In single-component homogeneous nucleation, the summation expression for the steady-state nucleation rate requires values of the forward rate constants and Gibbs free energies of cluster formation. If atomistic data are available for these quantities, then these could be used instead of CNT. In an atomistic approach, clusters are treated as distinct molecular species, rather than as a small piece of the bulk condensed phase. Examples are presented of atomistic data generated by means of computational chemistry for water clusters up to size 10, and for aluminum clusters up to size 60. In both cases, the free energy of cluster formation is found to be a multimodal function of cluster size, both quantitatively and qualitatively different than in CNT. Condensation rate constants can be affected by the need for a third body as a collision partner, and by attractive intermolecular forces in collisions between clusters and monomers. An approach is suggested for constructing a “master table” of free energies of cluster formation, based on a hybrid of atomistic data, experimental values inferred by means of the nucleation theorem, and extrapolations to larger cluster sizes based on CNT.

Clusters can form and grow from a supersaturated vapor by successive reactions in which molecules (or “monomers”) of the vapor collide with the cluster and stick. In general, these reactions are reversible. The net forward rate of each of these reactions is termed the “nucleation current” of clusters of the size formed by the reaction. If a steady-state cluster size distribution exists, then the nucleation currents for clusters of all sizes are identical and can be equated to the steady-state (or “stationary”) nucleation rate. In that case, one can derive a closed-form expression for the nucleation rate in terms of a summation over clusters of all sizes up to some arbitrarily large size. The key terms in this summation are the forward rate constants and the Gibbs free energies of cluster formation from the monomer vapor. Evaluating the summation requires size-dependent values of these terms. For saturation ratios that lie within the condensation–evaporation regime, the free energy of cluster formation has a maximum at the critical cluster size. The nucleation theorem relates this size to the dependence of the nucleation rate on saturation ratio.