  The classical theory of grain nucleation suffers from both theoretical and
predictive deficiencies. We strive to alleviate these deficiencies in our
understanding of dust formation and growth by utilizing an atomistic model of
nucleation. Carbon cluster geometries are determined with a set of global
minimization algorithms. Using density functional theory, the binding energies
of carbon clusters from $n=2$ to $n=99$ are then calculated. These energies are
used to calculate the critical size and nucleation rate of carbon clusters.
  We find that the critical cluster size is largely determined by the changes
in geometry of the clusters. Clusters with size $n=27$ and $n=8$, roughly
corresponding to the transition from ring-to-fullerene geometry and
chain-to-ring geometry respectively, are the critical sizes across the range of
temperature and saturation where nucleation is significant. In contrast to the
classical theory, nucleation is enhanced at low-temperatures, and suppressed at
high temperatures. These results will be applied to a modified chemical
evolution code using results from supernova simulations.
