  We present an extension to the iterative Boltzmann inversion method to
generate coarse-grained models with three-body intramolecular potentials that
can reproduce correlations in structural distribution functions. The
coarse-grained structural distribution functions are computed using kernel
density estimates to produce analytically differentiable distribution functions
with controllable smoothening via the kernel bandwidth parameters. Bicubic
interpolation is used to accurately interpolate the three-body potentials
trained by the method. To demonstrate this new approach, a coarse-grained model
of polyethylene is constructed in which each bead represents an ethylene
monomer. The resulting model reproduces the radial density function as well as
the joint probability distribution of bond-length and bond-angles sampled from
target atomistic simulations with only a 10% increase in the computational cost
compared to models with independent bond-length and bond-angle potentials.
Analysis of the predicted crystallization kinetics of the model developed by
the new approach reveals that the bandwidth parameters can be tuned to
accelerate the modeling of polymer crystallization. Specifically, computing
target RDF with larger bandwidth slows down the secondary crystallization, and
increasing the bandwidth in $\theta$-direction of bond-length and bond-angle
distribution reduces the primary crystallization rate.
