 Then, formula_115, and the cluster size distribution is
which implies an effective free energy landscape formula_117, in agreement with the form proposed by the simple theory.On the other hand, this derivation reveals the significant approximation in assuming spherical clusters with formula_118.In reality, the configuration integral formula_87 contains contributions from the full set of particle coordinates formula_120, thus including deviations from spherical shape as well as cluster degrees of freedom such as translation, vibration, and rotation.