  We investigate the crystallization of a single, flexible homopolymer chain
using transition path sampling (TPS). The chain consists of N identical
spherical monomers evolved according to Langevin dynamics. While neighboring
monomers are coupled via harmonic springs, the non-neighboring monomers
interact via a hard core and a short-ranged attractive potential. For a
sufficiently small interaction range {\lambda}, the system undergoes a
first-order freezing transition from an expanded, disordered phase to a compact
crystalline state. Using a new shooting move tailored to polymers combined with
a committor analysis, we study the transition state ensemble of an N=128 chain
and search for possible reaction coordinates based on likelihood maximization.
We find that typical transition states consist of a crystalline nucleus with
one or more chain fragments attached to it. Furthermore, we show that the
number of particles in the crystalline core is not well suited as a reaction
coordinate. We then present an improved reaction coordinate, which includes
information from the potential energy and the overall crystallinity of the
polymer.
