Comparison of Monte Carlo simulation methods for the calculation of the nucleation barrier of argon

We compare two molecular Monte Carlo simulation methods, the discrete summation method and the growth/decay method, which calculate the vapor-liquid nucleation free energy barrier by simulating isolated clusters of fixed size without the surrounding vapor. The methods are applied to calculations of nucleation barriers of Lennard–Jones argon at 60 K and 80 K. Both of these methods are computationally efficient, as only isolated clusters without the surrounding vapor are simulated, and the methods can be applied with any given cluster definition. They give equivalent results to other methods where the vapor phase is also included. The discrete summation method is based on the calculation of the difference in free energies between two systems containing an n-cluster and an (n − 1)-cluster plus one non-interacting (free) molecule. We show that the configurational space is not equivalent in the two systems. Hence, there has to be an additional term in the free energy calculation that accounts for several kT in magnitude. In contrast to previous studies we also show that it is not correct to prevent the overlap of the non-interacting molecule and another molecule by a zero or an arbitrarily small repulsive potential, but with a small excluded space around the free molecule.