Basic Theory with Applications" by Dimo Kashchiev (see chapter 3 concerning work of cluster formation). There is a subtle problem with the CNT formula since, the equation depends on a physical quantity which has to be (in principle) measured experimentally, that is the surface tension (in the case of 3D nucleation) or the line tension (in the case of 2D nucleation). In case you can measure nucleation rates, maybe you can get a good estimation of such a quantity and, hence, of the nucleation barrier. Otherwise, I think this formula will be useless.
I am trying to Model the freezing of PCM under large supercooling conditions. However, finding empirical values of the surface energies for those materials is still a difficult process.