Estimation of bulk liquid properties from Monte Carlo simulations of Lennard-Jones clusters.

In a pioneering study, Lee et al. demonstrated how free energies of Lennard-Jones LJ clusters could be determined from Monte Carlo MC simulations. Subsequently, Garcia and Torroja compared the simulation results with both classical nucleation theory and experimental values for argon nucleation. Since then, there have been many such comparisons as well as simulations to determine the properties of the bulk LJ fluid. Recently, Merikanto et al. showed that MC simulations for LJ and water cluster free energies agree with classical theory predictions provided a size-independent correction factor is included in the work of cluster formation and that there is a connection between the properties of small clusters and the lower order virial coefficients. They used a cluster defined by the Stillinger criterion all atoms within a specified distance Rs of at least one other cluster atom rather than the center of mass definition used by Lee et al. Here, we report results for center of mass clusters at various temperatures and show that they can be used to estimate certain bulk properties of the LJ fluid. We consider a cluster containing i atoms referred to as an i cluster interacting by the full i.e., not truncated LJ potential, u r =4 /r 12− /r 6 . Dimensionless quantities, denoted by an “ ,” are scaled by the appropriate combinations of and . We define an i cluster as any arrangement of i monomers within a specified distance Ri of their center of mass and took Ri= 15i 3 /4 1/3. The partition function of an i cluster is written as V 3 i−1 qi, where is the de Broglie wavelength and V is the container volume. The scaled partition function qi can be determined from,