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Gibbs free energy of ij-cluster formation ΔGij is obtained via the relation nij=Ne-ΔGij /kBT, where N is the number of molecules in the system, T is temperature, and kB is the Boltzmann constant. The saddle point on the free energy surface ΔGij versus i and j provides a measure of the activation barrier to nucleation ΔG *. A statistical mechanical formula of ΔGij is derived based on the physical-cluster theory of nucleation, and from which a molecular interpretation of ΔGij is given. We applied the Monte Carlo method to investigate the mutual enhancement of nucleation in a binary model system which is composed of spherical Lennard-Jones monomers and rigid Lennard-Jones dimers consisting of a monophilic atom and a monophobic atom. This model system bears some qualitative similarity to the partially miscible water/higher alcohol systems in which the mutual enhancement of nucleation has been observed experimentally. The simulation confirms the existence of mutual enhancement of nucleation in monomer-rich vapors, as originally predicted by Napari and Laaksonen from a density-functional theory [Napari and Laaksonen, Phys. Rev. Lett. 84, 2184 (2000)]. The nucleation enhancement is also seen in dimer-rich vapors at high supersaturations.