Extended (n/v)-Stillinger cluster for use in the theory of homogeneous nucleation

In this paper we develop a theory for an extended version of the (n/v)-Stillinger cluster that has been used in nucleation theory, where n means the number of particles constituting the cluster characterized by the volume v. The "extended cluster" incorporates some of the surrounding supersaturated vapor. This cluster, although requiring more extensive simulation than the original (n/v)-Stillinger cluster, is almost devoid of approximation. It maintains the non-ad-hoc nature of the original (n/v)-Stillinger cluster implicitly. The theory of the cluster is also applicable to clusters which avoid redundancy by some other means than the so-called "connectivity requirement." Simulation of the extended cluster is now being implemented and will be used in the theory of the homogeneous nucleation rate.