  In this article, we investigate the role of the self-interaction error in the
simulation of collisions using time-dependent density functional theory (TDDFT)
and Ehrenfest dynamics. We compare many different approximations of the
exchange and correlation potential, using as a test system the collision of
$\mathrm{H^+ + CH_4}$ at $30~\mathrm{eV}$. We find that semi-local
approximations, like PBE, and even hybrid functionals, like B3LYP, produce
qualitatively incorrect predictions for the scattering of the proton. This
discrepancy appears because the self-interaction error allows the electrons to
jump too easily to the proton, leading to radically different forces with
respect to the non-self-interacting case. From our results, we conclude that
using a functional that is self-interaction free is essential to properly
describe charge-transfer collisions between ions and molecules in TDDFT.
