Self-interaction effects on charge-transfer collisions

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.