  We investigate the crystallization mechanism of a single, flexible
homopolymer chain with short range attractions. For a sufficiently narrow
attractive well, the system undergoes a first-order like freezing transition
from an expanded disordered coil to a compact crystalline state. Based on a
maximum likelihood analysis of committor values computed for configurations
obtained by Wang-Landau sampling, we construct a non-linear string reaction
coordinate for the coil-to-crystal transition. In contrast to a linear reaction
coordinate, the string reaction coordinate captures the effect of different
degrees of freedom controlling different stages of the transition. Our analysis
indicates that a combination of the energy and the global crystallinity
parameter Q6 provide the most accurate measure for the progress of the
transition. While the crystallinity parameter Q6 is most relevant in the
initial stages of the crystallization, the later stages are dominated by a
decrease in the potential energy.
