  We reveal the microscopic self-diffusion process of compact tri-interstitials
in silicon using a combination of molecular dynamics and nudged elastic band
methods. We find that the compact tri-interstitial moves by a collective
displacement, involving both translation and rotation, of five atoms in a
screw-like motion along $[111]$ directions. The elucidation of this pathway
demonstrates the utility of combining tight-binding molecular dynamics with
\textit{ab initio} density functional calculations to probe diffusion
mechanisms. Using density functional theory to obtain diffusion barriers and
the prefactor, we calculate a diffusion constant of $ 4 \cdot 10^{-5} \exp (-
0.49 {\rm eV} / k_{B} T) {\rm cm^2/s} $. Because of the low diffusion barrier,
$I_{3}^{b}$ diffusion may be an important process under conditions such as ion
implantation that creates excess interstitials, hence favoring formation of
interstitial clusters.
