  The objective of this research is to explore the formation/binding energetics
and length scales associated with the interaction between He$_n$V clusters and
grain boundaries in bcc $\alpha$-Fe. In this work, we calculated
formation/binding energies for 1-8 He atoms in a monovacancy at all potential
grain boundary sites within 15 \AA\ of the ten grain boundaries selected
(122106 simulations total). The present results provide detailed information
about the interaction energies and length scales of 1--8 He atoms with grain
boundaries for the structures examined. A number of interesting new findings
emerge from the present study. First, the $\Sigma3$(112) `twin' GB has
significantly lower binding energies for all He$_n$V clusters than all other
boundaries in this study. For all grain boundary sites, the effect of the local
environment surrounding each site on the He$_n$V formation and binding energies
decreases with an increasing number of He atoms in the He$_n$V cluster. Based
on the calculated dataset, we formulated a model to capture the evolution of
the formation and binding energy of He$_n$V clusters as a function of distance
from the GB center, utilizing only constants related to the maximum binding
energy and the length scale.
