Statistical mechanics of nucleation: Incorporating translational and rotational free energy into thermodynamics of a microdroplet

Motivated by the original Lothe-Pound prescription, we derive a formula for the replacement partition function that is suitable for vapor to liquid phase nucleation in terms of the classical phase integral. The resulting expression was evaluated for truncated and shifted Lennard-Jones fluids by means of computer simulation. The corresponding Lothe-Pound correction factor, which is to multiply the classical expression for the nucleation rate, decreases significantly with increasing temperature and decreasing cluster size, and is in the range of ${10}^9\text{–}{10}^{13}$ for the temperatures and the cluster sizes we studied. This is somewhat smaller than the original estimate of ${10}^{17}$ by Lothe and Pound.